Enhanced Geographic Routing with One- and Two-Hop Movement Information in Opportunistic Ad Hoc Networks

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} div.type-section h2 { font-size: 20px; line-height: 26px; font-weight: 300; } div.type-section h3 { margin-left: 15px; margin-bottom: 0px; font-weight: 300; } .journal-tabs .tab-title.active a { } </style> <link rel="stylesheet" href="https://pub.mdpi-res.com/assets/css/slick.css?f38b2db10e01b157?1732286508"> <meta name="title" content="Enhanced Geographic Routing with One- and Two-Hop Movement Information in Opportunistic Ad Hoc Networks"> <meta name="description" content="Opportunistic ad hoc networks are characterized by intermittent and infrastructure-less connectivity among mobile nodes. Because of the lack of up-to-date network topology information and frequent link failures, geographic routing utilizes location information and adopts the store–carry–forward data delivery model to relay messages in a delay-tolerant manner. This paper proposes a message-forwarding policy based on movement patterns (MPMF). First, one- and two-hop location information in a geographic neighborhood is exploited to select relay nodes moving closer to a destination node. Message-forwarding decisions are made by referring to selected relay nodes’ weight values obtained by calculating the contact frequency of each node with the destination node. Second, when relays in the vicinity of a message-carrying node are not qualified due to the sparse node density and nodal motion status, the destination’s movement and the location information of a one-hop relay are jointly utilized to improve the message-forwarding decision. If the one-hop relay is not closer to the destination node or moving away from it, its centrality value in the network is used instead. Based on both synthetic and real mobility scenarios, the simulation results show that the proposed policy performs incomparable efforts to some typical routing policies, such as Epidemic, PRoPHETv2, temporal closeness and centrality-based (TCCB), transient community-based (TC), and geographic-based spray-and-relay (GSaR) routing policies." > <link rel="image_src" href="https://pub.mdpi-res.com/img/journals/futureinternet-logo.png?8600e93ff98dbf14" > <meta name="dc.title" content="Enhanced Geographic Routing with One- and Two-Hop Movement Information in Opportunistic Ad Hoc Networks"> <meta name="dc.creator" content="Mohd-Yaseen Mir"> <meta name="dc.creator" content="Hengbing Zhu"> <meta name="dc.creator" content="Chih-Lin Hu"> <meta name="dc.type" content="Article"> <meta name="dc.source" content="Future Internet 2022, Vol. 14, Page 214"> <meta name="dc.date" content="2022-07-20"> <meta name ="dc.identifier" content="10.3390/fi14070214"> <meta name="dc.publisher" content="Multidisciplinary Digital Publishing Institute"> <meta name="dc.rights" content="http://creativecommons.org/licenses/by/3.0/"> <meta name="dc.format" content="application/pdf" > <meta name="dc.language" content="en" > <meta name="dc.description" content="Opportunistic ad hoc networks are characterized by intermittent and infrastructure-less connectivity among mobile nodes. Because of the lack of up-to-date network topology information and frequent link failures, geographic routing utilizes location information and adopts the store–carry–forward data delivery model to relay messages in a delay-tolerant manner. This paper proposes a message-forwarding policy based on movement patterns (MPMF). First, one- and two-hop location information in a geographic neighborhood is exploited to select relay nodes moving closer to a destination node. Message-forwarding decisions are made by referring to selected relay nodes’ weight values obtained by calculating the contact frequency of each node with the destination node. Second, when relays in the vicinity of a message-carrying node are not qualified due to the sparse node density and nodal motion status, the destination’s movement and the location information of a one-hop relay are jointly utilized to improve the message-forwarding decision. If the one-hop relay is not closer to the destination node or moving away from it, its centrality value in the network is used instead. Based on both synthetic and real mobility scenarios, the simulation results show that the proposed policy performs incomparable efforts to some typical routing policies, such as Epidemic, PRoPHETv2, temporal closeness and centrality-based (TCCB), transient community-based (TC), and geographic-based spray-and-relay (GSaR) routing policies." > <meta name="dc.subject" content="message forwarding" > <meta name="dc.subject" content="geographic routing" > <meta name="dc.subject" content="relay selection" > <meta name="dc.subject" content="data dissemination" > <meta name="dc.subject" content="delay-tolerant networks" > <meta name="dc.subject" content="mobile opportunistic networks" > <meta name ="prism.issn" content="1999-5903"> <meta name ="prism.publicationName" content="Future Internet"> <meta name ="prism.publicationDate" content="2022-07-20"> <meta name ="prism.volume" content="14"> <meta name ="prism.number" content="7"> <meta name ="prism.section" content="Article" > <meta name ="prism.startingPage" content="214" > <meta name="citation_issn" content="1999-5903"> <meta name="citation_journal_title" content="Future Internet"> <meta name="citation_publisher" content="Multidisciplinary Digital Publishing Institute"> <meta name="citation_title" content="Enhanced Geographic Routing with One- and Two-Hop Movement Information in Opportunistic Ad Hoc Networks"> <meta name="citation_publication_date" content="2022/7"> <meta name="citation_online_date" content="2022/07/20"> <meta name="citation_volume" content="14"> <meta name="citation_issue" content="7"> <meta name="citation_firstpage" content="214"> <meta name="citation_author" content="Mir, Mohd-Yaseen"> <meta name="citation_author" content="Zhu, Hengbing"> <meta name="citation_author" content="Hu, Chih-Lin"> <meta name="citation_doi" content="10.3390/fi14070214"> <meta name="citation_id" content="mdpi-fi14070214"> <meta name="citation_abstract_html_url" content="https://www.mdpi.com/1999-5903/14/7/214"> <meta name="citation_pdf_url" content="https://www.mdpi.com/1999-5903/14/7/214/pdf?version=1658382432"> <link rel="alternate" type="application/pdf" title="PDF Full-Text" href="https://www.mdpi.com/1999-5903/14/7/214/pdf?version=1658382432"> <meta name="fulltext_pdf" content="https://www.mdpi.com/1999-5903/14/7/214/pdf?version=1658382432"> <meta name="citation_fulltext_html_url" content="https://www.mdpi.com/1999-5903/14/7/214/htm"> <link rel="alternate" type="text/html" title="HTML Full-Text" href="https://www.mdpi.com/1999-5903/14/7/214/htm"> <meta name="fulltext_html" content="https://www.mdpi.com/1999-5903/14/7/214/htm"> <link rel="alternate" type="text/xml" title="XML Full-Text" href="https://www.mdpi.com/1999-5903/14/7/214/xml"> <meta name="fulltext_xml" content="https://www.mdpi.com/1999-5903/14/7/214/xml"> <meta name="citation_xml_url" content="https://www.mdpi.com/1999-5903/14/7/214/xml"> <meta name="twitter:card" content="summary" /> <meta name="twitter:site" content="@MDPIOpenAccess" /> <meta name="twitter:image" content="https://pub.mdpi-res.com/img/journals/futureinternet-logo-social.png?8600e93ff98dbf14" /> <meta property="fb:app_id" content="131189377574"/> <meta property="og:site_name" content="MDPI"/> <meta property="og:type" content="article"/> <meta property="og:url" content="https://www.mdpi.com/1999-5903/14/7/214" /> <meta property="og:title" content="Enhanced Geographic Routing with One- and Two-Hop Movement Information in Opportunistic Ad Hoc Networks" /> <meta property="og:description" content="Opportunistic ad hoc networks are characterized by intermittent and infrastructure-less connectivity among mobile nodes. Because of the lack of up-to-date network topology information and frequent link failures, geographic routing utilizes location information and adopts the store–carry–forward data delivery model to relay messages in a delay-tolerant manner. This paper proposes a message-forwarding policy based on movement patterns (MPMF). First, one- and two-hop location information in a geographic neighborhood is exploited to select relay nodes moving closer to a destination node. Message-forwarding decisions are made by referring to selected relay nodes’ weight values obtained by calculating the contact frequency of each node with the destination node. Second, when relays in the vicinity of a message-carrying node are not qualified due to the sparse node density and nodal motion status, the destination’s movement and the location information of a one-hop relay are jointly utilized to improve the message-forwarding decision. If the one-hop relay is not closer to the destination node or moving away from it, its centrality value in the network is used instead. Based on both synthetic and real mobility scenarios, the simulation results show that the proposed policy performs incomparable efforts to some typical routing policies, such as Epidemic, PRoPHETv2, temporal closeness and centrality-based (TCCB), transient community-based (TC), and geographic-based spray-and-relay (GSaR) routing policies." /> <meta property="og:image" content="https://pub.mdpi-res.com/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g001-550.jpg?1658391448" /> <link rel="alternate" type="application/rss+xml" title="MDPI Publishing - Latest articles" href="https://www.mdpi.com/rss"> <meta name="google-site-verification" content="PxTlsg7z2S00aHroktQd57fxygEjMiNHydKn3txhvwY"> <meta name="facebook-domain-verification" content="mcoq8dtq6sb2hf7z29j8w515jjoof7" /> <script id="Cookiebot" data-cfasync="false" src="https://consent.cookiebot.com/uc.js" data-cbid="51491ddd-fe7a-4425-ab39-69c78c55829f" type="text/javascript" async></script>  <script type="text/plain" data-cookieconsent="statistics"> (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start': new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0], j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src= 'https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f); 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data-options='is_hover:true, hover_timeout:5000'> Mohd-Yaseen Mir</div><div id="profile-card-drop8266784" data-dropdown-content class="f-dropdown content profile-card-content" aria-hidden="true" tabindex="-1"><div class="profile-card__title"><div class="sciprofiles-link" style="display: inline-block"><div class="sciprofiles-link__link"><img class="sciprofiles-link__image" src="/bundles/mdpisciprofileslink/img/unknown-user.png" style="width: auto; height: 16px; border-radius: 50%;"><span class="sciprofiles-link__name">Mohd-Yaseen Mir</span></div></div></div><div class="profile-card__buttons" style="margin-bottom: 10px;"><a href="https://sciprofiles.com/profile/2208765?utm_source=mdpi.com&utm_medium=website&utm_campaign=avatar_name" class="button button--color-inversed" target="_blank"> SciProfiles </a><a href="https://scilit.net/scholars?q=Mohd-Yaseen%20Mir" class="button button--color-inversed" target="_blank"> Scilit </a><a 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-5px;"></a>, </span><span class="inlineblock "><div class='profile-card-drop' data-dropdown='profile-card-drop8266785' data-options='is_hover:true, hover_timeout:5000'> Hengbing Zhu</div><div id="profile-card-drop8266785" data-dropdown-content class="f-dropdown content profile-card-content" aria-hidden="true" tabindex="-1"><div class="profile-card__title"><div class="sciprofiles-link" style="display: inline-block"><div class="sciprofiles-link__link"><img class="sciprofiles-link__image" src="/bundles/mdpisciprofileslink/img/unknown-user.png" style="width: auto; height: 16px; border-radius: 50%;"><span class="sciprofiles-link__name">Hengbing Zhu</span></div></div></div><div class="profile-card__buttons" style="margin-bottom: 10px;"><a href="https://sciprofiles.com/profile/author/bTFWVFJtV1FydUNEdzFQeFEyRmlscXRib25ZVlZRbUJOQk5hUFhPNnNaQT0=?utm_source=mdpi.com&utm_medium=website&utm_campaign=avatar_name" class="button button--color-inversed" target="_blank"> SciProfiles </a><a href="https://scilit.net/scholars?q=Hengbing%20Zhu" class="button button--color-inversed" target="_blank"> Scilit </a><a href="https://www.preprints.org/search?search1=Hengbing%20Zhu&field1=authors" class="button button--color-inversed" target="_blank"> Preprints.org </a><a href="https://scholar.google.com/scholar?q=Hengbing%20Zhu" class="button button--color-inversed" target="_blank" rels="noopener noreferrer"> Google Scholar </a></div></div><sup></sup><span style="display: inline; margin-left: 5px;"></span><a class="toEncode emailCaptcha visibility-hidden" data-author-id="8266785" href="/cdn-cgi/l/email-protection#351a565b511856525c1a591a5058545c591845475a415056415c5a5b1605050551030d050305530554050405030553040705050451070d05530500050c050405010103055705020500"><sup><i class="fa fa-envelope-o"></i></sup></a> and </span><span class="inlineblock "><div class='profile-card-drop' data-dropdown='profile-card-drop8266786' data-options='is_hover:true, hover_timeout:5000'> Chih-Lin Hu</div><div id="profile-card-drop8266786" data-dropdown-content class="f-dropdown content profile-card-content" aria-hidden="true" tabindex="-1"><div class="profile-card__title"><div class="sciprofiles-link" style="display: inline-block"><div class="sciprofiles-link__link"><img class="sciprofiles-link__image" src="/bundles/mdpisciprofileslink/img/unknown-user.png" style="width: auto; height: 16px; border-radius: 50%;"><span class="sciprofiles-link__name">Chih-Lin Hu</span></div></div></div><div class="profile-card__buttons" style="margin-bottom: 10px;"><a href="https://sciprofiles.com/profile/author/Z0JQbTdxNTk2YU5FZUNUMXNPOEdOQT09?utm_source=mdpi.com&utm_medium=website&utm_campaign=avatar_name" class="button button--color-inversed" target="_blank"> SciProfiles </a><a href="https://scilit.net/scholars?q=Chih-Lin%20Hu" class="button button--color-inversed" target="_blank"> Scilit </a><a href="https://www.preprints.org/search?search1=Chih-Lin%20Hu&field1=authors" class="button 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class="affiliation-item"><sup>*</sup></div> <div class="affiliation-name ">Author to whom correspondence should be addressed. </div> </div> </div> </div> <div class="bib-identity" style="margin-bottom: 10px;"> <em>Future Internet</em> <b>2022</b>, <em>14</em>(7), 214; <a href="https://doi.org/10.3390/fi14070214">https://doi.org/10.3390/fi14070214</a> </div> <div class="pubhistory" style="font-weight: bold; padding-bottom: 10px;"> <span style="display: inline-block">Submission received: 7 May 2022</span> / <span style="display: inline-block">Revised: 18 July 2022</span> / <span style="display: inline-block">Accepted: 18 July 2022</span> / <span style="display: inline-block">Published: 20 July 2022</span> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Topic <a href="/topics/WCEC6G">Wireless Communications and Edge Computing in 6G</a>)<br/> </div> <div class="highlight-box1"> <div class="download"> <a class="button button--color-inversed button--drop-down" data-dropdown="drop-download-867499" aria-controls="drop-supplementary-867499" aria-expanded="false"> Download <i class="material-icons">keyboard_arrow_down</i> </a> <div id="drop-download-867499" class="f-dropdown label__btn__dropdown label__btn__dropdown--button" data-dropdown-content aria-hidden="true" tabindex="-1"> <a class="UD_ArticlePDF" href="/1999-5903/14/7/214/pdf?version=1658382432" data-name="Enhanced Geographic Routing with One- and Two-Hop Movement Information in Opportunistic Ad Hoc Networks" data-journal="futureinternet">Download PDF</a> <br/> <a id="js-pdf-with-cover-access-captcha" href="#" data-target="/1999-5903/14/7/214/pdf-with-cover" class="accessCaptcha">Download PDF with Cover</a> <br/> <a id="js-xml-access-captcha" href="#" data-target="/1999-5903/14/7/214/xml" class="accessCaptcha">Download XML</a> <br/> <a href="/1999-5903/14/7/214/epub" id="epub_link">Download Epub</a> <br/> </div> <div class="js-browse-figures" style="display: inline-block;"> <a href="#" class="button button--color-inversed margin-bottom-10 openpopupgallery UI_BrowseArticleFigures" data-target='article-popup' data-counterslink = "https://www.mdpi.com/1999-5903/14/7/214/browse" >Browse Figures</a> </div> <div id="article-popup" class="popupgallery" style="display: inline; line-height: 200%"> <a href="https://pub.mdpi-res.com/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g001.png?1658391447" title=" <strong>Figure 1</strong><br/> <p>(<b>a</b>) Front-side scanning with respect to a destination node, and (<b>b</b>) geometric angle formation at one- and two-hop distance.</p> "> </a> <a href="https://pub.mdpi-res.com/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g002.png?1658391452" title=" <strong>Figure 2</strong><br/> <p>Two-hop based routing between <span class="html-italic">s</span>, <math display="inline"><semantics> <msub> <mi>n</mi> <mi>i</mi> </msub> </semantics></math>, and <math display="inline"><semantics> <msub> <mi>n</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </semantics></math>.</p> "> </a> <a href="https://pub.mdpi-res.com/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g003.png?1658391437" title=" <strong>Figure 3</strong><br/> <p>Results by MPMF with different values of <math display="inline"><semantics> <mi>ϵ</mi> </semantics></math> and <math display="inline"><semantics> <msub> <mi>W</mi> <mn>0</mn> </msub> </semantics></math> under TVCM trace (TTL = 5 h and buffer size = 10 MB).</p> "> </a> <a href="https://pub.mdpi-res.com/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g004.png?1658391428" title=" <strong>Figure 4</strong><br/> <p>Results by MPMF with different values of <math display="inline"><semantics> <mi>ϵ</mi> </semantics></math> and <math display="inline"><semantics> <msub> <mi>W</mi> <mn>0</mn> </msub> </semantics></math> under NCCU trace (TTL = 5 h and buffer size = 10 MB).</p> "> </a> <a href="https://pub.mdpi-res.com/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g005.png?1658391441" title=" <strong>Figure 5</strong><br/> <p>Results by MPMF with different values of <math display="inline"><semantics> <mi>α</mi> </semantics></math> and <math display="inline"><semantics> <mi>ϵ</mi> </semantics></math> under TVCM trace (TTL = 5 h and buffer size = 10 MB).</p> "> </a> <a href="https://pub.mdpi-res.com/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g006.png?1658391448" title=" <strong>Figure 6</strong><br/> <p>Results by MPMF with different values of <math display="inline"><semantics> <mi>α</mi> </semantics></math> and <math display="inline"><semantics> <mi>ϵ</mi> </semantics></math> under NCCU trace (TTL = 5 h and buffer size = 10 MB).</p> "> </a> <a href="https://pub.mdpi-res.com/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g007.png?1658391426" title=" <strong>Figure 7</strong><br/> <p>Results by MPMF with different values of <span class="html-italic">L</span> and TTL under TVCM trace (buffer size = 10 MB).</p> "> </a> <a href="https://pub.mdpi-res.com/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g008.png?1658391439" title=" <strong>Figure 8</strong><br/> <p>Results by MPMF with different values of <span class="html-italic">L</span> and TTL under NCCU trace (buffer size = 10 MB).</p> "> </a> <a href="https://pub.mdpi-res.com/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g009a.png?1658391450" title=" <strong>Figure 9</strong><br/> <p>Performance comparison of MPMF in TVCM trace (<math display="inline"><semantics> <msub> <mi>W</mi> <mn>0</mn> </msub> </semantics></math> = 0.6, <span class="html-italic">L</span> = 10, <math display="inline"><semantics> <mi>ϵ</mi> </semantics></math> = 50, <math display="inline"><semantics> <mi>α</mi> </semantics></math> = 0.5, and buffer size = 10 MB).</p> "> </a> <a href="https://pub.mdpi-res.com/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g009b.png?1658391434" title=" <strong>Figure 9 Cont.</strong><br/> <p>Performance comparison of MPMF in TVCM trace (<math display="inline"><semantics> <msub> <mi>W</mi> <mn>0</mn> </msub> </semantics></math> = 0.6, <span class="html-italic">L</span> = 10, <math display="inline"><semantics> <mi>ϵ</mi> </semantics></math> = 50, <math display="inline"><semantics> <mi>α</mi> </semantics></math> = 0.5, and buffer size = 10 MB).</p> "> </a> <a href="https://pub.mdpi-res.com/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g010.png?1658391443" title=" <strong>Figure 10</strong><br/> <p>Performance comparison of MPMF in NCCU trace (<math display="inline"><semantics> <msub> <mi>W</mi> <mn>0</mn> </msub> </semantics></math> = 0.5, <span class="html-italic">L</span> = 10, <math display="inline"><semantics> <mi>ϵ</mi> </semantics></math> = 60, <math display="inline"><semantics> <mi>α</mi> </semantics></math> = 0.6, and buffer size = 10 MB).</p> "> </a> <a href="https://pub.mdpi-res.com/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g011.png?1658391430" title=" <strong>Figure 11</strong><br/> <p>Performance comparison of MPMF in TVCM trace (<math display="inline"><semantics> <msub> <mi>W</mi> <mn>0</mn> </msub> </semantics></math> = 0.5, <span class="html-italic">L</span> = 20, <math display="inline"><semantics> <mi>ϵ</mi> </semantics></math> = 60, <math display="inline"><semantics> <mi>α</mi> </semantics></math> = 0.6, and buffer size = 10 MB).</p> "> </a> </div> <a class="button button--color-inversed" href="/1999-5903/14/7/214/notes">Versions Notes</a> </div> </div> <div class="responsive-moving-container small hidden" data-id="article-counters" style="margin-top: 15px;"></div> <div class="html-dynamic"> <section> <div class="art-abstract art-abstract-new in-tab hypothesis_container"> <p> <div><section class="html-abstract" id="html-abstract"> <h2 id="html-abstract-title">Abstract</h2><b>:</b> <div class="html-p">Opportunistic ad hoc networks are characterized by intermittent and infrastructure-less connectivity among mobile nodes. Because of the lack of up-to-date network topology information and frequent link failures, geographic routing utilizes location information and adopts the store–carry–forward data delivery model to relay messages in a delay-tolerant manner. This paper proposes a message-forwarding policy based on movement patterns (MPMF). First, one- and two-hop location information in a geographic neighborhood is exploited to select relay nodes moving closer to a destination node. Message-forwarding decisions are made by referring to selected relay nodes’ weight values obtained by calculating the contact frequency of each node with the destination node. Second, when relays in the vicinity of a message-carrying node are not qualified due to the sparse node density and nodal motion status, the destination’s movement and the location information of a one-hop relay are jointly utilized to improve the message-forwarding decision. If the one-hop relay is not closer to the destination node or moving away from it, its centrality value in the network is used instead. Based on both synthetic and real mobility scenarios, the simulation results show that the proposed policy performs incomparable efforts to some typical routing policies, such as Epidemic, PRoPHETv2, temporal closeness and centrality-based (TCCB), transient community-based (TC), and geographic-based spray-and-relay (GSaR) routing policies.</div> </section> <div id="html-keywords"> <div class="html-gwd-group"><div id="html-keywords-title">Keywords: </div><a href="/search?q=message+forwarding">message forwarding</a>; <a href="/search?q=geographic+routing">geographic routing</a>; <a href="/search?q=relay+selection">relay selection</a>; <a href="/search?q=data+dissemination">data dissemination</a>; <a href="/search?q=delay-tolerant+networks">delay-tolerant networks</a>; <a href="/search?q=mobile+opportunistic+networks">mobile opportunistic networks</a></div> <div> </div> </div> </div> </p> </div> </section> </div> <div class="hypothesis_container"> <ul class="menu html-nav" data-prev-node="#html-quick-links-title"> </ul> <div class="html-body"> <section id='sec1-futureinternet-14-00214' type='intro'><h2 data-nested='1'> 1. Introduction</h2><div class='html-p'>The existence of end-to-end connectivity becomes infeasible in opportunistic ad hoc networks (OppNets) [<a href="#B1-futureinternet-14-00214" class="html-bibr">1</a>], where message forwarding services suffer from frequent disruption, sparse connectivity, and limited device capability. Unlike vehicular ad hoc networks (VANETs) [<a href="#B2-futureinternet-14-00214" class="html-bibr">2</a>,<a href="#B3-futureinternet-14-00214" class="html-bibr">3</a>] that broadcast data in confined and dense areas, OppNets are characterized by lower node density, intermittent connectivity, and infrastructure-less connectivity among mobile devices. Alternatively, the research in OppNets often employs the “store carry-and-forward” message delivery model: nodes can store messages in local buffers and carry them during movement, until any appropriate forwarding opportunities come out. Because OppNets cannot maintain up-to-date network topology information against frequent link disconnections, geographic routing techniques are employed to convey the message distribution in OppNets. Functionally, geographic routing is based on the location information of mobile devices to relay messages. It allows messages to approach and eventually reach a target node without relying on topology information [<a href="#B4-futureinternet-14-00214" class="html-bibr">4</a>,<a href="#B5-futureinternet-14-00214" class="html-bibr">5</a>,<a href="#B6-futureinternet-14-00214" class="html-bibr">6</a>,<a href="#B7-futureinternet-14-00214" class="html-bibr">7</a>].