Applying Mean-field Approximation to Continuous Time Markov Chains

<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> <html xmlns="http://www.w3.org/1999/xhtml"> <head> <title> Applying Mean-field Approximation to Continuous Time Markov Chains - IMT Institutional Repository</title> <link rel="icon" href="/favicon.ico" type="image/x-icon" /> <link rel="shortcut icon" href="/favicon.ico" type="image/x-icon" /> <meta name="eprints.eprintid" content="1620" /> <meta name="eprints.rev_number" content="9" /> <meta name="eprints.eprint_status" content="archive" /> <meta name="eprints.userid" content="6" /> <meta name="eprints.dir" content="disk0/00/00/16/20" /> <meta name="eprints.datestamp" content="2013-06-20 08:03:30" /> <meta name="eprints.lastmod" content="2013-06-20 08:03:30" /> <meta name="eprints.status_changed" content="2013-06-20 08:03:30" /> <meta name="eprints.type" content="monograph" /> <meta name="eprints.metadata_visibility" content="show" /> <meta name="eprints.creators_name" content="Kolesnichenko, Anna" /> <meta name="eprints.creators_name" content="Pourranjabar, Alireza" /> <meta name="eprints.creators_name" content="Senni, Valerio" /> <meta name="eprints.creators_id" content="valerio.senni@imtlucca.it" /> <meta name="eprints.title" content="Applying Mean-field Approximation to Continuous Time Markov Chains" /> <meta name="eprints.ispublished" content="pub" /> <meta name="eprints.subjects" content="QA75" /> <meta name="eprints.divisions" content="CSA" /> <meta name="eprints.full_text_status" content="public" /> <meta name="eprints.monograph_type" content="imt_cs_techninal_report" /> <meta name="eprints.keywords" content="Continuous Time Markov Chains; Mean-field Approximation; Performance Analysis; Model Checking" /> <meta name="eprints.abstract" content="The mean-field analysis technique is used to perform analysis of a systems with a large number of components to determine the emergent deterministic behaviour and how this behaviour modifies when its parameters are perturbed. The computer science performance modelling and analysis community has found the mean-field method useful for modelling large-scale computer and communication networks. Applying mean-field analysis from the computer science perspective requires the following major steps: (1) describing how the agents populations evolve by means of a system of differential equations, (2) finding the emergent deterministic behaviour of the system by solving such differential equations, and (3) analysing properties of this behaviour either by relying on simulation or by using logics. Depending on the system under analysis, performing these steps may become challenging. Often, modifications of the general idea are needed. In this tutorial we consider illustrating examples to discuss how the mean-field method is used in different application areas. Starting from the application of the classical technique, moving to cases where additional steps have to be used, such as systems with local communication. Finally we illustrate the application of the simulation and uid model checking analysis techniques. " /> <meta name="eprints.date" content="2013-06" /> <meta name="eprints.date_type" content="published" /> <meta name="eprints.number" content="8" /> <meta name="eprints.publisher" content="IMT Institute for Advanced Studies Lucca" /> <meta name="eprints.pages" content="47" /> <meta name="eprints.institution" content="IMT Institute for Advanced Studies Lucca" /> <meta name="eprints.citation" content=" Kolesnichenko, Anna and Pourranjabar, Alireza and Senni, Valerio Applying Mean-field Approximation to Continuous Time Markov Chains. CSA Technical Report #8/2013 IMT Institute for Advanced Studies Lucca " /> <meta name="eprints.document_url" content="http://eprints.imtlucca.it/1620/1/CSA_TR_2013_8.pdf" /> <link rel="schema.DC" href="http://purl.org/DC/elements/1.0/" /> <meta name="DC.relation" content="http://eprints.imtlucca.it/1620/" /> <meta name="DC.title" content="Applying Mean-field