</div><div class='html-p'>Due to the unpredictable nature of contacts between mobile nodes in OppNets, a majority of geographic routing policies replicate a message multiple times to increase the possibility that a target node receives that message. Generally, message replication is performed by either finding better candidate nodes capable of delivering messages to a target node or spraying a limited number of copies of a message in a network. The former policies use utility metrics to evaluate the nodal delivery potential, control replication, and find better candidate nodes to increase message delivery [<a href="#B6-futureinternet-14-00214" class="html-bibr">6</a>,<a href="#B8-futureinternet-14-00214" class="html-bibr">8</a>,<a href="#B9-futureinternet-14-00214" class="html-bibr">9</a>]. The latter policies assume that a sufficient number of nodes in a network move at higher speeds and in a large coverage area, encounter more nodes, and expedite message delivery to a target node [<a href="#B4-futureinternet-14-00214" class="html-bibr">4</a>,<a href="#B5-futureinternet-14-00214" class="html-bibr">5</a>]. Despite many efforts in selecting the best candidate node, the concerns of spreading messages toward the direction of a destination node as accurately as possible and the destination’s movement are still not well addressed yet for efficient message delivery in OppNets. When OppNets are characterized by the presence of a low node density, it is challenging to deal with the local maximum: a message carrier continues to carry its message in the absence of a better candidate node.</div><div class='html-p'>Previous studies employed utility-based [<a href="#B9-futureinternet-14-00214" class="html-bibr">9</a>,<a href="#B10-futureinternet-14-00214" class="html-bibr">10</a>,<a href="#B11-futureinternet-14-00214" class="html-bibr">11</a>,<a href="#B12-futureinternet-14-00214" class="html-bibr">12</a>,<a href="#B13-futureinternet-14-00214" class="html-bibr">13</a>] policies to exploit contact properties, such as contact duration, contact frequency, shorter residual contact time with a target node, etc., to find better candidate nodes. Utility calculated by these policies is commonly referred to as delivery probability (DP) or centrality/temporal closeness with respect to any particular destination. For example, Zhou et al. [<a href="#B9-futureinternet-14-00214" class="html-bibr">9</a>] used the duration and frequency of contacts between node pairs to deduce their respective temporal closeness. A node with a higher temporal centrality, calculated by taking all nodes into account or a higher future temporal closeness with a destination, was selected as the next candidate node. Li et al. [<a href="#B12-futureinternet-14-00214" class="html-bibr">12</a>] proposed a social energy-based routing (SEBAR) protocol based on the concept of a social energy metric. A node with multiple encounters can have higher social energy and be considered a better candidate node. Though these policies can obtain accurate DP or centrality/temporal closeness, they cannot predict if selected nodes are moving toward destinations. This is because the DP or centrality/temporal closeness estimate cannot timely reflect the movement behavior among neighbor nodes in geographic proximity. Additionally, in the absence of a better candidate node, the local maximum remains unresolved.</div><div class='html-p'>Exploiting the movement information of mobile nodes using geographic information can be beneficial in spraying a limited number of copies of a message toward a direction where a destination likely stays. Some geographic-based routing policies considered the movement range of a destination, the location and speed of a node, and the distance for selecting a candidate node to replicate a message with a limited number of copies in a network [<a href="#B4-futureinternet-14-00214" class="html-bibr">4</a>,<a href="#B5-futureinternet-14-00214" class="html-bibr">5</a>,<a href="#B8-futureinternet-14-00214" class="html-bibr">8</a>,<a href="#B14-futureinternet-14-00214" class="html-bibr">14</a>]. In a study by Cao et al. [<a href="#B14-futureinternet-14-00214" class="html-bibr">14</a>], the historical geographic information, including locations and moving speeds, was used to estimate a movement range of a destination, and messages were replicated by two-phase routing policies. Cao et al. [<a href="#B5-futureinternet-14-00214" class="html-bibr">5</a>] considered both homogeneous and heterogeneous scenarios with identical mobility patterns and mobility in restricted areas. Nodal moving speed, distance, and direction were considered in the homogeneous case. In the heterogeneous case, visiting preferences were also used in replicating a message with a limited number of copies. In the literature, most of the geographic routing policies have considered stationary target nodes and used only one-hop nodal information when selecting a candidate node despite using historical information for the movement range of the destination. However, some studies suggested that exploring two-hop neighborhood information can facilitate a good performance in a network where nodes move randomly [<a href="#B6-futureinternet-14-00214" class="html-bibr">6</a>,<a href="#B15-futureinternet-14-00214" class="html-bibr">15</a>,<a href="#B16-futureinternet-14-00214" class="html-bibr">16</a>]. Moreover, nodes moving closer to the destination do not indicate that they have frequent contacts with destinations in OppNets.</div><div class='html-p'>In this paper, we integrate movement information inside a range of one- and two-hop transmission distances and a weighted form of DP estimate for the relay node selection in OppNets. Comprehensively, the location information of the one-hop relay, the destination node’s moving direction, and the centrality value of a node are utilized to enhance the performance of a successful delivery ratio and reduce messaging overhead in OppNets. Accordingly, we propose a message-forwarding policy based on movement patterns, named MPMF for brevity, for efficient message distribution in OppNets. Our intention is threefold:</div><div class='html-p'><ul class='html-bullet'><li><div class='html-p'>All the location information regarding one-hop and two-hop relays and moving directions of two-hop relays with respect to any particular message-carrying node is exploited to select relay nodes moving closer to a destination node. Assuming high node density in the vicinity of a message-carrying node, one- and two-hop nodal information is thus leveraged to improve message forwarding.</div></li><li><div class='html-p'>A combined weight measure is obtained using the DP values of one-hop and two-hop relays and the moving direction of the two-hop relay. This combined weight is compared with a threshold of weight value to take a message-forwarding decision.</div></li><li><div class='html-p'>In the absence of two-hop relays, one-hop location information and the moving direction of the target node are exploited. This case is considered when fewer nodes are scattered in some geographic proximity. To resolve this case, the one-hop node’s centrality, which measures the node’s ability to communicate with other nodes in a network, is used to address the local maximum problem.</div></li></ul></div><div class='html-p'>We conduct an extensive simulation under two synthetic datasets, TVCM [<a href="#B17-futureinternet-14-00214" class="html-bibr">17</a>] and NCCU [<a href="#B18-futureinternet-14-00214" class="html-bibr">18</a>], to examine the efficiency of our proposed policy. The comparative results show that the proposed policy attains a comparable delivery rate with a lower cost than the Epidemic [<a href="#B19-futureinternet-14-00214" class="html-bibr">19</a>], geographic-based spray-and-relay (GSaR) [<a href="#B4-futureinternet-14-00214" class="html-bibr">4</a>], PRoPHETv2 [<a href="#B10-futureinternet-14-00214" class="html-bibr">10</a>], transient community-based (TC) [<a href="#B20-futureinternet-14-00214" class="html-bibr">20</a>], and temporal closeness and centrality-based (TCCB) [<a href="#B9-futureinternet-14-00214" class="html-bibr">9</a>] policies. Under TVCM, the proposed policy can achieve higher delivery rates of 10, 44, 17, 54, and 45% as compared with the Epidemic, PRoPHETv2, TCCB, TC, and GSaR policies. With a larger scale of the node population under the TVCM mobility model, our policy can achieve a comparable delivery rate at a very low cost. For example, when the number of nodes is 100, the proposed policy can achieve higher delivery rates of 11 and 9% as compared to the TCCB and TC policies and is only 9.5, 6, and 5% lower to those of the Epidemic, PROPHETv2, and GSaR policies. Conversely, when the number of nodes is 150, the delivery rate of our proposed policy is 6.4 and 10% higher to the TCCB and TC policies and is only 20, 9, and 24% lower to those of the Epidemic, PROPHETv2, and GSaR policies. However, in both cases, our policy keeps a significantly lower overhead. Under the NCCU trace, the delivery rate of our proposed policy is 12% higher to the GSaR policy and is only 3, 6, 2, and 4% lower to those of the Epidemic, PRoPHETv2, TC, and TCCB policies. However, our proposed policy has a much lower transmission overhead than other policies.</div><div class='html-p'>The rest of this paper is organized as follows. <a href="#sec2-futureinternet-14-00214" class="html-sec">Section 2</a> describes a concise review of the prior studies on routing in OppNets. <a href="#sec3-futureinternet-14-00214" class="html-sec">Section 3</a> describes the system model. <a href="#sec4-futureinternet-14-00214" class="html-sec">Section 4</a> describes the relay selection, and <a href="#sec5-futureinternet-14-00214" class="html-sec">Section 5</a> discusses the proposed message-forwarding policy. <a href="#sec6-futureinternet-14-00214" class="html-sec">Section 6</a> examines the relative performance under extensive simulation. The conclusion is given in <a href="#sec7-futureinternet-14-00214" class="html-sec">Section 7</a>.</div></section><section id='sec2-futureinternet-14-00214' type=''><h2 data-nested='1'> 2. Related Work</h2><div class='html-p'>This section reviews prior research on routing policies toward maximizing the successful message delivery and minimizing message overhead in OppNets. We first discuss routing policies that replicate a message with a limited number of copies, mention policies that find the best candidate nodes to replicate a message, and then briefly describe our proposed policy.</div><div class='html-p'>When spraying a limited number of copies of a message in a network, most policies assume a sufficient number of nodes in a network move at higher speeds and cover a large area. Therefore, they are likely to encounter more nodes and expedite the message delivery to a target node [<a href="#B4-futureinternet-14-00214" class="html-bibr">4</a>,<a href="#B5-futureinternet-14-00214" class="html-bibr">5</a>,<a href="#B21-futureinternet-14-00214" class="html-bibr">21</a>,<a href="#B22-futureinternet-14-00214" class="html-bibr">22</a>,<a href="#B23-futureinternet-14-00214" class="html-bibr">23</a>]. Spyropoulos et al. [<a href="#B22-futureinternet-14-00214" class="html-bibr">22</a>] considered spraying a limited number of copies of a message with the help of relays with diverse characteristics and mobility patterns. For example, nodes that have recently seen the destination, nodes that have high mobility and encounter many nodes, and nodes with unique contacts in different periods can replicate the message. However, Sandulescu et al. [<a href="#B24-futureinternet-14-00214" class="html-bibr">24</a>] pointed out that Spyropoulos et al. [<a href="#B22-futureinternet-14-00214" class="html-bibr">22</a>] did not consider the transmission bandwidth between mobile nodes when transferring a message. Similarly, Nelson et al. [<a href="#B21-futureinternet-14-00214" class="html-bibr">21</a>] used the past encounter rate as a metric to decide the number of replicas of a given message which would be sent to other nodes. Vasco et al. [<a href="#B23-futureinternet-14-00214" class="html-bibr">23</a>] selected a nearest relay to the destination node to receive a message by using the location information of the destination and all the nodes in its vicinity. Cao et al. [<a href="#B4-futureinternet-14-00214" class="html-bibr">4</a>], however, stated that Vasco et al. [<a href="#B23-futureinternet-14-00214" class="html-bibr">23</a>] require additional map topology information and to consider the stationary destination. With historical information such as location, speed, and time duration, Cao et al. [<a href="#B4-futureinternet-14-00214" class="html-bibr">4</a>] estimated the movement range of a destination and sprayed a limited number of copies of a message toward that range. However, Cao et al. [<a href="#B4-futureinternet-14-00214" class="html-bibr">4</a>] assumed encounter rates between mobile nodes to be identical and considered a stationary target node.</div><div class='html-p'>Finding better candidate nodes is usually achieved by maintaining some utility or fitness function by nodes. This utility or fitness function is then used as a metric to relay messages [<a href="#B9-futureinternet-14-00214" class="html-bibr">9</a>,<a href="#B12-futureinternet-14-00214" class="html-bibr">12</a>,<a href="#B13-futureinternet-14-00214" class="html-bibr">13</a>,<a href="#B25-futureinternet-14-00214" class="html-bibr">25</a>]. Xie et al. [<a href="#B25-futureinternet-14-00214" class="html-bibr">25</a>] considered meeting time to deduce the conditional meeting probability of nodes. The global centrality, i.e., the ability of a node to communicate with other nodes in a network, and predictability of meeting the destination node were used to select the best candidate node. Bi et al. [<a href="#B13-futureinternet-14-00214" class="html-bibr">13</a>] collected contact information to compute social ties such as the number of common nodes between a node pair and selected relays with strong social ties with the destination node. However, the local maximum problem remains unresolved in [<a href="#B13-futureinternet-14-00214" class="html-bibr">13</a>,<a href="#B25-futureinternet-14-00214" class="html-bibr">25</a>]. Forwarding a message to a node with a higher delivery chance does not mean that it is moving closer to the destination. In a study by Tao et al. [<a href="#B26-futureinternet-14-00214" class="html-bibr">26</a>], a node with a higher source-to-destination probability or higher global activeness was selected as the next candidate node. Based on the nodes’ contact patterns, the activeness and probability of reaching the destination were calculated. Though finding better candidate nodes can improve the message delivery service, a message replica may be transmitted multiple times, loop around the network, and induce more messaging overhead in a network [<a href="#B22-futureinternet-14-00214" class="html-bibr">22</a>]. This situation can be avoided by creating a limited number of copies of a message in a network.</div><div class='html-p'>The preceding literature presents significant efforts for message forwarding in OppNets. Our proposed policy adopts controlled replication and sprays a limited number of copies of a message in the network. Additionally, relays are selected by considering their location information, encounter frequency with the destination, moving direction of the destination, and centrality. Therefore, our policy exploits both the geographic information and contact frequency of relays to enhance the message delivery in OppNets.</div></section><section id='sec3-futureinternet-14-00214' type=''><h2 data-nested='1'> 3. System Model</h2><div class='html-p'>This section specifies the system model and geometric angle formation at one- and two-hop distances.</div><section id='sec3dot1-futureinternet-14-00214' type=''><h4 class='html-italic' data-nested='2'> 3.1. OppNets Environment</h4><div class='html-p'>Let mobile nodes in the network have access to the Global Positioning System (GPS) to obtain their respective real-time geographic information, including moving direction and current location. Mobile nodes move independently in an area with <math display='inline'><semantics> <mrow> <mi>K</mi> <mo>×</mo> <mi>K</mi> </mrow> </semantics></math> m<math display='inline'><semantics> <msup> <mrow/> <mn>2</mn> </msup> </semantics></math>, and each node has a fixed transmission range of <span class='html-italic'>r</span> meters. A contact is established when two nodes move in a mutual transmission range. If two nodes contact each other, the routing decision is made based on the relative opportunity of delivering a message to the target node. A relay node in a neighboring area can be appointed to carry a message if its moving direction is toward the destination and its weighted utility value, e.g., the estimate of delivery probability, DP, exceeds a specific threshold value, or its centrality is higher than the current message-carrying node.</div></section><section id='sec3dot2-futureinternet-14-00214' type=''><h4 class='html-italic' data-nested='2'> 3.2. Geometric Angle Formation</h4><div class='html-p'>The message-forwarding mechanism uses relay nodes to send messages from a source node <span class='html-italic'>s</span> to a destination node <span class='html-italic'>d</span>. <a href="#futureinternet-14-00214-f001" class="html-fig">Figure 1</a>. illustrates an idea of probing and selecting a relay at one- and two-hop transmission distances from a message-carrying node. Several referential lines <math display='inline'><semantics> <mover accent="true"> <mrow> <mi>s</mi> <mi>d</mi> </mrow> <mo>→</mo> </mover> </semantics></math>, <math display='inline'><semantics> <mover accent="true"> <mrow> <mi>s</mi> <msup> <mi>d</mi> <mo>′</mo> </msup> </mrow> <mo>→</mo> </mover> </semantics></math>, and <math display='inline'><semantics> <mover accent="true"> <mrow> <mi>s</mi> <msup> <mi>d</mi> <mo>″</mo> </msup> </mrow> <mo>→</mo> </mover> <mrow> </mrow> </semantics></math> show directional information and angle calculation. To select a one-hop relay, only the front direction with respect to <span class='html-italic'>d</span> is scanned, as shown in <a href="#futureinternet-14-00214-f001" class="html-fig">Figure 1</a>a. Thus, only <math display='inline'><semantics> <msub> <mi>n</mi> <mn>1</mn> </msub> </semantics></math> and <math display='inline'><semantics> <msub> <mi>n</mi> <mn>2</mn> </msub> </semantics></math> will be considered by relay selection and nodes <math display='inline'><semantics> <msub> <mi>n</mi> <mn>7</mn> </msub> </semantics></math> and <math display='inline'><semantics> <msub> <mi>n</mi> <mn>8</mn> </msub> </semantics></math> will be ignored. The scanning process helps in filtering relay nodes in a broadcast coverage and avoids redundant message overhead to other nodes in the backward direction. To select one- and two-hop relays, we measure the geometric angle at each of the one- and two-hop distances, as described in the following two steps.</div><div class='html-p'>First, the one-hop geometric angle, also known as the first offset angle, indicates that the angle of the first relay relative to <math display='inline'><semantics> <mover accent="true"> <mrow> <mi>s</mi> <mi>d</mi> </mrow> <mo>→</mo> </mover> </semantics></math> is calculated. As <a href="#futureinternet-14-00214-f001" class="html-fig">Figure 1</a>b depicts, two signs + and − are used to indicate the clockwise and counterclockwise direction with reference to <math display='inline'><semantics> <mover accent="true"> <mrow> <mi>s</mi> <mi>d</mi> </mrow> <mo>→</mo> </mover> </semantics></math>, respectively. Then, <math display='inline'><semantics> <msub> <mi>θ</mi> <mn>1</mn> </msub> </semantics></math> and <math display='inline'><semantics> <msub> <mi>θ</mi> <mn>2</mn> </msub> </semantics></math> with respect to <math display='inline'><semantics> <mover accent="true"> <mrow> <mi>s</mi> <mi>d</mi> </mrow> <mo>→</mo> </mover> </semantics></math> are two geometric angles formed at a one-hop distance. To determine the sign of any offset angle <math display='inline'><semantics> <msub> <mi>θ</mi> <mi>i</mi> </msub> </semantics></math>, the outer product of the vectors is used. For example, given <math display='inline'><semantics> <mrow> <mover accent="true"> <mrow> <mi>s</mi> <mi>d</mi> </mrow> <mo>→</mo> </mover> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>y</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </mrow> </semantics></math> and <math display='inline'><semantics> <mrow> <mover accent="true"> <mrow> <mi>s</mi> <msub> <mi>n</mi> <mi>i</mi> </msub> </mrow> <mo>→</mo> </mover> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>y</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </mrow> </semantics></math>, <math display='inline'><semantics> <mrow> <mover accent="true"> <mrow> <mi>s</mi> <mi>d</mi> </mrow> <mo>→</mo> </mover> <mo>×</mo> <mover accent="true"> <mrow> <mi>s</mi> <msub> <mi>n</mi> <mi>i</mi> </msub> </mrow> <mo>→</mo> </mover> <mo>=</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <msub> <mi>y</mi> <mn>2</mn> </msub> <mo>−</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <msub> <mi>y</mi> <mn>1</mn> </msub> </mrow> </semantics></math> will determine the sign of <math display='inline'><semantics> <msub> <mi>θ</mi> <mi>i</mi> </msub> </semantics></math>.</div><div class='html-p'>Second, to select a two-hop relay, the sum of the first offset angle and the two-hop offset angle is calculated, which is denoted as <math display='inline'><semantics> <msub> <mi>θ</mi> <mi>m</mi> </msub> </semantics></math>. For instance, by referring to <a href="#futureinternet-14-00214-f001" class="html-fig">Figure 1</a>b, there are <math display='inline'><semantics> <mrow> <msub> <mi>θ</mi> <mi>m</mi> </msub> <mo>=</mo> <mrow> <mo>|</mo> <mrow> <mo>(</mo> <mo>+</mo> <msub> <mi>θ</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mrow> <mo>(</mo> <mo>+</mo> <msub> <mi>θ</mi> <mn>3</mn> </msub> <mo>)</mo> </mrow> <mo>|</mo> </mrow> </mrow> </semantics></math> for <span class='html-italic'>s</span>, <math display='inline'><semantics> <msub> <mi>n</mi> <mn>1</mn> </msub> </semantics></math>, and <math display='inline'><semantics> <msub> <mi>n</mi> <mn>3</mn> </msub> </semantics></math>, and <math display='inline'><semantics> <mrow> <msub> <mi>θ</mi> <mi>m</mi> </msub> <mo>=</mo> <mrow> <mo>|</mo> <mrow> <mo>(</mo> <mo>+</mo> <msub> <mi>θ</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mrow> <mo>(</mo> <mo>−</mo> <msub> <mi>θ</mi> <mn>4</mn> </msub> <mo>)</mo> </mrow> <mo>|</mo> </mrow> </mrow> </semantics></math> for <span class='html-italic'>s</span>, <math display='inline'><semantics> <msub> <mi>n</mi> <mn>1</mn> </msub> </semantics></math>, and <math display='inline'><semantics> <msub> <mi>n</mi> <mn>4</mn> </msub> </semantics></math>. Similarly, other examples are <math display='inline'><semantics> <mrow> <msub> <mi>θ</mi> <mi>m</mi> </msub> <mo>=</mo> <mrow> <mo>|</mo> <mrow> <mo>(</mo> <mo>−</mo> <msub> <mi>θ</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mrow> <mo>(</mo> <mo>+</mo> <msub> <mi>θ</mi> <mn>5</mn> </msub> <mo>)</mo> </mrow> <mo>|</mo> </mrow> </mrow> </semantics></math> for <span class='html-italic'>s</span>, <math display='inline'><semantics> <msub> <mi>n</mi> <mn>2</mn> </msub> </semantics></math>, and <math display='inline'><semantics> <msub> <mi>n</mi> <mn>5</mn> </msub> </semantics></math>, and <math display='inline'><semantics> <mrow> <msub> <mi>θ</mi> <mi>m</mi> </msub> <mo>=</mo> <mrow> <mo>|</mo> <mrow> <mo>(</mo> <mo>−</mo> <msub> <mi>θ</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mrow> <mo>(</mo> <mo>−</mo> <msub> <mi>θ</mi> <mn>6</mn> </msub> <mo>)</mo> </mrow> <mo>|</mo> </mrow> </mrow> </semantics></math> for <span class='html-italic'>s</span>, <math display='inline'><semantics> <msub> <mi>n</mi> <mn>2</mn> </msub> </semantics></math>, and <math display='inline'><semantics> <msub> <mi>n</mi> <mn>6</mn> </msub> </semantics></math>. Note that <math display='inline'><semantics> <msub> <mi>θ</mi> <mn>3</mn> </msub> </semantics></math> and <math display='inline'><semantics> <msub> <mi>θ</mi> <mn>4</mn> </msub> </semantics></math> are formed with respect to the <math display='inline'><semantics> <mover accent="true"> <mrow> <mi>s</mi> <msup> <mi>d</mi> <mo>′</mo> </msup> </mrow> <mo>→</mo> </mover> </semantics></math>, while <math display='inline'><semantics> <msub> <mi>θ</mi> <mn>5</mn> </msub> </semantics></math> and <math display='inline'><semantics> <msub> <mi>θ</mi> <mn>6</mn> </msub> </semantics></math> are formed with respect to the <math display='inline'><semantics> <mover accent="true"> <mrow> <mi>s</mi> <msup> <mi>d</mi> <mo>″</mo> </msup> </mrow> <mo>→</mo> </mover> <mrow> </mrow> </semantics></math>.</div><div class='html-p'>With the above two cases, it is seen that the relay selection involves the use of threshold values, which will be further discussed in the next section. According to the relay scanning and angle formulation in one- and two-hop neighborhood areas, we develop a routing policy for message forwarding in OppNets.</div></section></section><section id='sec4-futureinternet-14-00214' type=''><h2 data-nested='1'> 4. Scheme Design: MPMF</h2><div class='html-p'><a href="#sec4dot1-futureinternet-14-00214" class="html-sec">Section 4.1</a> gives the design abstraction, and <a href="#sec4dot2-futureinternet-14-00214" class="html-sec">Section 4.2</a> discusses relay selection policies.</div><section id='sec4dot1-futureinternet-14-00214' type=''><h4 class='html-italic' data-nested='2'> 4.1. Design Abstraction</h4><div class='html-p'>The message-forwarding policy based on movement patterns (MPMF) considers the following cases when selecting a relay node for receiving a message:</div><div class='html-p'><ul class='html-bullet'><li><div class='html-p'>The MPMF policy decides the best relay that is one out from a candidate set of one- or two-hop relay nodes which are moving closer to the destination and have frequent contacts with the destination node. If the candidate node is found, any message-carrying node should forward the messages in buffer to this candidate node as it is going to leave beyond the coverage of a two-hop distance and move closer to the destination.</div></li><li><div class='html-p'>In presence of only one-hop relay with respect to a message-carrying node, a one-hop relay node is selected by considering its location and destination’s movement. A message-carrying node considers the destination’s and one-hop relay’s moving direction to take a forwarding decision. If the one-hop relay and the destination node are both moving in the same direction, the one-hop relay can be selected as a candidate node.</div></li><li><div class='html-p'>An additional metric, i.e., centrality of a node, is used to avoid the situation that a message-carrying node continually carries its message if the one-hop relay is not moving toward the destination node. The centrality metric measures the ability of a node to communicate with other nodes in a network. A relay node with a higher centrality implies its effectiveness to deliver messages to the destination node and can be considered the best candidate node for the next message-forwarding action.</div></li></ul></div></section><section id='sec4dot2-futureinternet-14-00214' type=''><h4 class='html-italic' data-nested='2'> 4.2. Relay Selection</h4><div class='html-p'><a href="#sec4dot2dot1-futureinternet-14-00214" class="html-sec">Section 4.2.1</a> describes the summation angle measurement and weight calculation along a two-hop distance. <a href="#sec4dot2dot2-futureinternet-14-00214" class="html-sec">Section 4.2.2</a> specifies summation angle measurement at one-hop distance, moving direction of the destination node, and handling the local maximum problem.</div><section id='sec4dot2dot1-futureinternet-14-00214' type=''><h4 class='' data-nested='3'> 4.2.1. Case 1</h4><div class='html-p'>When a message-carrying node encounters more than one relay at the one-hop distance in some geographic proximity, it looks for another relay beyond the coverage of one-hop distance to relay a message. When no candidate nodes are found qualified to receive this message, the message-carrying node holds this message in the hope of encountering more nodes in the near future. In this case, the location information of one-hop and two-hop relays with respect to the message-carrying node, their DP’s weight value, and the direction in which the two-hop relay moves are exploited to select the best relay nodes to carry a message. The steps involved are discussed as follows.</div><dl class='html-order'><dt id=''>1.</dt><dd><div class='html-p'>Summation angle measurement: The summation angle is used to indicate whether a relay node’s position is closer to a destination node.</div></dd><dt id=''>2.</dt><dd><div class='html-p'>DP’s weighting calculation in one-hop and two-hop distance levels: A relay node with more frequent contacts with a destination node will have a higher weight.</div></dd><dt id=''>3.</dt><dd><div class='html-p'>To select relay nodes, both one- and two-hop relays should be closer to the destination, their DP’s weight value calculated by considering their respective contact frequency with the destination should be higher, and the moving direction of the two-hop relay should be closer to the destination node.</div></dd></dl><div class='html-p'><a href="#futureinternet-14-00214-f002" class="html-fig">Figure 2</a> illustrates a scenario to ease exposition of the MPMF. Nodes <math display='inline'><semantics> <msub> <mi>n</mi> <mi>i</mi> </msub> </semantics></math> and <math display='inline'><semantics> <msub> <mi>n</mi> <mi>j</mi> </msub> </semantics></math> are in one-hop transmission range of <span class='html-italic'>s</span>. Node <math display='inline'><semantics> <msub> <mi>n</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </semantics></math> is in one-hop transmission range of <math display='inline'><semantics> <msub> <mi>n</mi> <mi>i</mi> </msub> </semantics></math>, as well as two-hop transmission range of <span class='html-italic'>s</span>.</div><div class='html-p'>Given that <math display='inline'><semantics> <msub> <mi>n</mi> <mi>i</mi> </msub> </semantics></math> lies at a one-hop distance from <span class='html-italic'>s</span> and forms the first offset angle <math display='inline'><semantics> <msub> <mi>θ</mi> <mi>i</mi> </msub> </semantics></math> with respect to <math display='inline'><semantics> <mover accent="true"> <mrow> <mi>s</mi> <msub> <mi>n</mi> <mi>i</mi> </msub> </mrow> <mo>→</mo> </mover> </semantics></math> and <math display='inline'><semantics> <mover accent="true"> <mrow> <mi>s</mi> <mi>d</mi> </mrow> <mo>→</mo> </mover> </semantics></math>, then <math display='inline'><semantics> <msub> <mi>θ</mi> <mi>i</mi> </msub> </semantics></math> is calculated by using (<a href="#FD1-futureinternet-14-00214" class="html-disp-formula">1</a>). <div class='html-disp-formula-info' id='FD1-futureinternet-14-00214'> <div class='f'> <math display='block'><semantics> <mrow> <msub> <mi>θ</mi> <mi>i</mi> </msub> <mo>=</mo> <mi>a</mi> <mi>r</mi> <mi>c</mi> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mfenced open="(" close=")"> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mrow> <mover accent="true"> <mrow> <mi>s</mi> <msub> <mi>n</mi> <mi>i</mi> </msub> </mrow> <mo>→</mo> </mover> <mo>·</mo> <mover accent="true"> <mrow> <mi>s</mi> <mi>d</mi> </mrow> <mo>→</mo> </mover> </mrow> <mrow> <mrow> <mo>∥</mo> <mover accent="true"> <mrow> <mi>s</mi> <msub> <mi>n</mi> <mi>i</mi> </msub> </mrow> <mo>→</mo> </mover> <mo>∥</mo> </mrow> <mo>·</mo> <mrow> <mo>∥</mo> <mover accent="true"> <mrow> <mi>s</mi> <mi>d</mi> </mrow> <mo>→</mo> </mover> <mo>∥</mo> </mrow> </mrow> </mfrac> </mstyle> </mfenced> <mo>,</mo> </mrow> </semantics></math> </div> <div class='l'> <label >(1)</label> </div> </div></div><div class='html-p'>In (<a href="#FD1-futureinternet-14-00214" class="html-disp-formula">1</a>), <math display='inline'><semantics> <mrow> <mo>∥</mo> <mover accent="true"> <mrow> <mi>s</mi> <msub> <mi>n</mi> <mi>i</mi> </msub> </mrow> <mo>→</mo> </mover> <mo>∥</mo> </mrow> </semantics></math> and <math display='inline'><semantics> <mrow> <mo>∥</mo> <mover accent="true"> <mrow> <mi>s</mi> <mi>d</mi> </mrow> <mo>→</mo> </mover> <mo>∥</mo> </mrow> </semantics></math> are Euclidean vectors, and <math display='inline'><semantics> <mrow> <mover accent="true"> <mrow> <mi>s</mi> <msub> <mi>n</mi> <mi>i</mi> </msub> </mrow> <mo>→</mo> </mover> <mo>·</mo> <mover accent="true"> <mrow> <mi>s</mi> <mi>d</mi> </mrow> <mo>→</mo> </mover> </mrow> </semantics></math> represents an inner product. Let <math display='inline'><semantics> <msub> <mi>n</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </semantics></math> be at one-hop distance from <math display='inline'><semantics> <msub> <mi>n</mi> <mi>i</mi> </msub> </semantics></math> and two-hop distance from <span class='html-italic'>s</span>; then, two second offset angles at the two-hop distance <math display='inline'><semantics> <msub> <mi>θ</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </semantics></math> and <math display='inline'><semantics> <msubsup> <mi>θ</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> <mo>′</mo> </msubsup> </semantics></math> with respect to <math display='inline'><semantics> <mover accent="true"> <mrow> <msub> <mi>n</mi> <mi>i</mi> </msub> <msub> <mi>n</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mrow> <mo>→</mo> </mover> </semantics></math> and <math display='inline'><semantics> <mover accent="true"> <mrow> <msub> <mi>n</mi> <mi>i</mi> </msub> <mi>d</mi> </mrow> <mo>→</mo> </mover> </semantics></math>, and <math display='inline'><semantics> <mover accent="true"> <mrow> <msub> <mi>n</mi> <mi>i</mi> </msub> <msub> <mi>n</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mrow> <mo>→</mo> </mover> </semantics></math> and <math display='inline'><semantics> <mover accent="true"> <mrow> <msub> <mi>n</mi> <mi>i</mi> </msub> <msup> <mi>d</mi> <mo>′</mo> </msup> </mrow> <mo>→</mo> </mover> </semantics></math> are formed. Because a smaller geometric angle with respect to <span class='html-italic'>d</span> implies that a node is moving toward the destination, then the first threshold value for one-hop relay selection is <math display='inline'><semantics> <mrow> <msub> <mi>θ</mi> <mi>i</mi> </msub> <mo>≤</mo> <mfrac> <mi>π</mi> <mn>2</mn> </mfrac> </mrow> </semantics></math>. The condition for two-hop relay follows by checking <math display='inline'><semantics> <mrow> <msub> <mi>θ</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>≤</mo> <mfrac> <mi>π</mi> <mn>2</mn> </mfrac> </mrow> </semantics></math> first, and then <math display='inline'><semantics> <mrow> <msub> <mi>θ</mi> <mi>m</mi> </msub> <mo>=</mo> <mrow> <mo>|</mo> <msub> <mi>θ</mi> <mi>i</mi> </msub> <mo>+</mo> <msubsup> <mi>θ</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> <mo>′</mo> </msubsup> <mo>|</mo> </mrow> <mo><</mo> <mi>ϵ</mi> </mrow> </semantics></math> for <math display='inline'><semantics> <mrow> <mi>ϵ</mi> <mo>∈</mo> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mfrac> <mi>π</mi> <mn>2</mn> </mfrac> <mo>]</mo> </mrow> </semantics></math>. Note that <math display='inline'><semantics> <msub> <mi>θ</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </semantics></math> and <math display='inline'><semantics> <msubsup> <mi>θ</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> <mo>′</mo> </msubsup> </semantics></math> are calculated by replacing <math display='inline'><semantics> <mover accent="true"> <mrow> <mi>s</mi> <msub> <mi>n</mi> <mi>i</mi> </msub> </mrow> <mo>→</mo> </mover> </semantics></math> and <math display='inline'><semantics> <mover accent="true"> <mrow> <mi>s</mi> <mi>d</mi> </mrow> <mo>→</mo> </mover> </semantics></math> with <math display='inline'><semantics> <mover accent="true"> <mrow> <msub> <mi>n</mi> <mi>i</mi> </msub> <msub> <mi>n</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mrow> <mo>→</mo> </mover> </semantics></math> and <math display='inline'><semantics> <mover accent="true"> <mrow> <msub> <mi>n</mi> <mi>i</mi> </msub> <mi>d</mi> </mrow> <mo>→</mo> </mover> </semantics></math> and <math display='inline'><semantics> <mover accent="true"> <mrow> <msub> <mi>n</mi> <mi>i</mi> </msub> <msub> <mi>n</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mrow> <mo>→</mo> </mover> </semantics></math> and <math display='inline'><semantics> <mover accent="true"> <mrow> <msub> <mi>n</mi> <mi>i</mi> </msub> <msup> <mi>d</mi> <mo>′</mo> </msup> </mrow> <mo>→</mo> </mover> </semantics></math> in (<a href="#FD1-futureinternet-14-00214" class="html-disp-formula">1</a>), respectively. Provided that <math display='inline'><semantics> <mrow> <msub> <mi>θ</mi> <mi>i</mi> </msub> <mo>≤</mo> <mfrac> <mi>π</mi> <mn>2</mn> </mfrac> </mrow> </semantics></math> is true, then at the two-hop distance, if <math display='inline'><semantics> <mrow> <msub> <mi>θ</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>≤</mo> <mfrac> <mi>π</mi> <mn>2</mn> </mfrac> </mrow> </semantics></math> and <math display='inline'><semantics> <mrow> <msub> <mi>θ</mi> <mi>m</mi> </msub> <mo><</mo> <mi>ϵ</mi> </mrow> </semantics></math>, the MPMF policy goes to the next phase, as follows.</div><div class='html-p'>Let <math display='inline'><semantics> <msub> <mi>p</mi> <mi>i</mi> </msub> </semantics></math> and <math display='inline'><semantics> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </semantics></math> denote the respective DP values of the one-hop <math display='inline'><semantics> <msub> <mi>n</mi> <mi>i</mi> </msub> </semantics></math> and the two-hop <math display='inline'><semantics> <msub> <mi>n</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </semantics></math> with respect to <span class='html-italic'>d</span>. With <math display='inline'><semantics> <msub> <mi>p</mi> <mi>i</mi> </msub> </semantics></math> and <math display='inline'><semantics> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </semantics></math>, a primary weighted DP form <math display='inline'><semantics> <msup> <mi>W</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </msup> </semantics></math> is given as <div class='html-disp-formula-info' id='FD2-futureinternet-14-00214'> <div class='f'> <math display='block'><semantics> <mrow> <msubsup> <mi>W</mi> <mi>i</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </msubsup> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mi>In</mi> <msub> <mi>p</mi> <mi>i</mi> </msub> <mo>·</mo> <mi>In</mi> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> <mspace width="0.277778em"/> <mo>,</mo> </mrow> </semantics></math> </div> <div class='l'> <label >(2)</label> </div> </div> where <math display='inline'><semantics> <msub> <mi>p</mi> <mi>i</mi> </msub> </semantics></math> and <math display='inline'><semantics> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </semantics></math> are calculated using (<a href="#FD3-futureinternet-14-00214" class="html-disp-formula">3</a>) as a result of PRoPHET [<a href="#B10-futureinternet-14-00214" class="html-bibr">10</a>]. <div class='html-disp-formula-info' id='FD3-futureinternet-14-00214'> <div class='f'> <math display='block'><semantics> <mrow> <msub> <mi>P</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> </mrow> </msub> <mo>=</mo> <msub> <mi>P</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> <mi>o</mi> <mi>l</mi> <mi>d</mi> </mrow> </msub> <mo>+</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>−</mo> <msub> <mi>P</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> <mi>o</mi> <mi>l</mi> <mi>d</mi> </mrow> </msub> <mo>)</mo> </mrow> <msub> <mi>P</mi> <mrow> <mi>i</mi> <mi>n</mi> <mi>i</mi> <mi>t</mi> </mrow> </msub> <mo>,</mo> </mrow> </semantics></math> </div> <div class='l'> <label >(3)</label> </div> </div> where <math display='inline'><semantics> <msub> <mi>P</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> </mrow> </msub> </semantics></math> and <math display='inline'><semantics> <msub> <mi>P</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> <mi>o</mi> <mi>l</mi> <mi>d</mi> </mrow> </msub> </semantics></math> represent the current and previous DP values with respect to two nodes <math display='inline'><semantics> <msub> <mi>n</mi> <mi>x</mi> </msub> </semantics></math> and <math display='inline'><semantics> <msub> <mi>n</mi> <mi>y</mi> </msub> </semantics></math>, and the value <math display='inline'><semantics> <mrow> <msub> <mi>P</mi> <mrow> <mi>i</mi> <mi>n</mi> <mi>i</mi> <mi>t</mi> </mrow> </msub> <mo>∈</mo> <mrow> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>]</mo> </mrow> </mrow> </semantics></math> is an initial constant. Here, for example, we have <math display='inline'><semantics> <mrow> <msub> <mi>p</mi> <mn>1</mn> </msub> <mo>=</mo> <msub> <mi>P</mi> <mrow> <mo>(</mo> <msub> <mi>n</mi> <mn>1</mn> </msub> <mo>,</mo> <mi>d</mi> <mo>)</mo> </mrow> </msub> </mrow> </semantics></math>, and <math display='inline'><semantics> <mrow> <msub> <mi>p</mi> <mn>2</mn> </msub> <mo>=</mo> <msub> <mi>P</mi> <mrow> <mo>(</mo> <msub> <mi>n</mi> <mn>2</mn> </msub> <mo>,</mo> <mi>d</mi> <mo>)</mo> </mrow> </msub> </mrow> </semantics></math>. If <math display='inline'><semantics> <msub> <mi>n</mi> <mi>x</mi> </msub> </semantics></math> and <math display='inline'><semantics> <msub> <mi>n</mi> <mi>y</mi> </msub> </semantics></math> have not contacted for a certain period, their DP values will decay and be updated by (<a href="#FD4-futureinternet-14-00214" class="html-disp-formula">4</a>). <div class='html-disp-formula-info' id='FD4-futureinternet-14-00214'> <div class='f'> <math display='block'><semantics> <mtable displaystyle="true"> <mtr> <mtd columnalign="right"> <mrow> <msub> <mi>P</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> </mrow> </msub> <mo>=</mo> <msub> <mi>P</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> <mi>o</mi> <mi>l</mi> <mi>d</mi> </mrow> </msub> <mo>×</mo> <msup> <mi>γ</mi> <mi>k</mi> </msup> <mo>,</mo> </mrow> </mtd> </mtr> </mtable> </semantics></math> </div> <div class='l'> <label >(4)</label> </div> </div> where <math display='inline'><semantics> <mrow> <mi>γ</mi> <mo>∈</mo> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>]</mo> </mrow> </semantics></math> is an aging coefficient, and <span class='html-italic'>k</span> denotes the number of expired time units after the last update of this DP value. Although the aging of <math display='inline'><semantics> <msub> <mi>P</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> </mrow> </msub> </semantics></math> is ongoing after the last contact, <math display='inline'><semantics> <msub> <mi>P</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> </mrow> </msub> </semantics></math> can still be increased by any other node <math display='inline'><semantics> <msub> <mi>n</mi> <mi>z</mi> </msub> </semantics></math> with <math display='inline'><semantics> <msub> <mi>P</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>z</mi> <mo>)</mo> </mrow> </msub> </semantics></math> and <math display='inline'><semantics> <msub> <mi>P</mi> <mrow> <mo>(</mo> <mi>z</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> </mrow> </msub> </semantics></math> as:<div class='html-disp-formula-info' id='FD5-futureinternet-14-00214'> <div class='f'> <math display='block'><semantics> <mrow> <msub> <mi>P</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> </mrow> </msub> <mo>=</mo> <msub> <mi>P</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> <mi>o</mi> <mi>l</mi> <mi>d</mi> </mrow> </msub> <mo>+</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>−</mo> <msub> <mi>P</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> <mi>o</mi> <mi>l</mi> <mi>d</mi> </mrow> </msub> <mo>)</mo> </mrow> <msub> <mi>P</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>z</mi> <mo>)</mo> </mrow> </msub> <msub> <mi>P</mi> <mrow> <mo>(</mo> <mi>z</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> </mrow> </msub> <mo>×</mo> <mi>β</mi> <mo>.</mo> </mrow> </semantics></math> </div> <div class='l'> <label >(5)</label> </div> </div> where <math display='inline'><semantics> <mi>β</mi> </semantics></math> is a parameter with value <math display='inline'><semantics> <mrow> <mo>∈</mo> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>]</mo> </mrow> </semantics></math>.</div><div class='html-p'>Let <math display='inline'><semantics> <mover accent="true"> <msub> <mi>n</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>→</mo> </mover> </semantics></math> be a directional vector of <math display='inline'><semantics> <msub> <mi>n</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </semantics></math>, then a new <math display='inline'><semantics> <mi>θ</mi> </semantics></math> is calculated with respect to <math display='inline'><semantics> <mover accent="true"> <msub> <mi>n</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>→</mo> </mover> </semantics></math> and <math display='inline'><semantics> <mover accent="true"> <mrow> <msub> <mi>n</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mi>d</mi> </mrow> <mo>→</mo> </mover> </semantics></math>. With <math display='inline'><semantics> <mi>θ</mi> </semantics></math>, a secondary weighted form <math display='inline'><semantics> <msup> <mi>W</mi> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </msup> </semantics></math> is given as <div class='html-disp-formula-info' id='FD6-futureinternet-14-00214'> <div class='f'> <math display='block'><semantics> <mrow> <msubsup> <mi>W</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </msubsup> <mo>=</mo> <mn>1</mn> <mo>−</mo> <mrow> <mo>|</mo> <mfrac> <mi>θ</mi> <mn>180</mn> </mfrac> <mo>|</mo> </mrow> <mo>.</mo> </mrow> </semantics></math> </div> <div class='l'> <label >(6)</label> </div> </div></div><div class='html-p'>Then, combining (<a href="#FD2-futureinternet-14-00214" class="html-disp-formula">2</a>) and (<a href="#FD6-futureinternet-14-00214" class="html-disp-formula">6</a>), we have a two-hop weighed form <math display='inline'><semantics> <msub> <mi>W</mi> <mi>p</mi> </msub> </semantics></math> subject to a tuning parameter <math display='inline'><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>)</mo> </mrow> </semantics></math> as <div class='html-disp-formula-info' id='FD7-futureinternet-14-00214'> <div class='f'> <math display='block'><semantics> <mtable> <mtr> <mtd columnalign="right"> <msub> <mi>W</mi> <mi>p</mi> </msub> </mtd> <mtd columnalign="left"> <mrow> <mo>=</mo> <mi>α</mi> <msubsup> <mi>W</mi> <mi>i</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </msubsup> <mo>+</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>−</mo> <mi>α</mi> <mo>)</mo> </mrow> <msubsup> <mi>W</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </msubsup> </mrow> </mtd> </mtr> <mtr> <mtd columnalign="right"> <mspace width="1.em"/> </mtd> <mtd columnalign="left"> <mrow> <mo>=</mo> <mi>α</mi> <mo>×</mo> <mfrac> <mn>1</mn> <mrow> <mi>In</mi> <msub> <mi>p</mi> <mi>i</mi> </msub> <mo>·</mo> <mi>In</mi> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> <mo>+</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>−</mo> <mi>α</mi> <mo>)</mo> </mrow> <mo>×</mo> <mn>1</mn> <mo>−</mo> <mrow> <mo>|</mo> <mfrac> <mi>θ</mi> <mn>180</mn> </mfrac> <mo>|</mo> </mrow> <mo>.</mo> </mrow> </mtd> </mtr> </mtable> </semantics></math> </div> <div class='l'> <label >(7)</label> </div> </div></div><div class='html-p'>If the resulting <math display='inline'><semantics> <msub> <mi>W</mi> <mi>p</mi> </msub> </semantics></math> is greater than a specific <math display='inline'><semantics> <msub> <mi>W</mi> <mn>0</mn> </msub> </semantics></math>, <math display='inline'><semantics> <msub> <mi>n</mi> <mi>i</mi> </msub> </semantics></math> and <math display='inline'><semantics> <msub> <mi>n</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </semantics></math> will be selected as candidate nodes to receive a message <math display='inline'><semantics> <msub> <mi>m</mi> <mi>i</mi> </msub> </semantics></math> from <span class='html-italic'>s</span>. First, <math display='inline'><semantics> <msub> <mi>n</mi> <mi>i</mi> </msub> </semantics></math> will receive <math display='inline'><semantics> <msub> <mi>m</mi> <mi>i</mi> </msub> </semantics></math> from <span class='html-italic'>s</span> and then replicate it to <math display='inline'><semantics> <msub> <mi>n</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </semantics></math>. The above relay node selection can be written as follows:<div class='html-disp-formula-info' id='FD8-futureinternet-14-00214'> <div class='f'> <math display='block'><semantics> <mrow> <mi>d</mi> <mrow> <mo>(</mo> <msub> <mi>m</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfenced separators="" open="{" close=""> <mtable> <mtr> <mtd columnalign="left"> <mrow> <mn>1</mn> <mo>,</mo> </mrow> </mtd> <mtd columnalign="left"> <mrow> <mrow> <mo>(</mo> <mrow> <mo>(</mo> <msub> <mi>θ</mi> <mi>i</mi> </msub> <mo>∧</mo> <msub> <mi>θ</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>≤</mo> <mfrac> <mi>π</mi> <mn>2</mn> </mfrac> <mo>)</mo> </mrow> <mo>∧</mo> <mrow> <mo>(</mo> <msub> <mi>θ</mi> <mi>m</mi> </msub> <mo>≤</mo> <mi>ϵ</mi> <mo>)</mo> </mrow> <mo>∧</mo> <mrow> <mo>(</mo> <msub> <mi>W</mi> <mi>p</mi> </msub> <mo>></mo> <msub> <mi>W</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mrow> <mn>0</mn> <mo>,</mo> </mrow> </mtd> <mtd columnalign="left"> <mrow> <mi>otherwise</mi> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mspace width="1.em"/> </mtd> <mtd columnalign="left"> <mrow> <mi>where</mi> <mi>ϵ</mi> <mo>∈</mo> <mrow> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mfrac> <mi>π</mi> <mn>2</mn> </mfrac> <mo>]</mo> </mrow> <mo>,</mo> <msub> <mi>W</mi> <mn>0</mn> </msub> <mo>∈</mo> <mrow> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>]</mo> </mrow> <mo>,</mo> <mspace width="4.pt"/> <mi>and</mi> <mspace width="0.277778em"/> <msub> <mi>θ</mi> <mi>m</mi> </msub> <mo>=</mo> <mrow> <mo>|</mo> <msub> <mi>θ</mi> <mi>i</mi> </msub> <mo>+</mo> <msubsup> <mi>θ</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> <mo>′</mo> </msubsup> <mo>|</mo> </mrow> <mo>.</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow> </semantics></math> </div> <div class='l'> <label >(8)</label> </div> </div></div><div class='html-p'>In (<a href="#FD8-futureinternet-14-00214" class="html-disp-formula">8</a>), if both <math display='inline'><semantics> <msub> <mi>θ</mi> <mi>i</mi> </msub> </semantics></math> and <math display='inline'><semantics> <mrow> <msub> <mi>θ</mi> <mi>i</mi> </msub> <mo>≤</mo> <mfrac> <mi>π</mi> <mn>2</mn> </mfrac> </mrow> </semantics></math>, <math display='inline'><semantics> <mrow> <msub> <mi>θ</mi> <mi>m</mi> </msub> <mo>≤</mo> <mi>ϵ</mi> </mrow> </semantics></math>, and <math display='inline'><semantics> <mrow> <msub> <mi>W</mi> <mi>p</mi> </msub> <mo>></mo> <msub> <mi>W</mi> <mn>0</mn> </msub> </mrow> </semantics></math>, then both <math display='inline'><semantics> <msub> <mi>n</mi> <mi>i</mi> </msub> </semantics></math> and <math display='inline'><semantics> <msub> <mi>n</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </semantics></math> will receive <math display='inline'><semantics> <msub> <mi>m</mi> <mi>i</mi> </msub> </semantics></math>. In the case of <math display='inline'><semantics> <mrow> <msub> <mi>W</mi> <mi>p</mi> </msub> <mo><</mo> <msub> <mi>W</mi> <mn>0</mn> </msub> </mrow> </semantics></math>, <span class='html-italic'>s</span> will look for another one-hop neighbor node <math display='inline'><semantics> <msubsup> <mi>n</mi> <mi>i</mi> <mo>′</mo> </msubsup> </semantics></math> and then repeat the above procedure to determine the next relay node. If no neighbor nodes can satisfy this selection policy, the original node keeps carrying the message during moving in OppNets.</div></section><section id='sec4dot2dot2-futureinternet-14-00214' type=''><h4 class='' data-nested='3'> 4.2.2. Case 2</h4><div class='html-p'>To select a one-hop relay node, its location and destination’s movement can be exploited to take a forwarding decision. This situation arises when a message-carrying node encounters only one-hop relay node during a message transfer session.