Approximation to Continuous Time Markov Chains" /> <meta name="DC.creator" content="Kolesnichenko, Anna" /> <meta name="DC.creator" content="Pourranjabar, Alireza" /> <meta name="DC.creator" content="Senni, Valerio" /> <meta name="DC.subject" content="QA75 Electronic computers. Computer science" /> <meta name="DC.description" content="The mean-field analysis technique is used to perform analysis of a systems with a large number of components to determine the emergent deterministic behaviour and how this behaviour modifies when its parameters are perturbed. The computer science performance modelling and analysis community has found the mean-field method useful for modelling large-scale computer and communication networks. Applying mean-field analysis from the computer science perspective requires the following major steps: (1) describing how the agents populations evolve by means of a system of differential equations, (2) finding the emergent deterministic behaviour of the system by solving such differential equations, and (3) analysing properties of this behaviour either by relying on simulation or by using logics. Depending on the system under analysis, performing these steps may become challenging. Often, modifications of the general idea are needed. In this tutorial we consider illustrating examples to discuss how the mean-field method is used in different application areas. Starting from the application of the classical technique, moving to cases where additional steps have to be used, such as systems with local communication. Finally we illustrate the application of the simulation and uid model checking analysis techniques. " /> <meta name="DC.publisher" content="IMT Institute for Advanced Studies Lucca" /> <meta name="DC.date" content="2013-06" /> <meta name="DC.type" content="Working Paper" /> <meta name="DC.type" content="NonPeerReviewed" /> <meta name="DC.format" content="application/pdf" /> <meta name="DC.language" content="en" /> <meta name="DC.identifier" content="http://eprints.imtlucca.it/1620/1/CSA_TR_2013_8.pdf" /> <meta name="DC.identifier" content=" Kolesnichenko, Anna and Pourranjabar, Alireza and Senni, Valerio Applying Mean-field Approximation to Continuous Time Markov Chains. 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value="ALL" /> <input type="hidden" name="_satisfyall" value="ALL" /> </form> </td> </tr> </table> </div> <div align="center"> <table width="720" class="ep_tm_main"><tr><td align="left"> <h1 class="ep_tm_pagetitle"> Applying Mean-field Approximation to Continuous Time Markov Chains </h1> <div class="ep_summary_content"><div class="ep_summary_content_left"></div><div class="ep_summary_content_right"></div><div class="ep_summary_content_top"></div><div class="ep_summary_content_main"> <p style="margin-bottom: 1em"> <span class="person_name">Kolesnichenko, Anna</span> and <span class="person_name">Pourranjabar, Alireza</span> and <span class="person_name">Senni, Valerio</span> <em>Applying Mean-field Approximation to Continuous Time Markov Chains.</em> CSA Technical Report #8/2013 IMT Institute for Advanced Studies Lucca </p> <table> <tr> <td valign="top" align="right"><a class="ep_document_link" onmouseover="EPJS_ShowPreview( event, 'doc_preview_1873' );" onmouseout="EPJS_HidePreview( event, 'doc_preview_1873' );" href="http://eprints.imtlucca.it/1620/1/CSA_TR_2013_8.pdf"><img class="ep_doc_icon" alt="[img]" src="http://eprints.imtlucca.it/1620/1.hassmallThumbnailVersion/CSA_TR_2013_8.pdf" border="0" /></a><div id="doc_preview_1873" class="ep_preview"><table><tr><td><img class="ep_preview_image" alt="" src="http://eprints.imtlucca.it/1620/1.haspreviewThumbnailVersion/CSA_TR_2013_8.pdf" border="0" /><div class="ep_preview_title">Preview</div></td></tr></table></div></td> <td valign="top">  <span class="ep_document_citation"> PDF - Published Version </span> <br /> <a href="http://eprints.imtlucca.it/1620/1/CSA_TR_2013_8.pdf">Download (1MB)</a> | <a href="http://eprints.imtlucca.it/1620/1.haspreviewThumbnailVersion/CSA_TR_2013_8.pdf" rel="lightbox[docs] nofollow" title=" PDF <http://eprints.imtlucca.it/1620/1/CSA_TR_2013_8.pdf> - Published Version ">Preview</a> <ul> </ul> </td> </tr> </table> <h2>Abstract</h2> <p style="text-align: left; margin: 1em auto 0em auto">The mean-field analysis technique is used to perform analysis of a systems with a large number of components to determine the emergent deterministic behaviour and how this behaviour modifies when its parameters are perturbed. The computer science performance modelling and analysis community has found the mean-field method useful for modelling large-scale computer and communication networks. Applying mean-field analysis from the computer science perspective requires the following major steps: (1) describing how the agents populations evolve by means of a system of differential equations, (2) finding the emergent deterministic behaviour of the system by solving such differential equations, and (3) analysing properties of this behaviour either by relying on simulation or by using logics. Depending on the system under analysis, performing these steps may become challenging. Often, modifications of the general idea are needed. In this tutorial we consider illustrating examples to discuss how the mean-field method is used in different application areas. Starting from the application of the classical technique, moving to cases where additional steps have to be used, such as systems with local communication. Finally we illustrate the application of the simulation and  uid model checking analysis techniques. </p> <table style="margin-bottom: 1em; margin-top: 1em;" cellpadding="3"> <tr> <th align="right">Item Type:</th> <td> Working Paper (CSA Technical Report) </td> </tr> <tr> </tr> <tr> </tr> <tr> <th align="right">Uncontrolled Keywords:</th> <td valign="top">Continuous Time Markov Chains; Mean-field Approximation; Performance Analysis; Model Checking</td> </tr> <tr> <th align="right">Subjects:</th> <td valign="top"><a href="http://eprints.imtlucca.it/view/subjects/QA75.html">Q Science > QA Mathematics > QA75 Electronic computers. Computer science</a></td> </tr> <tr> <th align="right">Research Area:</th> <td valign="top"><a href="http://eprints.imtlucca.it/view/divisions/CSA/">Computer Science and Applications</a></td> </tr> <tr> <th align="right">Depositing User:</th> <td valign="top"> <span class="ep_name_citation"><span class="person_name">Ms T. Iannizzi</span></span> </td> </tr> <tr> <th align="right">Date Deposited:</th> <td valign="top">20 Jun 2013 08:03</td> </tr> <tr> <th align="right">Last Modified:</th> <td valign="top">20 Jun 2013 08:03</td> </tr> <tr> <th align="right">URI:</th> <td valign="top"><a href="http://eprints.imtlucca.it/id/eprint/1620">http://eprints.imtlucca.it/id/eprint/1620</a></td> </tr> </table> <h3>Actions (login required)</h3> <table class="ep_summary_page_actions"> <tr> <td><a href="/cgi/users/home?screen=EPrint%3A%3AView&eprintid=1620"><img src="/style/images/action_view.png" title="Edit Item" alt="Edit Item" class="ep_form_action_icon" /></a></td> <td>Edit Item</td> </tr> </table> </div><div class="ep_summary_content_bottom"></div><div class="ep_summary_content_after"></div></div> </td></tr></table> </div> <div class="ep_tm_footer ep_noprint">  <hr class="ep_tm_last" /> <div style="float: right; margin-left: 1em"><a href="http://eprints.org/software/"><img alt="EPrints Logo" src="/images/eprintslogo.gif" border="0" /></a></div> <div style="font-size: 80%;"> <div>IMT Institutional Repository is powered by <em><a href="http://eprints.org/software/">EPrints 3</a></em> which is developed by the <a href="http://www.ecs.soton.ac.uk/">School of Electronics and Computer Science</a> at the University of Southampton. <a href="http://eprints.imtlucca.it/eprints/">More information and software credits</a>.</div> </div> </div> </body> </html>

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Applying Mean-field Approximation to Continuous Time Markov Chains - IMT Institutional Repository