</div><div class='html-p'>Let <span class='html-italic'>s</span> encounters <math display='inline'><semantics> <msub> <mi>n</mi> <mi>i</mi> </msub> </semantics></math> at any time instant. Without other node at the one-hop distance from <span class='html-italic'>s</span>, <math display='inline'><semantics> <msub> <mi>θ</mi> <mi>i</mi> </msub> </semantics></math> is calculated according to (<a href="#FD1-futureinternet-14-00214" class="html-disp-formula">1</a>). Let <math display='inline'><semantics> <mover accent="true"> <mi>d</mi> <mo>→</mo> </mover> </semantics></math> be a directional vector of <span class='html-italic'>d</span>. Given the next location of <span class='html-italic'>d</span> is known to <span class='html-italic'>s</span>, then <math display='inline'><semantics> <msub> <mi>θ</mi> <mi>d</mi> </msub> </semantics></math> is calculated with respect to <math display='inline'><semantics> <mover accent="true"> <mi>d</mi> <mo>→</mo> </mover> </semantics></math> and <math display='inline'><semantics> <mover accent="true"> <mrow> <mi>d</mi> <mi>s</mi> </mrow> <mo>→</mo> </mover> </semantics></math>. For the two geometric angles, i.e., <math display='inline'><semantics> <msub> <mi>θ</mi> <mi>i</mi> </msub> </semantics></math> and <math display='inline'><semantics> <msub> <mi>θ</mi> <mi>d</mi> </msub> </semantics></math>, the conditions for one-hop relay selection are that <math display='inline'><semantics> <msub> <mi>θ</mi> <mi>i</mi> </msub> </semantics></math> and <math display='inline'><semantics> <mrow> <msub> <mi>θ</mi> <mi>d</mi> </msub> <mo><</mo> <mfrac> <mi>π</mi> <mn>2</mn> </mfrac> </mrow> </semantics></math> and <math display='inline'><semantics> <msub> <mi>n</mi> <mi>i</mi> </msub> </semantics></math> and <span class='html-italic'>d</span> are moving in the same direction. The value obtained in <math display='inline'><semantics> <mfrac> <mrow> <mover accent="true"> <mrow> <mi>s</mi> <mi>d</mi> </mrow> <mo>→</mo> </mover> <mo>×</mo> <mover accent="true"> <mrow> <mi>s</mi> <msub> <mi>n</mi> <mi>i</mi> </msub> </mrow> <mo>→</mo> </mover> </mrow> <mrow> <mover accent="true"> <mrow> <mi>d</mi> <mi>s</mi> </mrow> <mo>→</mo> </mover> <mo>×</mo> <mover accent="true"> <mi>d</mi> <mo>→</mo> </mover> </mrow> </mfrac> </semantics></math> determines whether both the nodes are moving in the same direction or not. If <math display='inline'><semantics> <mrow> <mfrac> <mrow> <mover accent="true"> <mrow> <mi>s</mi> <mi>d</mi> </mrow> <mo>→</mo> </mover> <mo>×</mo> <mover accent="true"> <mrow> <mi>s</mi> <msub> <mi>n</mi> <mi>i</mi> </msub> </mrow> <mo>→</mo> </mover> </mrow> <mrow> <mover accent="true"> <mrow> <mi>d</mi> <mi>s</mi> </mrow> <mo>→</mo> </mover> <mo>×</mo> <mover accent="true"> <mi>d</mi> <mo>→</mo> </mover> </mrow> </mfrac> <mo><</mo> <mn>0</mn> </mrow> </semantics></math>, the nodes are moving in the same direction.</div><div class='html-p'>Node <span class='html-italic'>s</span> will continue to carry its messages when <math display='inline'><semantics> <msub> <mi>n</mi> <mi>i</mi> </msub> </semantics></math> is not moving in the direction of <span class='html-italic'>d</span>. The message delivery services may suffer if <span class='html-italic'>s</span> continues to keep the message without forwarding it because of the absence of better candidate nodes. Therefore, when a one- and two-hop relay does not qualify for receiving a message, a centrality metric value is used instead. Let the inter-contact between <math display='inline'><semantics> <msub> <mi>n</mi> <mi>i</mi> </msub> </semantics></math> and <math display='inline'><semantics> <msub> <mi>n</mi> <mi>j</mi> </msub> </semantics></math> follow an exponential distribution with a meeting rate <math display='inline'><semantics> <msub> <mi>λ</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> </semantics></math> [<a href="#B27-futureinternet-14-00214" class="html-bibr">27</a>], where <math display='inline'><semantics> <msub> <mi>λ</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> </semantics></math> is calculated by <math display='inline'><semantics> <mfrac> <mi>u</mi> <mrow> <msubsup> <mo>∑</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>u</mi> </msubsup> <msubsup> <mi>t</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> <mi>j</mi> </msubsup> </mrow> </mfrac> </semantics></math> corresponding to <span class='html-italic'>u</span> inter-contact time samples, i.e., <math display='inline'><semantics> <mrow> <msubsup> <mi>t</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> <mn>1</mn> </msubsup> <mo>,</mo> <msubsup> <mi>t</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> <mn>2</mn> </msubsup> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msubsup> <mi>t</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> <mi>u</mi> </msubsup> </mrow> </semantics></math> between <math display='inline'><semantics> <msub> <mi>n</mi> <mi>i</mi> </msub> </semantics></math> and <math display='inline'><semantics> <msub> <mi>n</mi> <mi>j</mi> </msub> </semantics></math> in a given time span <span class='html-italic'>t</span>. The contact probability between <math display='inline'><semantics> <msub> <mi>n</mi> <mi>i</mi> </msub> </semantics></math> and <math display='inline'><semantics> <msub> <mi>n</mi> <mi>j</mi> </msub> </semantics></math> within time <span class='html-italic'>t</span> is given by <math display='inline'><semantics> <mrow> <mn>1</mn> <mo>−</mo> <msup> <mi>e</mi> <mrow> <mo>−</mo> <msub> <mi>λ</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mi>t</mi> </mrow> </msup> </mrow> </semantics></math>. Given <span class='html-italic'>N</span> nodes in the network, the average probability that a node randomly contacts <math display='inline'><semantics> <msub> <mi>n</mi> <mi>i</mi> </msub> </semantics></math> within <span class='html-italic'>t</span> is given by (<a href="#FD9-futureinternet-14-00214" class="html-disp-formula">9</a>). <div class='html-disp-formula-info' id='FD9-futureinternet-14-00214'> <div class='f'> <math display='block'><semantics> <mrow> <msub> <mi>C</mi> <mi>i</mi> </msub> <mo>=</mo> <mn>1</mn> <mo>−</mo> <mfrac> <mn>1</mn> <mrow> <mi>N</mi> <mo>−</mo> <mn>1</mn> </mrow> </mfrac> <munder> <mo>∑</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> <mo>≠</mo> <mi>i</mi> </mrow> </munder> <msup> <mi>e</mi> <mrow> <msub> <mi>λ</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mi>t</mi> </mrow> </msup> <mo>.</mo> </mrow> </semantics></math> </div> <div class='l'> <label >(9)</label> </div> </div></div><div class='html-p'>In (<a href="#FD9-futureinternet-14-00214" class="html-disp-formula">9</a>), two nodes can compare their respective centrality values. A message-carrying node compares its centrality with the one-hop relay node. If its centrality value is smaller, the relay node will receive a message <math display='inline'><semantics> <msub> <mi>m</mi> <mi>i</mi> </msub> </semantics></math> from the message-carrying node. The above relay selection can be written as follows:<div class='html-disp-formula-info' id='FD10-futureinternet-14-00214'> <div class='f'> <math display='block'><semantics> <mrow> <mi>d</mi> <mrow> <mo>(</mo> <msub> <mi>m</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfenced separators="" open="{" close=""> <mtable> <mtr> <mtd columnalign="left"> <mrow> <mn>1</mn> <mo>,</mo> </mrow> </mtd> <mtd columnalign="left"> <mrow> <mfenced separators="" open="(" close=")"> <mrow> <mo>(</mo> <msub> <mi>θ</mi> <mi>i</mi> </msub> <mo>∧</mo> <msub> <mi>θ</mi> <mi>d</mi> </msub> <mo>)</mo> </mrow> <mo>≤</mo> <mfrac> <mi>π</mi> <mn>2</mn> </mfrac> <mo>∧</mo> <mfrac> <mrow> <mover accent="true"> <mrow> <mi>s</mi> <mi>d</mi> </mrow> <mo>→</mo> </mover> <mo>×</mo> <mover accent="true"> <mrow> <mi>s</mi> <msub> <mi>n</mi> <mi>i</mi> </msub> </mrow> <mo>→</mo> </mover> </mrow> <mrow> <mover accent="true"> <mrow> <mi>d</mi> <mi>s</mi> </mrow> <mo>→</mo> </mover> <mo>×</mo> <mover accent="true"> <mi>d</mi> <mo>→</mo> </mover> </mrow> </mfrac> <mo><</mo> <mn>0</mn> </mfenced> <mspace width="0.277778em"/> <mo>∨</mo> <mspace width="0.277778em"/> <mfenced separators="" open="(" close=")"> <msub> <mi>C</mi> <mi>s</mi> </msub> <mo>≤</mo> <msub> <mi>C</mi> <mi>i</mi> </msub> </mfenced> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mrow> <mn>0</mn> <mo>,</mo> </mrow> </mtd> <mtd columnalign="left"> <mrow> <mi>otherwise</mi> <mo>.</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow> </semantics></math> </div> <div class='l'> <label >(10)</label> </div> </div></div><div class='html-p'>Note that in (<a href="#FD9-futureinternet-14-00214" class="html-disp-formula">9</a>), <span class='html-italic'>t</span> is replaced by the current time-to-live of <math display='inline'><semantics> <msub> <mi>m</mi> <mi>i</mi> </msub> </semantics></math> to compute the centrality.</div></section></section></section><section id='sec5-futureinternet-14-00214' type=''><h2 data-nested='1'> 5. Message Forwarding</h2><div class='html-p'>This section discusses the message-forwarding policies in MPMF. <a href="#sec5dot1-futureinternet-14-00214" class="html-sec">Section 5.1</a> presents the procedural description of the MPMF. <a href="#sec5dot2-futureinternet-14-00214" class="html-sec">Section 5.2</a> gives the time complexity of the MPMF based on Algorithm 1. <table class='html-array_table'><tbody ><tr ><td style='border-top:solid thin;border-bottom:solid thin' ><b>Algorithm 1:</b> Message Forwarding Policy.</td></tr><tr ><td style='border-bottom:solid thin' ><span class='html-fig-inline' id = futureinternet-14-00214-i001 > <img alt="Futureinternet 14 00214 i001" data-lsrc="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-i001.png" /></span></td></tr></tbody></table></div><section id='sec5dot1-futureinternet-14-00214' type=''><h4 class='html-italic' data-nested='2'> 5.1. Message Forwarding in MPMF</h4><div class='html-p'>The message-forwarding policy decides the maximum number of message replicas of a message that a selected one-hop relay or one- and two-hop relays can further replicate. Let an initial value <span class='html-italic'>L</span> indicate the maximum number of replicas that can be created for a message in the network. We consider the following cases when deciding the number of replicas that a selected relay node can replicate.</div><dl class='html-order'><dt id=''>1.</dt><dd><div class='html-p'>Assuming that a message-carrying node encounters more than one node at the one-hop distance, i.e., case 1, the MPMF considers both one- and two-hop relays to receive only one message copy. Let <span class='html-italic'>s</span> be the message-carrying node and create a new message <math display='inline'><semantics> <msub> <mi>m</mi> <mi>i</mi> </msub> </semantics></math> for <span class='html-italic'>d</span>. When a one-hop relay receives this message copy from <span class='html-italic'>s</span>, it replicates this message to the two-hop-selected relay node. Node <span class='html-italic'>s</span> then updates the remaining message copies, denoted as <math display='inline'><semantics> <mrow> <msub> <mi>L</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>m</mi> </mrow> </msub> <mo>=</mo> <mi>L</mi> <mo>−</mo> <mn>2</mn> </mrow> </semantics></math> for the transferred message <math display='inline'><semantics> <msub> <mi>m</mi> <mi>i</mi> </msub> </semantics></math> in its buffer, and both the one- and two-hop relays update <math display='inline'><semantics> <mrow> <msub> <mi>L</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>m</mi> </mrow> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> in their respective buffers for the same message. Both nodes will transfer this message to the <span class='html-italic'>d</span> only. However, <span class='html-italic'>s</span> can continue to replicate the message to any encountered node until <math display='inline'><semantics> <mrow> <msub> <mi>L</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>m</mi> </mrow> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> and then wait for <span class='html-italic'>d</span> to transfer the message directly.</div></dd><dt id=''>2.</dt><dd><div class='html-p'>In the presence of only one relay at one-hop distance, i.e., case 2, a one-hop relay receives half of the remaining copies to distribute in the network. When <span class='html-italic'>s</span> forwards a message to a one-hop relay, both <span class='html-italic'>s</span> and the one-hop relay update <math display='inline'><semantics> <mrow> <msub> <mi>L</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>m</mi> </mrow> </msub> <mo>=</mo> <mi>L</mi> <mo>/</mo> <mn>2</mn> </mrow> </semantics></math> copies for the message in their respective buffers. Then, both nodes can replicate this message further to other encountered nodes and reduce <math display='inline'><semantics> <msub> <mi>L</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>m</mi> </mrow> </msub> </semantics></math>. When <math display='inline'><semantics> <mrow> <msub> <mi>L</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>m</mi> </mrow> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, the replication stops, and a relay node waits for the destination node to transfer the message.</div></dd></dl><div class='html-p'>Let <math display='inline'><semantics> <msub> <mi>N</mi> <mi>i</mi> </msub> </semantics></math> denote a set of one-hop neighbor nodes in <span class='html-italic'>r</span> of the message-carrying node <span class='html-italic'>s</span> and <math display='inline'><semantics> <msub> <mi>N</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> </semantics></math> denote a set of one-hop neighbor nodes of <math display='inline'><semantics> <mrow> <msub> <mi>n</mi> <mi>i</mi> </msub> <mo>∈</mo> <msub> <mi>N</mi> <mi>i</mi> </msub> </mrow> </semantics></math>. Any <math display='inline'><semantics> <mrow> <msub> <mi>n</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>∈</mo> <msub> <mi>N</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> </mrow> </semantics></math> is at the two-hop distance from <span class='html-italic'>s</span>. Suppose <span class='html-italic'>s</span> contains <math display='inline'><semantics> <msub> <mi>m</mi> <mi>i</mi> </msub> </semantics></math> with a remaining time-to-live period, denoted as TTL<math display='inline'><semantics> <msubsup> <mrow/> <mi>i</mi> <mi>m</mi> </msubsup> </semantics></math>. With the information of location and the vector of every node in <math display='inline'><semantics> <msub> <mi>N</mi> <mi>i</mi> </msub> </semantics></math> and <math display='inline'><semantics> <msub> <mi>N</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> </semantics></math>, <span class='html-italic'>s</span> and <math display='inline'><semantics> <msub> <mi>n</mi> <mi>i</mi> </msub> </semantics></math> can compute <math display='inline'><semantics> <msub> <mi>θ</mi> <mi>i</mi> </msub> </semantics></math> and <math display='inline'><semantics> <msub> <mi>θ</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> </semantics></math>, respectively. To transfer <math display='inline'><semantics> <msub> <mi>m</mi> <mi>i</mi> </msub> </semantics></math> to <math display='inline'><semantics> <msub> <mi>n</mi> <mi>i</mi> </msub> </semantics></math>, <span class='html-italic'>s</span> applies the MPMF message scheduling, as specified in Algorithm 1. This algorithm consists of two sub-routines: two-hop message forwarding and one-hop message forwarding. In the sub-routine of two-hop message forwarding, <math display='inline'><semantics> <msub> <mi>n</mi> <mi>i</mi> </msub> </semantics></math> receives <math display='inline'><semantics> <msub> <mi>m</mi> <mi>i</mi> </msub> </semantics></math> from <span class='html-italic'>s</span> and then replicates it to <math display='inline'><semantics> <mrow> <msub> <mi>n</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>∈</mo> <msub> <mi>N</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> </mrow> </semantics></math>. In the sub-routine of one-hop message forwarding, only <math display='inline'><semantics> <msub> <mi>n</mi> <mi>i</mi> </msub> </semantics></math> receives <math display='inline'><semantics> <msub> <mi>m</mi> <mi>i</mi> </msub> </semantics></math> from <span class='html-italic'>s</span>.</div><div class='html-p'>Regarding the two-hop message forwarding, the summation angle <math display='inline'><semantics> <msub> <mi>θ</mi> <mi>i</mi> </msub> </semantics></math> is checked inside each iteration of a for-loop procedure (lines 6–19), while <math display='inline'><semantics> <msub> <mi>θ</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> </semantics></math> is checked inside each iteration of a for-loop procedure (8–17). If <span class='html-italic'>s</span> has more than one neighbor node in its vicinity as line 5, it seeks to filter out neighbor nodes that are moving away from <span class='html-italic'>d</span> and select <math display='inline'><semantics> <msub> <mi>n</mi> <mi>i</mi> </msub> </semantics></math> with <math display='inline'><semantics> <mrow> <msub> <mi>θ</mi> <mi>i</mi> </msub> <mo>≤</mo> <mfrac> <mi>π</mi> <mn>2</mn> </mfrac> </mrow> </semantics></math>, as lines 6–7. In lines 8–9, a two-hop relay <math display='inline'><semantics> <msub> <mi>n</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> </semantics></math> is selected by calculating the summation angle <math display='inline'><semantics> <msub> <mi>θ</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> </semantics></math>. Provided that <math display='inline'><semantics> <mrow> <msub> <mi>θ</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>≤</mo> <mfrac> <mi>π</mi> <mn>2</mn> </mfrac> </mrow> </semantics></math>, <math display='inline'><semantics> <mrow> <msub> <mi>θ</mi> <mi>m</mi> </msub> <mo>≤</mo> <mi>ϵ</mi> </mrow> </semantics></math>, and <math display='inline'><semantics> <mrow> <msub> <mi>W</mi> <mi>p</mi> </msub> <mo>></mo> <msub> <mi>W</mi> <mn>0</mn> </msub> </mrow> </semantics></math>, <math display='inline'><semantics> <msub> <mi>n</mi> <mi>i</mi> </msub> </semantics></math> will receive <math display='inline'><semantics> <msub> <mi>m</mi> <mi>i</mi> </msub> </semantics></math> from <span class='html-italic'>s</span> and transfer it to <math display='inline'><semantics> <msub> <mi>n</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> </semantics></math> as lines 9–12. After the message transfer, <span class='html-italic'>s</span> will update <math display='inline'><semantics> <mrow> <msub> <mi>L</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>m</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>L</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>m</mi> </mrow> </msub> <mo>−</mo> </mrow> </semantics></math>2 and both <math display='inline'><semantics> <msub> <mi>n</mi> <mi>i</mi> </msub> </semantics></math> and <math display='inline'><semantics> <msub> <mi>n</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> </semantics></math> will update <math display='inline'><semantics> <mrow> <msub> <mi>L</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>m</mi> </mrow> </msub> <mo>=</mo> </mrow> </semantics></math> 1 for <math display='inline'><semantics> <msub> <mi>m</mi> <mi>i</mi> </msub> </semantics></math> in their respective buffers, as lines 13–14.</div><div class='html-p'>Regarding the sub-routine of one-hop message forwarding, if the number of nodes in <math display='inline'><semantics> <msub> <mi>N</mi> <mi>i</mi> </msub> </semantics></math> equals to 1, then the summation angles <math display='inline'><semantics> <msub> <mi>θ</mi> <mi>i</mi> </msub> </semantics></math> and <math display='inline'><semantics> <msub> <mi>θ</mi> <mi>d</mi> </msub> </semantics></math>, directional vectors, and centrality values of <math display='inline'><semantics> <msub> <mi>n</mi> <mi>i</mi> </msub> </semantics></math> and <span class='html-italic'>d</span> are compared (lines 21–30). If both <math display='inline'><semantics> <msub> <mi>θ</mi> <mi>i</mi> </msub> </semantics></math> and <math display='inline'><semantics> <msub> <mi>θ</mi> <mi>s</mi> </msub> </semantics></math> are less or equal to <math display='inline'><semantics> <mfrac> <mi>π</mi> <mn>2</mn> </mfrac> </semantics></math>, <math display='inline'><semantics> <msub> <mi>n</mi> <mi>i</mi> </msub> </semantics></math> will receive <math display='inline'><semantics> <msub> <mi>m</mi> <mi>i</mi> </msub> </semantics></math> from <span class='html-italic'>s</span> when <math display='inline'><semantics> <msub> <mi>n</mi> <mi>i</mi> </msub> </semantics></math> and <span class='html-italic'>d</span> move in the same direction, as lines 21–22. If <math display='inline'><semantics> <msub> <mi>n</mi> <mi>i</mi> </msub> </semantics></math> and <span class='html-italic'>d</span> are moving away from each other, then the centrality of <span class='html-italic'>s</span> and <math display='inline'><semantics> <msub> <mi>n</mi> <mi>i</mi> </msub> </semantics></math> is checked. If <math display='inline'><semantics> <mrow> <msub> <mi>C</mi> <mi>i</mi> </msub> <mo>></mo> <msub> <mi>C</mi> <mi>s</mi> </msub> </mrow> </semantics></math>, <math display='inline'><semantics> <msub> <mi>n</mi> <mi>i</mi> </msub> </semantics></math> will receive <math display='inline'><semantics> <msub> <mi>m</mi> <mi>i</mi> </msub> </semantics></math> from <span class='html-italic'>s</span>, as lines 26–27. In both the cases, <span class='html-italic'>s</span> and <math display='inline'><semantics> <msub> <mi>n</mi> <mi>i</mi> </msub> </semantics></math> update <math display='inline'><semantics> <mrow> <msub> <mi>L</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>m</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>L</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>m</mi> </mrow> </msub> <mo>/</mo> </mrow> </semantics></math>2 for <math display='inline'><semantics> <msub> <mi>m</mi> <mi>i</mi> </msub> </semantics></math>, as lines 23 and 28.</div><div class='html-p'>In summary, Algorithm 1 presents a novel relay selection and message forwarding based on one- and two-hop neighborhood information. Correspondingly, its pseudo-procedure comprises of three functions, i.e., summation angle at one- and two-hop, one-hop and destination’s movement, and centrality of a relay to select best one-hop relay or one- and two-hop relay nodes to receive messages. Therefore, the proposed policy can be implemented and will be examined with others in the next section.</div></section><section id='sec5dot2-futureinternet-14-00214' type=''><h4 class='html-italic' data-nested='2'> 5.2. Complexity</h4><div class='html-p'>The analysis of time complexity for the message-forwarding policy comprises two parts according to Algorithm 1. First, it is to determine a one-hop relay from <math display='inline'><semantics> <msub> <mi>N</mi> <mi>i</mi> </msub> </semantics></math> and a two-hop relay from <math display='inline'><semantics> <msub> <mi>N</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> </semantics></math> by calculating the summation angle of one- and two-hop relays, the two-hop relay’s moving direction, and the combined weight and two-hop offset angle. Second, it shall select a one-hop relay by determining the geometric angle of the one-hop relay and destination node, the one-hop relay’s and the destination’s moving directions, and the centrality of the one-hop relay and destination node.</div><div class='html-p'>The time complexity for the first part will be <math display='inline'><semantics> <mrow> <mi mathvariant="script">O</mi> <mo>(</mo> <mo>|</mo> <msub> <mi>N</mi> <mi>i</mi> </msub> <mo>|</mo> <mo>×</mo> <mo>|</mo> <msub> <mi>N</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>|</mo> <mo>)</mo> </mrow> </semantics></math>. As referring to Algorithm 1, <math display='inline'><semantics> <msub> <mi>θ</mi> <mi>i</mi> </msub> </semantics></math> is checked inside each iteration of a for-loop procedure (lines 6–19), and <math display='inline'><semantics> <msub> <mi>θ</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> </semantics></math> is checked inside each iteration of a for-loop procedure (8–17); the complexity in the worst case will be <math display='inline'><semantics> <mrow> <mi mathvariant="script">O</mi> <mo>(</mo> <mo>|</mo> <msub> <mi>N</mi> <mi>i</mi> </msub> <mo>|</mo> <mo>×</mo> <mo>|</mo> <msub> <mi>N</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>|</mo> <mo>)</mo> </mrow> </semantics></math>. For the second part, the time complexity will be <math display='inline'><semantics> <mrow> <mi mathvariant="script">O</mi> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </semantics></math>. Therefore, the overall time complexity of Algorithm 1 is <math display='inline'><semantics> <mrow> <mi mathvariant="script">O</mi> <mo>(</mo> <mo>|</mo> <msub> <mi>N</mi> <mi>i</mi> </msub> <mo>|</mo> <mo>×</mo> <mo>|</mo> <msub> <mi>N</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>|</mo> <mo>)</mo> </mrow> </semantics></math>.</div></section></section><section id='sec6-futureinternet-14-00214' type=''><h2 data-nested='1'> 6. Performance Evaluation</h2><div class='html-p'><a href="#sec6dot1-futureinternet-14-00214" class="html-sec">Section 6.1</a> mentions the OppNet environment establishment based on the ONE simulation platform and describes the comparative experiments and performance metrics. <a href="#sec6dot2-futureinternet-14-00214" class="html-sec">Section 6.2</a> describes the performance examination on the essential factors of the MPMF policy. <a href="#sec6dot3-futureinternet-14-00214" class="html-sec">Section 6.3</a> describes the relative performance between Epidemic [<a href="#B19-futureinternet-14-00214" class="html-bibr">19</a>], GSaR [<a href="#B4-futureinternet-14-00214" class="html-bibr">4</a>], TCCB [<a href="#B9-futureinternet-14-00214" class="html-bibr">9</a>], TC [<a href="#B20-futureinternet-14-00214" class="html-bibr">20</a>], and PRoPHETv2 [<a href="#B10-futureinternet-14-00214" class="html-bibr">10</a>].</div><section id='sec6dot1-futureinternet-14-00214' type=''><h4 class='html-italic' data-nested='2'> 6.1. Simulation Setting and Performance Metrics</h4><div class='html-p'>This section describes the simulation platform, different mobility scenarios, experimental cases for performance study, and evaluation metrics.</div><section id='sec6dot1dot1-futureinternet-14-00214' type=''><h4 class='' data-nested='3'> 6.1.1. Simulation Model and Node Mobility Scenarios</h4><div class='html-p'>The OppNet research commonly uses the Opportunistic Networking Environment (ONE) [<a href="#B28-futureinternet-14-00214" class="html-bibr">28</a>] simulator to investigate the routing and buffer management policies. The ONE simulator provides configurable functions to model the data networking and store–carry–forward message delivery without the need for physical-layer modeling, such as signaling and media access control. The ONE platform executes the primary agents, so-called nodes. Each node is assigned a set of primitive attributes, including radio interface, storage, message routing, movement, energy consumption, etc. Given a node population, they follow a defined mobility scenario to move on a given network map.</div><div class='html-p'>Our simulation employs two mobility scenarios for the behavior of node movement: the real trace-based dataset of National Chengchi University (NCCU) [<a href="#B18-futureinternet-14-00214" class="html-bibr">18</a>] and the time-variant community mobility model (TVCM) [<a href="#B17-futureinternet-14-00214" class="html-bibr">17</a>]. Both mobility scenarios are scripted into the configurations of the nodes’ movement, which are managed by the ONE simulator</div><ul class='html-bullet'><li><div class='html-p'>The TVCM model is proposed to capture the realistic mobility characteristics observed from various WLANs, so it is suitable for the simulation of MANET and OppNets. In a TVCM-specific mobility scenario, 50, 100, and 150 mobile nodes move in an area of 1500 × 1500 m<math display='inline'><semantics> <msup> <mrow/> <mn>2</mn> </msup> </semantics></math>. Each node was randomly assigned to several community homes on a plane during the simulation. The simulation time was divided into equal time slots. The nodes moved in random waypoint trips in each time slot with a probability <span class='html-italic'>p</span> of staying inside or (returning to) their homes and a probability of <math display='inline'><semantics> <mrow> <mn>1</mn> <mo>−</mo> <mi>p</mi> </mrow> </semantics></math> roaming outside their homes. By assigning different probabilities to each node, a wide range of heterogeneous node behavior can be reproduced.</div></li><li><div class='html-p'>The NCCU dataset is a real trace dataset collected at the National Chengchi University campus. These data were collected using an Android app installed on the smartphones of students attending NCCU, Taiwan. The trace contains the data of GPS, Wi-Fi access points, and Bluetooth devices connected in physical communication proximity. The trace was collected from 115 students moving in 3764 × 3420 m<math display='inline'><semantics> <msup> <mrow/> <mn>2</mn> </msup> </semantics></math> over 15 days. The NCCU real dataset is available [<a href="#B29-futureinternet-14-00214" class="html-bibr">29</a>].</div></li></ul><div class='html-p'>The output trace file of the above mobility models contains a series of mobile trajectory records, each of which indicates the data of the time stamp, x-position, and y-position with respect to the two-dimension position of any particular node at different time moments. <a href="#futureinternet-14-00214-t001" class="html-table">Table 1</a> shows the simulation parameters and their values used in the simulation. Specifically, the ONE simulator imports a mobility scenario script, i.e., a simple text-based configuration file, which contains various parameters of the simulation model, user interface, event generation, report parameters, etc. The ONE simulator will output a message statistics report module gathering the overall performance statistics, such as the number of created messages, the number of messages that have been delivered, the number of messages that have been relayed, etc.</div><div class='html-p'>For both NCCU and TVCM, the configuration file contains a chronological list of location records that describe the waypoint locations of mobile nodes in the Cartesian coordinate system at a time dimension. During the simulation, the ONE simulator continues to vary the next waypoint location of each node by referring to the sequence of generated records in the trace file. For each node, the movement speed between two locations is set in a range of 0.5 to 1.5 m/s. In addition, the ONE simulator provides different functional modules to access the up-to-date information of the node’s current position, movement path, neighbors, etc. Given a node pair of source and destination nodes, the source node generates a new message of 100 KB per 300 s. When two nodes appear in the mutual transmission range, they can transfer messages with each other. The ONE simulator runs both mobility scenarios for 24 h.</div></section><section id='sec6dot1dot2-futureinternet-14-00214' type=''><h4 class='' data-nested='3'> 6.1.2. Experimental Cases</h4><div class='html-p'>Our study examines the relative performance between the MPMF, Epidemic, GSaR, TCCB, TC, and PRoPHETv2 routing policies in OppNets. The performance results by the variances of the TTL period are investigated. Epidemic duplicates a message copy to each encountered node. PRoPHETv2 calculates the DP estimates of directly encountered nodes with the destination and avoids blind replication. GSaR uses historical information such as location, speed, and time duration to estimate the movement range of the destination node and sprays a limited number of copies of a message in the network. TCCB exploits the social contact patterns from the temporal perspective. It predicts temporal closeness by considering the average time span of a node pair, i.e., the duration plus inter-contact time between two nodes in a network. TC computes the probability/possibility of a node that will appear in a destination community, so as to forward a message in a network. Communities are formed by exploiting pairwise contacts, where the regular appearance of a contact pattern between a node pair is emphasized. All the MPMF, PRoPHETv2, GSaR, TCCB, TC, and Epidemic policies adopt the FIFO dropping policy as a plain comparative base.</div></section><section id='sec6dot1dot3-futureinternet-14-00214' type=''><h4 class='' data-nested='3'> 6.1.3. Evaluation Metrics</h4><div class='html-p'>With the message statistics report by the ONE simulator, we can calculate the number of created messages, number of messages that have been delivered, number of messages that have been relayed, average delay of messages, and average number of hops a message has passed. Accordingly, four performance metrics, successful delivery rate, transmission overhead ratio, average latency, and average hop count, are examined.</div><div class='html-p'>Let <math display='inline'><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mi>s</mi> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics></math> be the number of original messages that are generated by source nodes, <math display='inline'><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mi>d</mi> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics></math> be the number of distinct messages delivered to the destinations in the network, and <math display='inline'><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mi>f</mi> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics></math> be the total number of times by forwarding messages between any two relay nodes in a network.</div><ul class='html-bullet'><li><div class='html-p'>Successful message delivery rate: This metric indicates the rate of the number of original messages created in the network to the number of distinct messages that were successfully received by their destinations during the simulation. With <math display='inline'><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mi>s</mi> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics></math> and <math display='inline'><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mi>d</mi> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics></math>, the measure turns out to the value of <math display='inline'><semantics> <mfrac> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mi>d</mi> </msub> <mrow> <mo>|</mo> </mrow> </mrow> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mi>s</mi> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </mfrac> </semantics></math>.</div></li><li><div class='html-p'>Transmission overhead ratio: This metric is the ratio of the total times any original messages and replicas were transferred between intermediate nodes to the total amount of distinct messages received by their destinations during the simulation. With <math display='inline'><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mi>f</mi> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics></math> and <math display='inline'><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mi>d</mi> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics></math>, the overhead ratio is given as <math display='inline'><semantics> <mfrac> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mi>f</mi> </msub> <mrow> <mo>|</mo> </mrow> </mrow> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mi>d</mi> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </mfrac> </semantics></math>.</div></li><li><div class='html-p'>Latency: This metric indicates the duration from the time instance which a message is generated by a source node to the time instance which the message is successfully received by its destination.</div></li><li><div class='html-p'>Hop count: This measure is equal to the number of hops that a message has passed through during its delivery to the destination.</div></li></ul></section></section><section id='sec6dot2-futureinternet-14-00214' type=''><h4 class='html-italic' data-nested='2'> 6.2. Sensitivity to MPMF’s Factors of <math display='inline'><semantics> <msub> <mi>W</mi> <mn>0</mn> </msub> </semantics></math>, <math display='inline'><semantics> <mi>α</mi> </semantics></math>, <span class='html-italic'>L</span>, and <math display='inline'><semantics> <mi>ϵ</mi> </semantics></math></h4><div class='html-p'>This section inspects the performance sensitivity of the delivery rate and transmission overhead ratio against three MPMF-specific coefficients, including the <math display='inline'><semantics> <mi>α</mi> </semantics></math> parameter in (<a href="#FD7-futureinternet-14-00214" class="html-disp-formula">7</a>), the threshold of the weight value <math display='inline'><semantics> <msub> <mi>W</mi> <mn>0</mn> </msub> </semantics></math>, the threshold of the sum of the geometric angles at one- and two-hop distances <math display='inline'><semantics> <mi>ϵ</mi> </semantics></math> in (<a href="#FD8-futureinternet-14-00214" class="html-disp-formula">8</a>), and each message’s initial copy number <span class='html-italic'>L</span>. A smaller value of <math display='inline'><semantics> <mi>ϵ</mi> </semantics></math> indicates that one- and two-hop nodes closer to the destination node are considered as candidate nodes. A larger value of <math display='inline'><semantics> <msub> <mi>W</mi> <mn>0</mn> </msub> </semantics></math> implies that one-hop relay frequently contacting the destination and two-hop relay closer to and frequently contacting the destination are selected as candidate nodes. A larger value of <span class='html-italic'>L</span> indicates that an original message will be replicated at most <span class='html-italic'>L</span> times. After extensive simulation under TVCM and NCCU, we obtain the appropriate values of <math display='inline'><semantics> <mi>ϵ</mi> </semantics></math>, <math display='inline'><semantics> <msub> <mi>W</mi> <mn>0</mn> </msub> </semantics></math>, <span class='html-italic'>L</span>, and <math display='inline'><semantics> <mi>α</mi> </semantics></math> used for the performance comparison among Epidemic, PRoPHETv2, GSaR, TC, and TCCB.</div><div class='html-p'><a href="#futureinternet-14-00214-f003" class="html-fig">Figure 3</a> and <a href="#futureinternet-14-00214-f004" class="html-fig">Figure 4</a> depict the influence of <math display='inline'><semantics> <mi>ϵ</mi> </semantics></math> and <math display='inline'><semantics> <msub> <mi>W</mi> <mn>0</mn> </msub> </semantics></math> on the performance of the MPMF under TVCM and NCCU. In TVCM, the threshold <math display='inline'><semantics> <mi>ϵ</mi> </semantics></math> affects the delivery rate and overhead ratio, while the change in <math display='inline'><semantics> <msub> <mi>W</mi> <mn>0</mn> </msub> </semantics></math> has a minor effect on the overhead ratio. In NCCU, the threshold <math display='inline'><semantics> <msub> <mi>W</mi> <mn>0</mn> </msub> </semantics></math> affects the delivery rate and overhead ratio, while the change in <math display='inline'><semantics> <mi>ϵ</mi> </semantics></math> has a minor effect on the delivery rate. In TVCM, with the incremental values of <math display='inline'><semantics> <mi>ϵ</mi> </semantics></math> from 40 to 60, the delivery ratio decreases while the overhead ratio increases. The delivery rate and overhead ratio remain almost the same for <math display='inline'><semantics> <mrow> <mi>ϵ</mi> <mo>≥</mo> </mrow> </semantics></math> 70. When <math display='inline'><semantics> <mi>ϵ</mi> </semantics></math> is smaller than 60 in TVCM, the nodes moving closer to the destination node are selected as the candidate nodes, then the possibility of delivering messages earlier increases, which considerably effects the delivery rate and overhead ratio. Compared with TVCM, NCCU has a higher node population distributed in a large area. Thus, the variation of <math display='inline'><semantics> <mi>ϵ</mi> </semantics></math> shows little effect on the delivery rate and overhead ratio. In <a href="#futureinternet-14-00214-f004" class="html-fig">Figure 4</a>, as <math display='inline'><semantics> <msub> <mi>W</mi> <mn>0</mn> </msub> </semantics></math> increases from 0.5 to 0.6, the delivery rate decreases while the overhead ratio increases. However, as <math display='inline'><semantics> <msub> <mi>W</mi> <mn>0</mn> </msub> </semantics></math> increases from 0.6 to 0.8, the delivery rate and the overhead ratio remain the same.</div><div class='html-p'><a href="#futureinternet-14-00214-f005" class="html-fig">Figure 5</a> and <a href="#futureinternet-14-00214-f006" class="html-fig">Figure 6</a> depict the influence of <math display='inline'><semantics> <mi>α</mi> </semantics></math> and <math display='inline'><semantics> <mi>ϵ</mi> </semantics></math> on the performance of the MPMF under TVCM and NCCU. Given the buffer size of 10 MB on each node and message TTL 5 h, <a href="#futureinternet-14-00214-f005" class="html-fig">Figure 5</a> exhibits that the delivery rate decreases and the overhead ratio increases as <math display='inline'><semantics> <mi>ϵ</mi> </semantics></math> increases from 50 to 70. However, the variation of <math display='inline'><semantics> <mi>α</mi> </semantics></math> does not affect the results of either delivery rate or overhead ratio. In <a href="#futureinternet-14-00214-f006" class="html-fig">Figure 6</a>, as <math display='inline'><semantics> <mi>α</mi> </semantics></math> increases from 0.6 to 0.9, the delivery rate decreases while the overhead ratio increases.</div><div class='html-p'><a href="#futureinternet-14-00214-f007" class="html-fig">Figure 7</a> and <a href="#futureinternet-14-00214-f008" class="html-fig">Figure 8</a> display the influence of <span class='html-italic'>L</span> with respect to the variance of the TTL values in the range of [2, 6] h under TVCM and NCCU. Given the buffer size of 10 MB on each node, the results in <a href="#futureinternet-14-00214-f007" class="html-fig">Figure 7</a> exhibit that both the delivery rate and overhead ratio increase as <span class='html-italic'>L</span> increases from 5 to 15 regardless of the TTL values. The overhead ratio increases as <span class='html-italic'>L</span> increases from 5 to 15 in <a href="#futureinternet-14-00214-f008" class="html-fig">Figure 8</a>, whereas the delivery rate increases as <span class='html-italic'>L</span> increases from 5 to 10. However, for <math display='inline'><semantics> <mrow> <mi>L</mi> <mo>=</mo> </mrow> </semantics></math> 15, the delivery rate decreases for the TTL from 3 to 6. A buffer overflow possibly occurs more times with the limited buffer and higher node population in NCCU. It is noted that the overhead ratio is more sensitive to the incremental TTL values. This is because with a larger <span class='html-italic'>L</span> value, more pending messages in the finite buffer capacity could be replaced frequently, thereby causing higher transmission overhead, as shown in <a href="#futureinternet-14-00214-f007" class="html-fig">Figure 7</a>b and <a href="#futureinternet-14-00214-f008" class="html-fig">Figure 8</a>b.</div><div class='html-p'>In summary, the above findings point out that the relay node selected by the MPMF with a smaller <math display='inline'><semantics> <mi>ϵ</mi> </semantics></math> and <math display='inline'><semantics> <msub> <mi>W</mi> <mn>0</mn> </msub> </semantics></math> can facilitate the message distribution at the higher delivery rate and lower overhead ratio, as displayed in <a href="#futureinternet-14-00214-f003" class="html-fig">Figure 3</a>, <a href="#futureinternet-14-00214-f004" class="html-fig">Figure 4</a>, <a href="#futureinternet-14-00214-f005" class="html-fig">Figure 5</a> and <a href="#futureinternet-14-00214-f006" class="html-fig">Figure 6</a>. Therefore, in order to strike a better performance, it is beneficial to take <math display='inline'><semantics> <mrow> <mi>ϵ</mi> <mo>=</mo> </mrow> </semantics></math> 50, <math display='inline'><semantics> <mrow> <msub> <mi>W</mi> <mn>0</mn> </msub> <mo>=</mo> </mrow> </semantics></math> 0.6, and <math display='inline'><semantics> <mrow> <mi>α</mi> <mo>=</mo> </mrow> </semantics></math> 0.5 in TVCM and <math display='inline'><semantics> <mrow> <mi>ϵ</mi> <mo>=</mo> </mrow> </semantics></math> 60, <math display='inline'><semantics> <mrow> <msub> <mi>W</mi> <mn>0</mn> </msub> <mo>=</mo> </mrow> </semantics></math> 0.5, and <math display='inline'><semantics> <mrow> <mi>α</mi> <mo>=</mo> </mrow> </semantics></math>0.6 in NCCU. With the performance results against the quantity of <span class='html-italic'>L</span>, as shown in <a href="#futureinternet-14-00214-f007" class="html-fig">Figure 7</a> and <a href="#futureinternet-14-00214-f008" class="html-fig">Figure 8</a>, it is unnecessary to maximize the <span class='html-italic'>L</span> value, but a moderate value is applicable to sustain the transmission overhead ratio while the delivery rate is maintained. Thus, <math display='inline'><semantics> <mrow> <mi>L</mi> <mo>=</mo> </mrow> </semantics></math> 10 will be used in the following experimental cases.</div></section><section id='sec6dot3-futureinternet-14-00214' type='results'><h4 class='html-italic' data-nested='2'> 6.3. Results by Epidemic, GSaR, TCCB, TC, and PRoPHETv2</h4><div class='html-p'>This section presents the relative performance of the MPMF in comparison with the Epidemic, PRoPHETv2, GSaR, TC, and TCCB routing policies. As <a href="#futureinternet-14-00214-f009" class="html-fig">Figure 9</a>, <a href="#futureinternet-14-00214-f010" class="html-fig">Figure 10</a> and <a href="#futureinternet-14-00214-f011" class="html-fig">Figure 11</a> depict, the performance results are examined in a linear yardstick of TTL = [1, 2, …, 10] h under TVCM and NCCU. In <a href="#sec6dot3dot1-futureinternet-14-00214" class="html-sec">Section 6.3.1</a>, we first consider the node population N = 50 in TVCM and N = 116 in NCCU, and in <a href="#sec6dot3dot2-futureinternet-14-00214" class="html-sec">Section 6.3.2</a>, we consider N = 100 and 150 in the TVCM case. Note that because NCCU is a real-life trace collected on a university campus, the node population is fixed. In <a href="#sec6dot3dot3-futureinternet-14-00214" class="html-sec">Section 6.3.3</a>, we evaluate other performance metrics, including the average time a message takes in a buffer and the amount of messages dropped, relayed, and aborted when TTL = [1, 3, 5, 7, 10] h.</div><section id='sec6dot3dot1-futureinternet-14-00214' type=''><h4 class='' data-nested='3'> 6.3.1. Case (a)</h4><div class='html-p'><a href="#futureinternet-14-00214-f009" class="html-fig">Figure 9</a> depicts that all the policies can increase the successful delivery rate with a longer TTL period. Epidemic and TCCB unboundedly replicate messages to the encountered nodes, thereby inducing more message traffic. When the TTL > 8 h in Epidemic and GSaR and the TTL > 9 h in the TCCB, the delivery rate decreases, as shown in <a href="#futureinternet-14-00214-f009" class="html-fig">Figure 9</a>a. However, in the MPMF, it continues to increase when the TTL > 8 h. In <a href="#futureinternet-14-00214-f009" class="html-fig">Figure 9</a>b, when the TTL > 3 h, the MPMF has a lower overhead ratio compared with the other policies. In <a href="#futureinternet-14-00214-f009" class="html-fig">Figure 9</a>c, Epidemic outperforms the other policies regarding average latency. However, as depicted in <a href="#futureinternet-14-00214-f009" class="html-fig">Figure 9</a>d, it has a higher average hop count (hops) in comparison with the other polices. Relatively, TC attains the lowest delivery rate when compared with all the other policies.</div><div class='html-p'>Both the MPMF and GSaR consider the location information and spray a limited number of copies of a message in the network, while PRoPHETv2 considers the DP estimates of directly encountered nodes with the destination and generates more messages than the MPMF and GSaR. Epidemic performs in a flooding-like message replication, and with a sufficient buffer and lower TTL, it can have a high delivery rate but induce more overhead. Likewise, the TCCB considers temporal closeness with the destination or higher centrality in the network to take a forwarding decision. It cannot avoid repeatedly replicating messages to other nodes in closer social relationships, resulting in a considerable overhead ratio. In TC, a message is forwarded when a message-carrying node and an encountered node belong to the same group/community, or if the encountered node has better data forwarding capabilities.</div><div class='html-p'>With a longer TTL period, the MPMF will hold messages longer on nodes and induce a limited amount of message replicating and relaying operations. Thus, a buffer overflow can be mitigated so that messages can reach their destinations at higher chances. Although both GSaR and MPMF replicate a message with a limited number of copies to nodes moving closer to the destination, GSaR fails to achieve a sound performance. In GSaR, when a message-carrying node encounters a relay closer to a destination and can deliver a message earlier, it replicates the message to this relay and deletes that message from its buffer. The policy of deleting messages possibly degrades the performance of message delivery. With only one copy left for a message, GSaR will still replicate the message. Those buffer replacement operations possibly cause other messages to be removed and induce more overhead in the network. While TCCB uses temporal closeness and centrality to avoid blind replication, its overhead ratio becomes lower than Epidemic. Epidemic policy replicating a message multiple times increases the possibility that one of the message copies is successfully delivered within the shortest time. At the same time, creating more copies increases the average hop count. This observation is apparent from <a href="#futureinternet-14-00214-f009" class="html-fig">Figure 9</a>c,d, where Epidemic has a lower latency when the TTL = 5 → 9 h and a higher value of hops for TTL = 1 → 10 h. For the MPMF, a limited number of copies are replicated for each message, which results in lower hop counts than Epidemic and PRoPHETv2. Conversely, messages with a longer TTL remain in the buffer for a longer time, resulting in higher latency. In TC, when a message-carrying node has not encountered other nodes with higher relaying capabilities in some time period, it removes the message from its buffer. By this way, fewer copies of the message are relayed in the network, resulting in lower delivery rate and overhead ratio.</div><div class='html-p'><a href="#futureinternet-14-00214-f010" class="html-fig">Figure 10</a> depicts the comparative results under the NCCU trace. As the results in <a href="#futureinternet-14-00214-f010" class="html-fig">Figure 10</a>a indicate, Epidemic, TCCB, TC, and PRoPHETv2 perform better. However, as depicted in <a href="#futureinternet-14-00214-f010" class="html-fig">Figure 10</a>b, the overhead ratio is higher and drastically increases as TTL > 8 h. GSaR induces more overhead ratio and a lower delivery rate when the TTL increases from 1 to 8. As depicted in <a href="#futureinternet-14-00214-f010" class="html-fig">Figure 10</a>c,d, both latency and hops in GSaR are higher as compared with other policies. In the case of NCCU with a higher node density, nodes have higher chances of contacting other nodes. A message replicated more times can induce higher hops. In GSaR, the policy of deleting a message probably decreases the chances of reaching the message earlier to the destination and thus causes higher latency.</div><div class='html-p'>Because Epidemic, TCCB, TC, and PRoPHETv2 do not use control-based replication, their replication policies in the NCCU trace generate many message copies for long-TTL messages, which results in a higher overhead ratio. <a href="#futureinternet-14-00214-f010" class="html-fig">Figure 10</a>c depicts that PRoPHETv2, TC, and TCCB have lower latency because of many messages created in both the policies. With a higher node population in NCCU, more communities are formed in TC. As a result, the amount of message forwarding increases, resulting in a higher overhead ratio and delivery rate. There is an interesting case as TTL > 8 h in <a href="#futureinternet-14-00214-f010" class="html-fig">Figure 10</a>b. Both PRoPHETv2 and TCCB have huge overhead. This is possibly due to buffer replacement operations frequently occurring by comparing Epidemic with PRoPHETv2 and TCCB. Older messages in Epidemic are replaced frequently, and the number of replicas created for such messages is less than those in the PRoPHETv2 and TCCB cases. In PRoPHETv2 and TCCB, messages with a higher TTL have higher chances of remaining in the buffer, and with a higher node population, older message are replicated more times. Although the node population is higher in NCCU, the MPMF creates fixed replicas for each message. As depicted in <a href="#futureinternet-14-00214-f010" class="html-fig">Figure 10</a>, the delivery rate in the case of MPMF is similar for long-TTL messages as compared with other policies. In addition, the MPMF induces a minimal overhead ratio as in <a href="#futureinternet-14-00214-f010" class="html-fig">Figure 10</a>b.</div></section><section id='sec6dot3dot2-futureinternet-14-00214' type=''><h4 class='' data-nested='3'> 6.3.2. Case (b)</h4><div class='html-p'>To examine the performance against the node population, we vary the number of nodes from 100 to 150 and use <math display='inline'><semantics> <mrow> <mi>L</mi> <mo>=</mo> <mn>20</mn> </mrow> </semantics></math> in the simulation. The rest of the settings are same as those used in <a href="#sec6dot3dot1-futureinternet-14-00214" class="html-sec">Section 6.3.1</a>.</div><div class='html-p'>As shown in <a href="#futureinternet-14-00214-f011" class="html-fig">Figure 11</a>, all policies can increase the successful delivery rate with a longer TTL, where the number of nodes is set to be N = 100 in <a href="#futureinternet-14-00214-f011" class="html-fig">Figure 11</a>a,b, and N = 150 in <a href="#futureinternet-14-00214-f011" class="html-fig">Figure 11</a>c,d. Epidemic and GSaR unbound replicate messages, thereby inducing more message overhead. Similar to <a href="#futureinternet-14-00214-f009" class="html-fig">Figure 9</a>a, <a href="#futureinternet-14-00214-f010" class="html-fig">Figure 10</a>a and <a href="#futureinternet-14-00214-f011" class="html-fig">Figure 11</a>a,c depict the decrease in delivery rate when the TTL > 8 h in Epidemic and TCCB. Compared with <a href="#futureinternet-14-00214-f009" class="html-fig">Figure 9</a> and <a href="#futureinternet-14-00214-f011" class="html-fig">Figure 11</a>b,d, an increase in the overhead ratio is displayed. In the MPMF, the increase in overhead is lower with a larger TTL than the other policies. Although increasing the node population can increase the encounter rate, the delivery rate is not affected in the case of MPMF. In the MPMF, the number of message copies for each message is fixed; then, nodes with a copy of the message keep waiting for the destination without forwarding. This makes messages kept in the buffer longer. Because of the TTL timeout or buffer overflow, messages are unable to reach the destination node. Notice that in the case of NCCU, nodes are scattered in a large space, while nodes move in the same confined area in TVCM. Therefore, in the case of GSaR, messages have higher chances of reaching a destination. With the increase in contact frequency in the case of a larger node population, the numbers of forwarded messages in GSaR and PRoPHETv2 increase, thus resulting in a higher delivery rate and overhead ratio. In TC, with the increase in node population, the number of formed communities becomes larger. Therefore, a node can belong to several communities and help deliver messages to a target node, resulting in a higher delivery rate, as shown in <a href="#futureinternet-14-00214-f011" class="html-fig">Figure 11</a>a,c.</div><div class='html-p'>From the above results, we can explain that the MPMF policy is suitable for delivering messages with longer TTLs when the node population is small. However, given a larger node population, the policy can still result in lower overhead while maintaining a comparable delivery rate.</div></section><section id='sec6dot3dot3-futureinternet-14-00214' type=''><h4 class='' data-nested='3'> 6.3.3. Case (c)</h4><div class='html-p'>Let <math display='inline'><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>d</mi> <mi>r</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics></math> be the total amount of messages dropped by nodes due to buffer overflows and TTL expirations, <math display='inline'><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>a</mi> <mi>b</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics></math> be the total amount of messages aborted in the network, and <math display='inline'><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>b</mi> <mi>t</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics></math> be the average time duration that messages take in buffers. The higher the value of <math display='inline'><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mi>f</mi> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics></math> and <math display='inline'><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>d</mi> <mi>r</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics></math>, the more buffer space and resources are used to forward messages toward target nodes. Therefore, higher values of <math display='inline'><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mi>f</mi> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics></math> and <math display='inline'><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>d</mi> <mi>r</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics></math> can be considered additional overhead in a network. <a href="#futureinternet-14-00214-t002" class="html-table">Table 2</a> presents the performance comparison between the Epidemic, PRoPHETv2, TCCB, GSaR, MPMF, and TC policies in terms of <math display='inline'><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mi>f</mi> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics></math>, <math display='inline'><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>d</mi> <mi>r</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics></math>, <math display='inline'><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>a</mi> <mi>b</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics></math>, and <math display='inline'><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>b</mi> <mi>t</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics></math>. Note that the <math display='inline'><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>b</mi> <mi>t</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics></math> denotes the average time duration in seconds. As <a href="#futureinternet-14-00214-t002" class="html-table">Table 2</a> shows, a longer TTL results in higher values in all metrics for all policies. It is apparent that the MPMF results in lower <math display='inline'><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mi>f</mi> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics></math> and <math display='inline'><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>d</mi> <mi>r</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics></math> regardless of the TTL as compared with other policies. With the increase in the TTL and node population in TVCM, Epidemic, PRoPHETv2, TC, and GSaR result in higher values of <math display='inline'><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mi>f</mi> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics></math> and <math display='inline'><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>d</mi> <mi>r</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics></math>. In NCCU, all the policies result in higher values of <math display='inline'><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mi>f</mi> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics></math> and <math display='inline'><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>d</mi> <mi>r</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics></math> for longer TTL values. Messages in the MPMF are relayed at a limited number of times. Messages will likely remain in buffers for a longer time; thus, buffer overflow occurs infrequently. Thus, <math display='inline'><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>b</mi> <mi>t</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics></math> is higher in the MPMF as compared with the other policies.</div><div class='html-p'>According to the results in <a href="#futureinternet-14-00214-t002" class="html-table">Table 2</a>, it is clear that the MPMF policy can result in lower additional overhead in comparison with all other policies.</div></section></section></section><section id='sec7-futureinternet-14-00214' type=''><h2 data-nested='1'> 7. Concluding Remarks and Future Work</h2><div class='html-p'>In this paper, we propose the MPMF routing policy which can perform efficiently and cost-effectively for message forwarding in OppNets. The MPMF policy is based on control-based replication that distributes only a limited number of copies of a message in the network. The MPMF policy selects the profitable relay node according to the nodes’ moving direction and two-hop neighborhood information. Relays moving closer to a destination node and having higher weight values are selected to carry messages in the network. When relays in the vicinity of a message-carrying node are not qualified due to sparse node density and nodal motion status, the moving direction of the destination node, the location information of a one-hop node, and a centrality value of a node are jointly utilized to improve the message delivery service. The use of joint utilization design can avoid messages being kept longer in a buffer in the absence of better candidate nodes. In comparison with Epidemic, TCCB, GSaR, TC, and PRoPHETv2, the MPMF policy is feasible for distributing long-TTL messages in OppNets, resulting in a low messaging overhead ratio and high message delivery rate. Our future study will focus on developing enhanced methods for relay node selection and will adopt additional application scenarios such as unmanned aerial vehicles into OppNets.</div></section> </div> <div class="html-back"> <section class='html-notes'><h2 >Author Contributions</h2><div class='html-p'>The work described in this article is a collaborative effort from all of the authors. Conceptualization: M.-Y.M., H.Z. and C.-L.H.; methodology: M.-Y.M., H.Z. and C.-L.H.; design, implementation, and generation of results: M.-Y.M. and H.Z.; analysis and interpretation of results: M.-Y.M. and C.-L.H.; preparing the draft, review, and editing: M.-Y.M. and C.-L.H.; visualization: M.-Y.M. and C.-L.H. All authors have read and agreed to the published version of the manuscript.</div></section><section class='html-notes'><h2>Funding</h2><div class='html-p'>This work was supported in part by the Ministry of Science and Technology, Taiwan, under Contract MOST-108-2221-E-008-021 and Contract MOST-109-2221-E-008-051.</div></section><section class='html-notes'><h2 >Institutional Review Board Statement</h2><div class='html-p'>Not applicable.</div></section><section class='html-notes'><h2 >Informed Consent Statement</h2><div class='html-p'>Not applicable.</div></section><section class='html-notes'><h2 >Data Availability Statement</h2><div class='html-p'>The data that support the findings of this study are available from the corresponding author upon reasonable request.</div></section><section id='html-ack' class='html-ack'><h2 >Acknowledgments</h2><div class='html-p'>We thank the anonymous reviewers for carefully reading our manuscript and for many insightful comments and suggestions.</div></section><section class='html-notes'><h2 >Conflicts of Interest</h2><div class='html-p'>The authors declare no conflict of interest.</div></section><section id='html-glossary'><h2 >Abbreviations</h2><div class='html-p'>The following abbreviations are used in this manuscript: <table class='html-array_table'><tbody ><tr ><td align='left' valign='middle' class='html-align-left' >MPMF</td><td align='left' valign='middle' class='html-align-left' >Message-forwarding policy based on movement patterns</td></tr><tr ><td align='left' valign='middle' class='html-align-left' >TCCB</td><td align='left' valign='middle' class='html-align-left' >Temporal closeness and centrality-based</td></tr><tr ><td align='left' valign='middle' class='html-align-left' >TC</td><td align='left' valign='middle' class='html-align-left' >Transient community-based</td></tr><tr ><td align='left' valign='middle' class='html-align-left' >GSaR</td><td align='left' valign='middle' class='html-align-left' >Geographic-based spray-and-relay</td></tr><tr ><td align='left' valign='middle' class='html-align-left' >OppNets</td><td align='left' valign='middle' class='html-align-left' >Opportunistic ad hoc networks</td></tr><tr ><td align='left' valign='middle' class='html-align-left' >NCCU</td><td align='left' valign='middle' class='html-align-left' >National Chengchi University trace</td></tr><tr ><td align='left' valign='middle' class='html-align-left' >TVCM</td><td align='left' valign='middle' class='html-align-left' >Time-variant community mobility model</td></tr><tr ><td align='left' valign='middle' class='html-align-left' >ONE</td><td align='left' valign='middle' class='html-align-left' >Opportunistic networking environment</td></tr><tr ><td align='left' valign='middle' class='html-align-left' >DP</td><td align='left' valign='middle' class='html-align-left' >Delivery probability</td></tr><tr ><td align='left' valign='middle' class='html-align-left' >TTL</td><td align='left' valign='middle' class='html-align-left' >Time-to-live</td></tr></tbody></table></div></section><section id='html-references_list'><h2>References</h2><ol class='html-xx'><li id='B1-futureinternet-14-00214' class='html-x' data-content='1.'>Trifunovic, S.; Kouyoumdjieva, S.T.; Distl, B.; Pajevic, L.; Karlsson, G.; Plattner, B. 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Available online: <a href='https://github.com/NCCU-MCLAB/NCCU-Trace-Data' target='_blank' rel="noopener noreferrer" >https://github.com/NCCU-MCLAB/NCCU-Trace-Data</a> (accessed on 1 March 2022).</li></ol></section><section id='FiguresandTables' type='display-objects'><div class="html-fig-wrap" id="futureinternet-14-00214-f001"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/1999-5903/14/7/214/display" href="#fig_body_display_futureinternet-14-00214-f001"> <img alt="Futureinternet 14 00214 g001 550" data-large="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g001.png" data-original="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g001.png" data-lsrc="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g001-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/1999-5903/14/7/214/display" href="#fig_body_display_futureinternet-14-00214-f001"></a> </div> </div> <div class="html-fig_description"> <b>Figure 1.</b> (<b>a</b>) Front-side scanning with respect to a destination node, and (<b>b</b>) geometric angle formation at one- and two-hop distance.  </div> </div> <div class="html-fig_show mfp-hide" id ="fig_body_display_futureinternet-14-00214-f001" > <div class="html-caption" > <b>Figure 1.</b> (<b>a</b>) Front-side scanning with respect to a destination node, and (<b>b</b>) geometric angle formation at one- and two-hop distance.</div> <div class="html-img"><img alt="Futureinternet 14 00214 g001" data-large="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g001.png" data-original="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g001.png" data-lsrc="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g001.png" /></div> </div><div class="html-fig-wrap" id="futureinternet-14-00214-f002"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/1999-5903/14/7/214/display" href="#fig_body_display_futureinternet-14-00214-f002"> <img alt="Futureinternet 14 00214 g002 550" data-large="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g002.png" data-original="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g002.png" data-lsrc="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g002-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/1999-5903/14/7/214/display" href="#fig_body_display_futureinternet-14-00214-f002"></a> </div> </div> <div class="html-fig_description"> <b>Figure 2.</b> Two-hop based routing between <span class='html-italic'>s</span>, <math display='inline'><semantics> <msub> <mi>n</mi> <mi>i</mi> </msub> </semantics></math>, and <math display='inline'><semantics> <msub> <mi>n</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </semantics></math>.  </div> </div> <div class="html-fig_show mfp-hide" id ="fig_body_display_futureinternet-14-00214-f002" > <div class="html-caption" > <b>Figure 2.</b> Two-hop based routing between <span class='html-italic'>s</span>, <math display='inline'><semantics> <msub> <mi>n</mi> <mi>i</mi> </msub> </semantics></math>, and <math display='inline'><semantics> <msub> <mi>n</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </semantics></math>.</div> <div class="html-img"><img alt="Futureinternet 14 00214 g002" data-large="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g002.png" data-original="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g002.png" data-lsrc="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g002.png" /></div> </div><div class="html-fig-wrap" id="futureinternet-14-00214-f003"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/1999-5903/14/7/214/display" href="#fig_body_display_futureinternet-14-00214-f003"> <img alt="Futureinternet 14 00214 g003 550" data-large="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g003.png" data-original="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g003.png" data-lsrc="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g003-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/1999-5903/14/7/214/display" href="#fig_body_display_futureinternet-14-00214-f003"></a> </div> </div> <div class="html-fig_description"> <b>Figure 3.</b> Results by MPMF with different values of <math display='inline'><semantics> <mi>ϵ</mi> </semantics></math> and <math display='inline'><semantics> <msub> <mi>W</mi> <mn>0</mn> </msub> </semantics></math> under TVCM trace (TTL = 5 h and buffer size = 10 MB).  </div> </div> <div class="html-fig_show mfp-hide" id ="fig_body_display_futureinternet-14-00214-f003" > <div class="html-caption" > <b>Figure 3.</b> Results by MPMF with different values of <math display='inline'><semantics> <mi>ϵ</mi> </semantics></math> and <math display='inline'><semantics> <msub> <mi>W</mi> <mn>0</mn> </msub> </semantics></math> under TVCM trace (TTL = 5 h and buffer size = 10 MB).</div> <div class="html-img"><img alt="Futureinternet 14 00214 g003" data-large="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g003.png" data-original="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g003.png" data-lsrc="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g003.png" /></div> </div><div class="html-fig-wrap" id="futureinternet-14-00214-f004"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/1999-5903/14/7/214/display" href="#fig_body_display_futureinternet-14-00214-f004"> <img alt="Futureinternet 14 00214 g004 550" data-large="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g004.png" data-original="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g004.png" data-lsrc="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g004-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/1999-5903/14/7/214/display" href="#fig_body_display_futureinternet-14-00214-f004"></a> </div> </div> <div class="html-fig_description"> <b>Figure 4.</b> Results by MPMF with different values of <math display='inline'><semantics> <mi>ϵ</mi> </semantics></math> and <math display='inline'><semantics> <msub> <mi>W</mi> <mn>0</mn> </msub> </semantics></math> under NCCU trace (TTL = 5 h and buffer size = 10 MB).  </div> </div> <div class="html-fig_show mfp-hide" id ="fig_body_display_futureinternet-14-00214-f004" > <div class="html-caption" > <b>Figure 4.</b> Results by MPMF with different values of <math display='inline'><semantics> <mi>ϵ</mi> </semantics></math> and <math display='inline'><semantics> <msub> <mi>W</mi> <mn>0</mn> </msub> </semantics></math> under NCCU trace (TTL = 5 h and buffer size = 10 MB).</div> <div class="html-img"><img alt="Futureinternet 14 00214 g004" data-large="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g004.png" data-original="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g004.png" data-lsrc="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g004.png" /></div> </div><div class="html-fig-wrap" id="futureinternet-14-00214-f005"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/1999-5903/14/7/214/display" href="#fig_body_display_futureinternet-14-00214-f005"> <img alt="Futureinternet 14 00214 g005 550" data-large="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g005.png" data-original="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g005.png" data-lsrc="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g005-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/1999-5903/14/7/214/display" href="#fig_body_display_futureinternet-14-00214-f005"></a> </div> </div> <div class="html-fig_description"> <b>Figure 5.</b> Results by MPMF with different values of <math display='inline'><semantics> <mi>α</mi> </semantics></math> and <math display='inline'><semantics> <mi>ϵ</mi> </semantics></math> under TVCM trace (TTL = 5 h and buffer size = 10 MB).  </div> </div> <div class="html-fig_show mfp-hide" id ="fig_body_display_futureinternet-14-00214-f005" > <div class="html-caption" > <b>Figure 5.</b> Results by MPMF with different values of <math display='inline'><semantics> <mi>α</mi> </semantics></math> and <math display='inline'><semantics> <mi>ϵ</mi> </semantics></math> under TVCM trace (TTL = 5 h and buffer size = 10 MB).</div> <div class="html-img"><img alt="Futureinternet 14 00214 g005" data-large="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g005.png" data-original="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g005.png" data-lsrc="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g005.png" /></div> </div><div class="html-fig-wrap" id="futureinternet-14-00214-f006"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/1999-5903/14/7/214/display" href="#fig_body_display_futureinternet-14-00214-f006"> <img alt="Futureinternet 14 00214 g006 550" data-large="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g006.png" data-original="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g006.png" data-lsrc="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g006-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/1999-5903/14/7/214/display" href="#fig_body_display_futureinternet-14-00214-f006"></a> </div> </div> <div class="html-fig_description"> <b>Figure 6.</b> Results by MPMF with different values of <math display='inline'><semantics> <mi>α</mi> </semantics></math> and <math display='inline'><semantics> <mi>ϵ</mi> </semantics></math> under NCCU trace (TTL = 5 h and buffer size = 10 MB).  </div> </div> <div class="html-fig_show mfp-hide" id ="fig_body_display_futureinternet-14-00214-f006" > <div class="html-caption" > <b>Figure 6.</b> Results by MPMF with different values of <math display='inline'><semantics> <mi>α</mi> </semantics></math> and <math display='inline'><semantics> <mi>ϵ</mi> </semantics></math> under NCCU trace (TTL = 5 h and buffer size = 10 MB).</div> <div class="html-img"><img alt="Futureinternet 14 00214 g006" data-large="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g006.png" data-original="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g006.png" data-lsrc="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g006.png" /></div> </div><div class="html-fig-wrap" id="futureinternet-14-00214-f007"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/1999-5903/14/7/214/display" href="#fig_body_display_futureinternet-14-00214-f007"> <img alt="Futureinternet 14 00214 g007 550" data-large="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g007.png" data-original="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g007.png" data-lsrc="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g007-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/1999-5903/14/7/214/display" href="#fig_body_display_futureinternet-14-00214-f007"></a> </div> </div> <div class="html-fig_description"> <b>Figure 7.</b> Results by MPMF with different values of <span class='html-italic'>L</span> and TTL under TVCM trace (buffer size = 10 MB).  </div> </div> <div class="html-fig_show mfp-hide" id ="fig_body_display_futureinternet-14-00214-f007" > <div class="html-caption" > <b>Figure 7.</b> Results by MPMF with different values of <span class='html-italic'>L</span> and TTL under TVCM trace (buffer size = 10 MB).</div> <div class="html-img"><img alt="Futureinternet 14 00214 g007" data-large="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g007.png" data-original="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g007.png" data-lsrc="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g007.png" /></div> </div><div class="html-fig-wrap" id="futureinternet-14-00214-f008"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/1999-5903/14/7/214/display" href="#fig_body_display_futureinternet-14-00214-f008"> <img alt="Futureinternet 14 00214 g008 550" data-large="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g008.png" data-original="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g008.png" data-lsrc="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g008-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/1999-5903/14/7/214/display" href="#fig_body_display_futureinternet-14-00214-f008"></a> </div> </div> <div class="html-fig_description"> <b>Figure 8.</b> Results by MPMF with different values of <span class='html-italic'>L</span> and TTL under NCCU trace (buffer size = 10 MB).  </div> </div> <div class="html-fig_show mfp-hide" id ="fig_body_display_futureinternet-14-00214-f008" > <div class="html-caption" > <b>Figure 8.</b> Results by MPMF with different values of <span class='html-italic'>L</span> and TTL under NCCU trace (buffer size = 10 MB).</div> <div class="html-img"><img alt="Futureinternet 14 00214 g008" data-large="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g008.png" data-original="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g008.png" data-lsrc="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g008.png" /></div> </div><div class="html-fig-wrap" id="futureinternet-14-00214-f009"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/1999-5903/14/7/214/display" href="#fig_body_display_futureinternet-14-00214-f009"> <img alt="Futureinternet 14 00214 g009a 550" data-large="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g009a.png" data-original="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g009a.png" data-lsrc="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g009a-550.jpg" /><img alt="Futureinternet 14 00214 g009b 550" data-large="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g009b.png" data-original="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g009b.png" data-lsrc="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g009b-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/1999-5903/14/7/214/display" href="#fig_body_display_futureinternet-14-00214-f009"></a> </div> </div> <div class="html-fig_description"> <b>Figure 9.</b> Performance comparison of MPMF in TVCM trace (<math display='inline'><semantics> <msub> <mi>W</mi> <mn>0</mn> </msub> </semantics></math> = 0.6, <span class='html-italic'>L</span> = 10, <math display='inline'><semantics> <mi>ϵ</mi> </semantics></math> = 50, <math display='inline'><semantics> <mi>α</mi> </semantics></math> = 0.5, and buffer size = 10 MB).  </div> </div> <div class="html-fig_show mfp-hide" id ="fig_body_display_futureinternet-14-00214-f009" > <div class="html-caption" > <b>Figure 9.</b> Performance comparison of MPMF in TVCM trace (<math display='inline'><semantics> <msub> <mi>W</mi> <mn>0</mn> </msub> </semantics></math> = 0.6, <span class='html-italic'>L</span> = 10, <math display='inline'><semantics> <mi>ϵ</mi> </semantics></math> = 50, <math display='inline'><semantics> <mi>α</mi> </semantics></math> = 0.5, and buffer size = 10 MB).</div> <div class="html-img"><img alt="Futureinternet 14 00214 g009a" data-large="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g009a.png" data-original="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g009a.png" data-lsrc="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g009a.png" /><img alt="Futureinternet 14 00214 g009b" data-large="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g009b.png" data-original="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g009b.png" data-lsrc="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g009b.png" /></div> </div><div class="html-fig-wrap" id="futureinternet-14-00214-f010"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/1999-5903/14/7/214/display" href="#fig_body_display_futureinternet-14-00214-f010"> <img alt="Futureinternet 14 00214 g010 550" data-large="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g010.png" data-original="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g010.png" data-lsrc="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g010-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/1999-5903/14/7/214/display" href="#fig_body_display_futureinternet-14-00214-f010"></a> </div> </div> <div class="html-fig_description"> <b>Figure 10.</b> Performance comparison of MPMF in NCCU trace (<math display='inline'><semantics> <msub> <mi>W</mi> <mn>0</mn> </msub> </semantics></math> = 0.5, <span class='html-italic'>L</span> = 10, <math display='inline'><semantics> <mi>ϵ</mi> </semantics></math> = 60, <math display='inline'><semantics> <mi>α</mi> </semantics></math> = 0.6, and buffer size = 10 MB).  </div> </div> <div class="html-fig_show mfp-hide" id ="fig_body_display_futureinternet-14-00214-f010" > <div class="html-caption" > <b>Figure 10.</b> Performance comparison of MPMF in NCCU trace (<math display='inline'><semantics> <msub> <mi>W</mi> <mn>0</mn> </msub> </semantics></math> = 0.5, <span class='html-italic'>L</span> = 10, <math display='inline'><semantics> <mi>ϵ</mi> </semantics></math> = 60, <math display='inline'><semantics> <mi>α</mi> </semantics></math> = 0.6, and buffer size = 10 MB).</div> <div class="html-img"><img alt="Futureinternet 14 00214 g010" data-large="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g010.png" data-original="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g010.png" data-lsrc="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g010.png" /></div> </div><div class="html-fig-wrap" id="futureinternet-14-00214-f011"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/1999-5903/14/7/214/display" href="#fig_body_display_futureinternet-14-00214-f011"> <img alt="Futureinternet 14 00214 g011 550" data-large="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g011.png" data-original="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g011.png" data-lsrc="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g011-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/1999-5903/14/7/214/display" href="#fig_body_display_futureinternet-14-00214-f011"></a> </div> </div> <div class="html-fig_description"> <b>Figure 11.</b> Performance comparison of MPMF in TVCM trace (<math display='inline'><semantics> <msub> <mi>W</mi> <mn>0</mn> </msub> </semantics></math> = 0.5, <span class='html-italic'>L</span> = 20, <math display='inline'><semantics> <mi>ϵ</mi> </semantics></math> = 60, <math display='inline'><semantics> <mi>α</mi> </semantics></math> = 0.6, and buffer size = 10 MB).  </div> </div> <div class="html-fig_show mfp-hide" id ="fig_body_display_futureinternet-14-00214-f011" > <div class="html-caption" > <b>Figure 11.</b> Performance comparison of MPMF in TVCM trace (<math display='inline'><semantics> <msub> <mi>W</mi> <mn>0</mn> </msub> </semantics></math> = 0.5, <span class='html-italic'>L</span> = 20, <math display='inline'><semantics> <mi>ϵ</mi> </semantics></math> = 60, <math display='inline'><semantics> <mi>α</mi> </semantics></math> = 0.6, and buffer size = 10 MB).</div> <div class="html-img"><img alt="Futureinternet 14 00214 g011" data-large="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g011.png" data-original="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g011.png" data-lsrc="/futureinternet/futureinternet-14-00214/article_deploy/html/images/futureinternet-14-00214-g011.png" /></div> </div><div class="html-table-wrap" id="futureinternet-14-00214-t001"> <div class="html-table_wrap_td" > <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/1999-5903/14/7/214/display" href='#table_body_display_futureinternet-14-00214-t001'> <img alt="Table" data-lsrc="https://www.mdpi.com/img/table.png" /> <a class="html-expand html-tablepopup" data-counterslinkmanual = "https://www.mdpi.com/1999-5903/14/7/214/display" href="#table_body_display_futureinternet-14-00214-t001"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table 1.</b> Simulation Parameters. </div> </div> <div class="html-table_show mfp-hide " id ="table_body_display_futureinternet-14-00214-t001" > <div class="html-caption" ><b>Table 1.</b> Simulation Parameters.</div> <table > <thead ><tr ><th align='center' valign='middle' style='border-bottom:solid thin;border-top:solid thin' class='html-align-center' >Parameters</th><th align='center' valign='middle' style='border-bottom:solid thin;border-top:solid thin' class='html-align-center' >TVCM</th><th align='center' valign='middle' style='border-bottom:solid thin;border-top:solid thin' class='html-align-center' >NCCU</th></tr></thead><tbody ><tr ><td align='center' valign='middle' class='html-align-center' >Number of nodes</td><td align='center' valign='middle' class='html-align-center' >50</td><td align='center' valign='middle' class='html-align-center' >116</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >Map size</td><td align='center' valign='middle' class='html-align-center' >1500 × 1500 m<math display='inline'><semantics> <msup> <mrow/> <mn>2</mn> </msup> </semantics></math></td><td align='center' valign='middle' class='html-align-center' >3764 × 3420 m<math display='inline'><semantics> <msup> <mrow/> <mn>2</mn> </msup> </semantics></math></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >Simulation time</td><td align='center' valign='middle' class='html-align-center' >24 h</td><td align='center' valign='middle' class='html-align-center' >24 h</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >Time-to-live (TTL) duration</td><td align='center' valign='middle' class='html-align-center' >1 to 10 h</td><td align='center' valign='middle' class='html-align-center' >1 to 10 h</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >Message size</td><td align='center' valign='middle' class='html-align-center' >100 KB</td><td align='center' valign='middle' class='html-align-center' >100 KB</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >Buffer size</td><td align='center' valign='middle' class='html-align-center' >10 MB</td><td align='center' valign='middle' class='html-align-center' >10 MB</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >Message creation intervals</td><td align='center' valign='middle' class='html-align-center' >300 s</td><td align='center' valign='middle' class='html-align-center' >300 s</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >Transmission speed</td><td align='center' valign='middle' class='html-align-center' >2 MB/s</td><td align='center' valign='middle' class='html-align-center' >2 MB/s</td></tr><tr ><td align='center' valign='middle' class='html-align-center' ><math display='inline'><semantics> <msub> <mi>W</mi> <mn>0</mn> </msub> </semantics></math> in MPMF</td><td align='center' valign='middle' class='html-align-center' >0.6</td><td align='center' valign='middle' class='html-align-center' >0.5</td></tr><tr ><td align='center' valign='middle' class='html-align-center' ><math display='inline'><semantics> <mi>ϵ</mi> </semantics></math> in MPMF</td><td align='center' valign='middle' class='html-align-center' >50, 100, and 150</td><td align='center' valign='middle' class='html-align-center' >60</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><math display='inline'><semantics> <mi>α</mi> </semantics></math> in MPMF</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.5</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.6</td></tr></tbody> </table> </div><div class="html-table-wrap" id="futureinternet-14-00214-t002"> <div class="html-table_wrap_td" > <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/1999-5903/14/7/214/display" href='#table_body_display_futureinternet-14-00214-t002'> <img alt="Table" data-lsrc="https://www.mdpi.com/img/table.png" /> <a class="html-expand html-tablepopup" data-counterslinkmanual = "https://www.mdpi.com/1999-5903/14/7/214/display" href="#table_body_display_futureinternet-14-00214-t002"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table 2.</b> Performance comparison between Epidemic, PRoPHETv2, TCCB, GSaR, MPMF, and TC policies. </div> </div> <div class="html-table_show mfp-hide " id ="table_body_display_futureinternet-14-00214-t002" > <div class="html-caption" ><b>Table 2.</b> Performance comparison between Epidemic, PRoPHETv2, TCCB, GSaR, MPMF, and TC policies.</div> <table > <thead ><tr ><th align='center' valign='middle' style='border-bottom:solid thin;border-top:solid thin' class='html-align-center' >Model</th><th align='center' valign='middle' style='border-bottom:solid thin;border-top:solid thin' class='html-align-center' >Node <br> Population</th><th align='center' valign='middle' style='border-bottom:solid thin;border-top:solid thin' class='html-align-center' >TTL</th><th align='center' valign='middle' style='border-bottom:solid thin;border-top:solid thin' class='html-align-center' >Metric</th><th align='center' valign='middle' style='border-bottom:solid thin;border-top:solid thin' class='html-align-center' >Epidemic</th><th align='center' valign='middle' style='border-bottom:solid thin;border-top:solid thin' class='html-align-center' >PRoPHETv2</th><th align='center' valign='middle' style='border-bottom:solid thin;border-top:solid thin' class='html-align-center' >TCCB</th><th align='center' valign='middle' style='border-bottom:solid thin;border-top:solid thin' class='html-align-center' >GSaR</th><th align='center' valign='middle' style='border-bottom:solid thin;border-top:solid thin' class='html-align-center' >MPMF</th><th align='center' valign='middle' style='border-bottom:solid thin;border-top:solid thin' class='html-align-center' >TC</th></tr></thead><tbody ><tr ><td align='center' rowspan='60' valign='middle' style='border-bottom:solid thin' class='html-align-center' >TVCM</td><td align='center' rowspan='20' valign='middle' style='border-bottom:solid thin' class='html-align-center' >50</td><td align='center' rowspan='4' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1</td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mi>f</mi> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >1993</td><td align='center' valign='middle' class='html-align-center' >423</td><td align='center' valign='middle' class='html-align-center' >640</td><td align='center' valign='middle' class='html-align-center' >451</td><td align='center' valign='middle' class='html-align-center' >895</td><td align='center' valign='middle' class='html-align-center' >272</td></tr><tr ><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>d</mi> <mi>r</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >2143</td><td align='center' valign='middle' class='html-align-center' >680</td><td align='center' valign='middle' class='html-align-center' >850</td><td align='center' valign='middle' class='html-align-center' >621</td><td align='center' valign='middle' class='html-align-center' >1104</td><td align='center' valign='middle' class='html-align-center' >529</td></tr><tr ><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>b</mi> <mi>t</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >2104</td><td align='center' valign='middle' class='html-align-center' >2782</td><td align='center' valign='middle' class='html-align-center' >2488</td><td align='center' valign='middle' class='html-align-center' >2364</td><td align='center' valign='middle' class='html-align-center' >2578</td><td align='center' valign='middle' class='html-align-center' >2860</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>a</mi> <mi>b</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >123</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >29</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >36</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >35</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2</td></tr><tr ><td align='center' rowspan='4' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3</td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mi>f</mi> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >7445</td><td align='center' valign='middle' class='html-align-center' >1381</td><td align='center' valign='middle' class='html-align-center' >1938</td><td align='center' valign='middle' class='html-align-center' >1513</td><td align='center' valign='middle' class='html-align-center' >1690</td><td align='center' valign='middle' class='html-align-center' >720</td></tr><tr ><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>d</mi> <mi>r</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >6911</td><td align='center' valign='middle' class='html-align-center' >1531</td><td align='center' valign='middle' class='html-align-center' >2002</td><td align='center' valign='middle' class='html-align-center' >1030</td><td align='center' valign='middle' class='html-align-center' >1714</td><td align='center' valign='middle' class='html-align-center' >910</td></tr><tr ><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>b</mi> <mi>t</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >5208</td><td align='center' valign='middle' class='html-align-center' >6089</td><td align='center' valign='middle' class='html-align-center' >5965</td><td align='center' valign='middle' class='html-align-center' >4676</td><td align='center' valign='middle' class='html-align-center' >7397</td><td align='center' valign='middle' class='html-align-center' >6877</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>a</mi> <mi>b</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >215</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >15</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >36</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >58</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >42</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2</td></tr><tr ><td align='center' rowspan='4' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5</td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mi>f</mi> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >9564</td><td align='center' valign='middle' class='html-align-center' >2533</td><td align='center' valign='middle' class='html-align-center' >3516</td><td align='center' valign='middle' class='html-align-center' >2453</td><td align='center' valign='middle' class='html-align-center' >1950</td><td align='center' valign='middle' class='html-align-center' >1254</td></tr><tr ><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>d</mi> <mi>r</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >7860</td><td align='center' valign='middle' class='html-align-center' >2572</td><td align='center' valign='middle' class='html-align-center' >3181</td><td align='center' valign='middle' class='html-align-center' >1047</td><td align='center' valign='middle' class='html-align-center' >1764</td><td align='center' valign='middle' class='html-align-center' >1367</td></tr><tr ><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>b</mi> <mi>t</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >10,084</td><td align='center' valign='middle' class='html-align-center' >8912</td><td align='center' valign='middle' class='html-align-center' >8622</td><td align='center' valign='middle' class='html-align-center' >5566</td><td align='center' valign='middle' class='html-align-center' >12,998</td><td align='center' valign='middle' class='html-align-center' >10,067</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>a</mi> <mi>b</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >229</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >35</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >67</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >129</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >43</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2</td></tr><tr ><td align='center' rowspan='4' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7</td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mi>f</mi> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >10,724</td><td align='center' valign='middle' class='html-align-center' >3869</td><td align='center' valign='middle' class='html-align-center' >5190</td><td align='center' valign='middle' class='html-align-center' >3211</td><td align='center' valign='middle' class='html-align-center' >2225</td><td align='center' valign='middle' class='html-align-center' >2118</td></tr><tr ><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>d</mi> <mi>r</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >7820</td><td align='center' valign='middle' class='html-align-center' >3763</td><td align='center' valign='middle' class='html-align-center' >5896</td><td align='center' valign='middle' class='html-align-center' >967</td><td align='center' valign='middle' class='html-align-center' >1782</td><td align='center' valign='middle' class='html-align-center' >1991</td></tr><tr ><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>b</mi> <mi>t</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >14,889</td><td align='center' valign='middle' class='html-align-center' >11,650</td><td align='center' valign='middle' class='html-align-center' >10,952</td><td align='center' valign='middle' class='html-align-center' >5983</td><td align='center' valign='middle' class='html-align-center' >17,906</td><td align='center' valign='middle' class='html-align-center' >2</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>a</mi> <mi>b</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >232</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >49</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >83</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >155</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >46</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11,514</td></tr><tr ><td align='center' rowspan='4' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10</td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mi>f</mi> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >18,816</td><td align='center' valign='middle' class='html-align-center' >6425</td><td align='center' valign='middle' class='html-align-center' >9762</td><td align='center' valign='middle' class='html-align-center' >4705</td><td align='center' valign='middle' class='html-align-center' >2382</td><td align='center' valign='middle' class='html-align-center' >3991</td></tr><tr ><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>d</mi> <mi>r</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >14,838</td><td align='center' valign='middle' class='html-align-center' >5718</td><td align='center' valign='middle' class='html-align-center' >7456</td><td align='center' valign='middle' class='html-align-center' >1244</td><td align='center' valign='middle' class='html-align-center' >1584</td><td align='center' valign='middle' class='html-align-center' >3495</td></tr><tr ><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>b</mi> <mi>t</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >9732</td><td align='center' valign='middle' class='html-align-center' >12,538</td><td align='center' valign='middle' class='html-align-center' >8889</td><td align='center' valign='middle' class='html-align-center' >4674</td><td align='center' valign='middle' class='html-align-center' >24,896</td><td align='center' valign='middle' class='html-align-center' >11,586</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>a</mi> <mi>b</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >245</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >71</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >98</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >103</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >47</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2</td></tr><tr ><td align='center' rowspan='20' valign='middle' style='border-bottom:solid thin' class='html-align-center' >100</td><td align='center' rowspan='4' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1</td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mi>f</mi> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >12,748</td><td align='center' valign='middle' class='html-align-center' >3247</td><td align='center' valign='middle' class='html-align-center' >527</td><td align='center' valign='middle' class='html-align-center' >10,696</td><td align='center' valign='middle' class='html-align-center' >1493</td><td align='center' valign='middle' class='html-align-center' >1245</td></tr><tr ><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>d</mi> <mi>r</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >12,208</td><td align='center' valign='middle' class='html-align-center' >3253</td><td align='center' valign='middle' class='html-align-center' >783</td><td align='center' valign='middle' class='html-align-center' >3062</td><td align='center' valign='middle' class='html-align-center' >1677</td><td align='center' valign='middle' class='html-align-center' >1487</td></tr><tr ><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>b</mi> <mi>t</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >1973</td><td align='center' valign='middle' class='html-align-center' >2072</td><td align='center' valign='middle' class='html-align-center' >2225</td><td align='center' valign='middle' class='html-align-center' >552</td><td align='center' valign='middle' class='html-align-center' >2236</td><td align='center' valign='middle' class='html-align-center' >2221</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>a</mi> <mi>b</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >671</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >123</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >24</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >479</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >54</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >14</td></tr><tr ><td align='center' rowspan='4' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3</td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mi>f</mi> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >18,030</td><td align='center' valign='middle' class='html-align-center' >8528</td><td align='center' valign='middle' class='html-align-center' >3184</td><td align='center' valign='middle' class='html-align-center' >45,829</td><td align='center' valign='middle' class='html-align-center' >2679</td><td align='center' valign='middle' class='html-align-center' >14,795</td></tr><tr ><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>d</mi> <mi>r</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >15,078</td><td align='center' valign='middle' class='html-align-center' >7073</td><td align='center' valign='middle' class='html-align-center' >3265</td><td align='center' valign='middle' class='html-align-center' >6796</td><td align='center' valign='middle' class='html-align-center' >2420</td><td align='center' valign='middle' class='html-align-center' >14,208</td></tr><tr ><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>b</mi> <mi>t</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >7789</td><td align='center' valign='middle' class='html-align-center' >5648</td><td align='center' valign='middle' class='html-align-center' >4613</td><td align='center' valign='middle' class='html-align-center' >836</td><td align='center' valign='middle' class='html-align-center' >7206</td><td align='center' valign='middle' class='html-align-center' >7016</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>a</mi> <mi>b</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >685</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >216</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >42</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >783</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >72</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >27</td></tr><tr ><td align='center' rowspan='4' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5</td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mi>f</mi> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >20,559</td><td align='center' valign='middle' class='html-align-center' >13,100</td><td align='center' valign='middle' class='html-align-center' >6537</td><td align='center' valign='middle' class='html-align-center' >77,243</td><td align='center' valign='middle' class='html-align-center' >3209</td><td align='center' valign='middle' class='html-align-center' >25,144</td></tr><tr ><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>d</mi> <mi>r</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >15,207</td><td align='center' valign='middle' class='html-align-center' >10,073</td><td align='center' valign='middle' class='html-align-center' >6109</td><td align='center' valign='middle' class='html-align-center' >7688</td><td align='center' valign='middle' class='html-align-center' >2495</td><td align='center' valign='middle' class='html-align-center' >23,140</td></tr><tr ><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>b</mi> <mi>t</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >12,816</td><td align='center' valign='middle' class='html-align-center' >9273</td><td align='center' valign='middle' class='html-align-center' >7624</td><td align='center' valign='middle' class='html-align-center' >974</td><td align='center' valign='middle' class='html-align-center' >12,265</td><td align='center' valign='middle' class='html-align-center' >1939</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>a</mi> <mi>b</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >694</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >237</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >93</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >917</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >73</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >32</td></tr><tr ><td align='center' rowspan='4' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7</td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mi>f</mi> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >23,537</td><td align='center' valign='middle' class='html-align-center' >16,612</td><td align='center' valign='middle' class='html-align-center' >9797</td><td align='center' valign='middle' class='html-align-center' >104,336</td><td align='center' valign='middle' class='html-align-center' >3628</td><td align='center' valign='middle' class='html-align-center' >28,443</td></tr><tr ><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>d</mi> <mi>r</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >15,785</td><td align='center' valign='middle' class='html-align-center' >11,723</td><td align='center' valign='middle' class='html-align-center' >7689</td><td align='center' valign='middle' class='html-align-center' >7136</td><td align='center' valign='middle' class='html-align-center' >2487</td><td align='center' valign='middle' class='html-align-center' >24,456</td></tr><tr ><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>b</mi> <mi>t</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >16,308</td><td align='center' valign='middle' class='html-align-center' >13,109</td><td align='center' valign='middle' class='html-align-center' >11,395</td><td align='center' valign='middle' class='html-align-center' >1055</td><td align='center' valign='middle' class='html-align-center' >16,736</td><td align='center' valign='middle' class='html-align-center' >3137</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>a</mi> <mi>b</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >713</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >278</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >105</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >989</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >76</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >37</td></tr><tr ><td align='center' rowspan='4' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10</td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mi>f</mi> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >82,837</td><td align='center' valign='middle' class='html-align-center' >73,821</td><td align='center' valign='middle' class='html-align-center' >12,641</td><td align='center' valign='middle' class='html-align-center' >134,930</td><td align='center' valign='middle' class='html-align-center' >3162</td><td align='center' valign='middle' class='html-align-center' >34,108</td></tr><tr ><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>d</mi> <mi>r</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >73,073</td><td align='center' valign='middle' class='html-align-center' >67,239</td><td align='center' valign='middle' class='html-align-center' >8434</td><td align='center' valign='middle' class='html-align-center' >8178</td><td align='center' valign='middle' class='html-align-center' >1493</td><td align='center' valign='middle' class='html-align-center' >26,959</td></tr><tr ><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>b</mi> <mi>t</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >4794</td><td align='center' valign='middle' class='html-align-center' >3239</td><td align='center' valign='middle' class='html-align-center' >12,656</td><td align='center' valign='middle' class='html-align-center' >997</td><td align='center' valign='middle' class='html-align-center' >21,054</td><td align='center' valign='middle' class='html-align-center' >4038</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>a</mi> <mi>b</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >834</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >456</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >111</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1094</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >84</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >44</td></tr><tr ><td align='center' rowspan='20' valign='middle' style='border-bottom:solid thin' class='html-align-center' >150</td><td align='center' rowspan='4' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1</td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mi>f</mi> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >24,395</td><td align='center' valign='middle' class='html-align-center' >7886</td><td align='center' valign='middle' class='html-align-center' >1174</td><td align='center' valign='middle' class='html-align-center' >19,029</td><td align='center' valign='middle' class='html-align-center' >1654</td><td align='center' valign='middle' class='html-align-center' >1898</td></tr><tr ><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>d</mi> <mi>r</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >23,037</td><td align='center' valign='middle' class='html-align-center' >7359</td><td align='center' valign='middle' class='html-align-center' >1214</td><td align='center' valign='middle' class='html-align-center' >2935</td><td align='center' valign='middle' class='html-align-center' >1810</td><td align='center' valign='middle' class='html-align-center' >2100</td></tr><tr ><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>b</mi> <mi>t</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >2279</td><td align='center' valign='middle' class='html-align-center' >1866</td><td align='center' valign='middle' class='html-align-center' >2095</td><td align='center' valign='middle' class='html-align-center' >292</td><td align='center' valign='middle' class='html-align-center' >2477</td><td align='center' valign='middle' class='html-align-center' >1943</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>a</mi> <mi>b</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >952</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >358</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >45</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >376</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >79</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6</td></tr><tr ><td align='center' rowspan='4' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3</td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mi>f</mi> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >34,563</td><td align='center' valign='middle' class='html-align-center' >17,287</td><td align='center' valign='middle' class='html-align-center' >5837</td><td align='center' valign='middle' class='html-align-center' >72,682</td><td align='center' valign='middle' class='html-align-center' >2873</td><td align='center' valign='middle' class='html-align-center' >9997</td></tr><tr ><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>d</mi> <mi>r</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >29,557</td><td align='center' valign='middle' class='html-align-center' >14,323</td><td align='center' valign='middle' class='html-align-center' >4576</td><td align='center' valign='middle' class='html-align-center' >9084</td><td align='center' valign='middle' class='html-align-center' >2623</td><td align='center' valign='middle' class='html-align-center' >9535</td></tr><tr ><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>b</mi> <mi>t</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >7493</td><td align='center' valign='middle' class='html-align-center' >6119</td><td align='center' valign='middle' class='html-align-center' >4355</td><td align='center' valign='middle' class='html-align-center' >593</td><td align='center' valign='middle' class='html-align-center' >7345</td><td align='center' valign='middle' class='html-align-center' >4245</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>a</mi> <mi>b</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1159</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >467</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >153</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1240</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >94</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >33</td></tr><tr ><td align='center' rowspan='4' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5</td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mi>f</mi> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >41,085</td><td align='center' valign='middle' class='html-align-center' >22,687</td><td align='center' valign='middle' class='html-align-center' >11,011</td><td align='center' valign='middle' class='html-align-center' >131,691</td><td align='center' valign='middle' class='html-align-center' >3566</td><td align='center' valign='middle' class='html-align-center' >18,148</td></tr><tr ><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>d</mi> <mi>r</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >32,456</td><td align='center' valign='middle' class='html-align-center' >16,444</td><td align='center' valign='middle' class='html-align-center' >7333</td><td align='center' valign='middle' class='html-align-center' >12,276</td><td align='center' valign='middle' class='html-align-center' >2937</td><td align='center' valign='middle' class='html-align-center' >15,027</td></tr><tr ><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>b</mi> <mi>t</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >12,330</td><td align='center' valign='middle' class='html-align-center' >10,013</td><td align='center' valign='middle' class='html-align-center' >6280</td><td align='center' valign='middle' class='html-align-center' >747</td><td align='center' valign='middle' class='html-align-center' >12,082</td><td align='center' valign='middle' class='html-align-center' >7547</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>a</mi> <mi>b</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1224</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >544</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >166</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1645</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >96</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >44</td></tr><tr ><td align='center' rowspan='4' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7</td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mi>f</mi> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >42,257</td><td align='center' valign='middle' class='html-align-center' >27,591</td><td align='center' valign='middle' class='html-align-center' >16,575</td><td align='center' valign='middle' class='html-align-center' >188,247</td><td align='center' valign='middle' class='html-align-center' >3850</td><td align='center' valign='middle' class='html-align-center' >23,045</td></tr><tr ><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>d</mi> <mi>r</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >30,043</td><td align='center' valign='middle' class='html-align-center' >17,787</td><td align='center' valign='middle' class='html-align-center' >10,470</td><td align='center' valign='middle' class='html-align-center' >14,942</td><td align='center' valign='middle' class='html-align-center' >2867</td><td align='center' valign='middle' class='html-align-center' >16,390</td></tr><tr ><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>b</mi> <mi>t</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >18,416</td><td align='center' valign='middle' class='html-align-center' >12,515</td><td align='center' valign='middle' class='html-align-center' >8861</td><td align='center' valign='middle' class='html-align-center' >935</td><td align='center' valign='middle' class='html-align-center' >17,760</td><td align='center' valign='middle' class='html-align-center' >11,298</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>a</mi> <mi>b</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1223</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >582</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >189</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1789</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >102</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >46</td></tr><tr ><td align='center' rowspan='4' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10</td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mi>f</mi> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >368,546</td><td align='center' valign='middle' class='html-align-center' >654,804</td><td align='center' valign='middle' class='html-align-center' >28,053</td><td align='center' valign='middle' class='html-align-center' >262,574</td><td align='center' valign='middle' class='html-align-center' >3751</td><td align='center' valign='middle' class='html-align-center' >44,759</td></tr><tr ><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>d</mi> <mi>r</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >353,795</td><td align='center' valign='middle' class='html-align-center' >641,748</td><td align='center' valign='middle' class='html-align-center' >18,995</td><td align='center' valign='middle' class='html-align-center' >17,810</td><td align='center' valign='middle' class='html-align-center' >2365</td><td align='center' valign='middle' class='html-align-center' >34,547</td></tr><tr ><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>b</mi> <mi>t</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >2109</td><td align='center' valign='middle' class='html-align-center' >635</td><td align='center' valign='middle' class='html-align-center' >11,355</td><td align='center' valign='middle' class='html-align-center' >823</td><td align='center' valign='middle' class='html-align-center' >26,109</td><td align='center' valign='middle' class='html-align-center' >6671</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>a</mi> <mi>b</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1699</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1740</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >292</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2072</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >104</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >50</td></tr><tr ><td align='center' rowspan='20' valign='middle' style='border-bottom:solid thin' class='html-align-center' >NCCU</td><td align='center' rowspan='20' valign='middle' style='border-bottom:solid thin' class='html-align-center' >116</td><td align='center' rowspan='4' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1</td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mi>f</mi> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >27,270</td><td align='center' valign='middle' class='html-align-center' >13,911</td><td align='center' valign='middle' class='html-align-center' >12,608</td><td align='center' valign='middle' class='html-align-center' >30,786</td><td align='center' valign='middle' class='html-align-center' >1646</td><td align='center' valign='middle' class='html-align-center' >96,105</td></tr><tr ><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>d</mi> <mi>r</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >27,182</td><td align='center' valign='middle' class='html-align-center' >13,887</td><td align='center' valign='middle' class='html-align-center' >12,608</td><td align='center' valign='middle' class='html-align-center' >6468</td><td align='center' valign='middle' class='html-align-center' >1730</td><td align='center' valign='middle' class='html-align-center' >96,043</td></tr><tr ><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>b</mi> <mi>t</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >2980</td><td align='center' valign='middle' class='html-align-center' >2546</td><td align='center' valign='middle' class='html-align-center' >2724</td><td align='center' valign='middle' class='html-align-center' >422</td><td align='center' valign='middle' class='html-align-center' >3113</td><td align='center' valign='middle' class='html-align-center' >700</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>a</mi> <mi>b</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >483</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >447</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >348</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1162</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >51</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >278</td></tr><tr ><td align='center' rowspan='4' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3</td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mi>f</mi> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >29,075</td><td align='center' valign='middle' class='html-align-center' >20,029</td><td align='center' valign='middle' class='html-align-center' >17,974</td><td align='center' valign='middle' class='html-align-center' >46,901</td><td align='center' valign='middle' class='html-align-center' >1927</td><td align='center' valign='middle' class='html-align-center' >106,515</td></tr><tr ><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>d</mi> <mi>r</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >27,749</td><td align='center' valign='middle' class='html-align-center' >19,872</td><td align='center' valign='middle' class='html-align-center' >17,396</td><td align='center' valign='middle' class='html-align-center' >12,402</td><td align='center' valign='middle' class='html-align-center' >1902</td><td align='center' valign='middle' class='html-align-center' >105,315</td></tr><tr ><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>b</mi> <mi>t</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >9908</td><td align='center' valign='middle' class='html-align-center' >7894</td><td align='center' valign='middle' class='html-align-center' >8043</td><td align='center' valign='middle' class='html-align-center' >1538</td><td align='center' valign='middle' class='html-align-center' >9558</td><td align='center' valign='middle' class='html-align-center' >2378</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>a</mi> <mi>b</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >544</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >542</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >416</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2116</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >50</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >334</td></tr><tr ><td align='center' rowspan='4' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5</td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mi>f</mi> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >29,358</td><td align='center' valign='middle' class='html-align-center' >22,850</td><td align='center' valign='middle' class='html-align-center' >20,462</td><td align='center' valign='middle' class='html-align-center' >53,991</td><td align='center' valign='middle' class='html-align-center' >2005</td><td align='center' valign='middle' class='html-align-center' >107,222</td></tr><tr ><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>d</mi> <mi>r</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >25,794</td><td align='center' valign='middle' class='html-align-center' >21,409</td><td align='center' valign='middle' class='html-align-center' >19,331</td><td align='center' valign='middle' class='html-align-center' >15,259</td><td align='center' valign='middle' class='html-align-center' >1866</td><td align='center' valign='middle' class='html-align-center' >103,797</td></tr><tr ><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>b</mi> <mi>t</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >17,086</td><td align='center' valign='middle' class='html-align-center' >13,875</td><td align='center' valign='middle' class='html-align-center' >13,891</td><td align='center' valign='middle' class='html-align-center' >3032</td><td align='center' valign='middle' class='html-align-center' >16,468</td><td align='center' valign='middle' class='html-align-center' >3990</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>a</mi> <mi>b</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >549</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >614</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >437</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2733</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >50</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >349</td></tr><tr ><td align='center' rowspan='4' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7</td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mi>f</mi> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >29,401</td><td align='center' valign='middle' class='html-align-center' >23,829</td><td align='center' valign='middle' class='html-align-center' >21,179</td><td align='center' valign='middle' class='html-align-center' >53,789</td><td align='center' valign='middle' class='html-align-center' >2012</td><td align='center' valign='middle' class='html-align-center' >107,362</td></tr><tr ><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>d</mi> <mi>r</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >23,411</td><td align='center' valign='middle' class='html-align-center' >20,875</td><td align='center' valign='middle' class='html-align-center' >18,727</td><td align='center' valign='middle' class='html-align-center' >15,963</td><td align='center' valign='middle' class='html-align-center' >1777</td><td align='center' valign='middle' class='html-align-center' >101,608</td></tr><tr ><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>b</mi> <mi>t</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >24,283</td><td align='center' valign='middle' class='html-align-center' >20,411</td><td align='center' valign='middle' class='html-align-center' >20,535</td><td align='center' valign='middle' class='html-align-center' >4921</td><td align='center' valign='middle' class='html-align-center' >23,678</td><td align='center' valign='middle' class='html-align-center' >5328</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>a</mi> <mi>b</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >548</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >633</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >438</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2787</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >50</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >332</td></tr><tr ><td align='center' rowspan='4' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10</td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mi>f</mi> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >682,029</td><td align='center' valign='middle' class='html-align-center' >1,558,748</td><td align='center' valign='middle' class='html-align-center' >1,563,459</td><td align='center' valign='middle' class='html-align-center' >57,559</td><td align='center' valign='middle' class='html-align-center' >2010</td><td align='center' valign='middle' class='html-align-center' >138,850</td></tr><tr ><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>d</mi> <mi>r</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >673,928</td><td align='center' valign='middle' class='html-align-center' >1,553,953</td><td align='center' valign='middle' class='html-align-center' >1,559,990</td><td align='center' valign='middle' class='html-align-center' >16,017</td><td align='center' valign='middle' class='html-align-center' >1516</td><td align='center' valign='middle' class='html-align-center' >130,890</td></tr><tr ><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>b</mi> <mi>t</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >915</td><td align='center' valign='middle' class='html-align-center' >331</td><td align='center' valign='middle' class='html-align-center' >304</td><td align='center' valign='middle' class='html-align-center' >7184</td><td align='center' valign='middle' class='html-align-center' >33,502</td><td align='center' valign='middle' class='html-align-center' >4864</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>M</mi> <mrow> <mi>a</mi> <mi>b</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >984</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1392</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1324</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2882</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >48</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >336</td></tr></tbody> </table> </div></section><section class='html-fn_group'><table><tr id=''><td></td><td><div class='html-p'><b>Publisher’s Note:</b> MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.</div></td></tr></table></section> <section id="html-copyright"><br>© 2022 by the authors. 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Enhanced Geographic Routing with One- and Two-Hop Movement Information in Opportunistic Ad Hoc Networks. <em>Future Internet</em> <b>2022</b>, <em>14</em>, 214. https://doi.org/10.3390/fi14070214 </p> <div style="display: block"> <b>AMA Style</b><br> <p> Mir M-Y, Zhu H, Hu C-L. Enhanced Geographic Routing with One- and Two-Hop Movement Information in Opportunistic Ad Hoc Networks. <em>Future Internet</em>. 2022; 14(7):214. https://doi.org/10.3390/fi14070214 </p> <b>Chicago/Turabian Style</b><br> <p> Mir, Mohd-Yaseen, Hengbing Zhu, and Chih-Lin Hu. 2022. "Enhanced Geographic Routing with One- and Two-Hop Movement Information in Opportunistic Ad Hoc Networks" <em>Future Internet</em> 14, no. 7: 214. https://doi.org/10.3390/fi14070214 </p> <b>APA Style</b><br> <p> Mir, M. -Y., Zhu, H., & Hu, C. -L. (2022). 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