Document Zbl 1263.90022

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The original formulations considered linear costs, and the resulting policy is puzzling in many ways. The main one is that, either for preemptive or nonpreemptive problems, it results in a priority ordering of the different classes of customers being served that is insensitive to the individual load each class imposes on the server and insensitive to the overall load the server experiences. This policy is known as the $c\mu $-rule.<br class="zbmathjax-paragraph"> We claim and show that for convex costs, the optimal policy depends on the individual loads. Therefore, there is a need for an alternative generalization of the $c\mu $-rule. The main feature of our generalization consists on first-order differences of the single stage cost function, rather than on its derivatives. The resulting policy is able to reach near optimal performances and is a function of the individual loads.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6151426">Cited in <strong>3</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A90B22" title="MSC2020">90B22</a> </td> <td class="space"> Queues and service in operations research </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A90C39" title="MSC2020">90C39</a> </td> <td class="space"> Dynamic programming </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A90C40" title="MSC2020">90C40</a> </td> <td class="space"> Markov and semi-Markov decision processes </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Ascheduling">scheduling</a>; <a href="/?q=ut%3Aproduction+control">production control</a>; <a href="/?q=ut%3Aqueuing+systems">queuing systems</a>; <a href="/?q=ut%3Adynamic+priorities">dynamic priorities</a>; <a href="/?q=ut%3A%5C%28c%5Cmu+%5C%29-rule">$c\mu $-rule</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1263.90022" data-ciurl="/ci/06151426" data-biburl="/bibtex/06151426.bib" data-amsurl="/amsrefs/06151426.bib" data-xmlurl="/xml/06151426.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06151426.pdf" title="Zbl 1263.90022 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1007/s11134-012-9316-8" aria-label="DOI for “The single-server scheduling problem with convex costs”" title="10.1007/s11134-012-9316-8">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Ansell, P.S., Glazebrook, K.D., Niño-Mora, J., O’Keeffe, M.: Whittle’s index policy for a multi-class queueing system with convex holding costs. Math. Methods Oper. Res. 57(1), 21–29 (2003) · <a href="/1023.90010" class="nowrap">Zbl 1023.90010</a> · <a href="https://doi.org/10.1007/s001860200257" class="nowrap">doi:10.1007/s001860200257</a></td> </tr><tr> <td>[2]</td> <td class="space">Atar, R., Giat, C., Shimpkin, N.: On the asymptotic optimality of the c{$\mu$}/{$\theta$} rule under ergodic cost. Queueing Syst. 67(2), 127–144 (2011) · <a href="/1217.90063" class="nowrap">Zbl 1217.90063</a> · <a href="https://doi.org/10.1007/s11134-010-9206-x" class="nowrap">doi:10.1007/s11134-010-9206-x</a></td> </tr><tr> <td>[3]</td> <td class="space">Ayesta, U., Jacko, P., Novak, V.: A nearly-optimal index rule for scheduling of users with abandonment. In: Proceedings IEEE INFOCOM, 2011 pp. 2849–2857 (2011)</td> </tr><tr> <td>[4]</td> <td class="space">Baras, J.S., Dorsey, A.J., Makowski, A.M.: Two competing queues with linear costs: the {$\mu$}c rule is often optimal. Adv. Appl. Probab. 17, 186–209 (1985) · <a href="/0554.60087" class="nowrap">Zbl 0554.60087</a> · <a href="https://doi.org/10.2307/1427059" class="nowrap">doi:10.2307/1427059</a></td> </tr><tr> <td>[5]</td> <td class="space">Bertsekas, D.P.: Dynamic Programming and Optimal Control. Athena Scientific, Nashua (1995) · <a href="/0904.90170" class="nowrap">Zbl 0904.90170</a></td> </tr><tr> <td>[6]</td> <td class="space">Buyukkoc, C., Varaiya, P., Walrand, J.: The c{$\mu$} rule revisited. Adv. Appl. Probab. 17(1), 237–238 (1985) · <a href="/0557.60082" class="nowrap">Zbl 0557.60082</a> · <a href="https://doi.org/10.2307/1427064" class="nowrap">doi:10.2307/1427064</a></td> </tr><tr> <td>[7]</td> <td class="space">Cassandras, C.G.: Discrete Event Systems: Modeling and Performance Analysis. Richard D. Irwin/Aksen Associates, Homewood/Pacific Palisades (1993)</td> </tr><tr> <td>[8]</td> <td class="space">Cox, D.R., Smith, W.L.: Queues. Chapman &amp; Hall, London (1961)</td> </tr><tr> <td>[9]</td> <td class="space">Dai, J.G., Lin, W.: Maximum pressure policies in stochastic processing networks. Oper. Res. 53(2), 197–218 (2005) · <a href="/1165.90359" class="nowrap">Zbl 1165.90359</a> · <a href="https://doi.org/10.1287/opre.1040.0170" class="nowrap">doi:10.1287/opre.1040.0170</a></td> </tr><tr> <td>[10]</td> <td class="space">Dai, J.G., Lin, W.: Asymptotic optimality of maximum pressure policies in stochastic processing networks. Ann. Appl. Probab. 18(6), 2239–2299 (2008) · <a href="/1175.90083" class="nowrap">Zbl 1175.90083</a> · <a href="https://doi.org/10.1214/08-AAP522" class="nowrap">doi:10.1214/08-AAP522</a></td> </tr><tr> <td>[11]</td> <td class="space">Down, D.G., Koole, G., Lewis, M.E.: Dynamic control of a single-server system with abandonments. Queueing Syst. 67(1), 63–90 (2011) · <a href="/1230.90106" class="nowrap">Zbl 1230.90106</a> · <a href="https://doi.org/10.1007/s11134-010-9201-2" class="nowrap">doi:10.1007/s11134-010-9201-2</a></td> </tr><tr> <td>[12]</td> <td class="space">Glazebrook, K.D., Lumley, R.R., Ansell, P.S.: Index heuristics for multiclass M/G/1 systems with nonpreemptive service and convex holding costs. Queueing Syst. 45(2), 81–111 (2003) · <a href="/1036.90030" class="nowrap">Zbl 1036.90030</a> · <a href="https://doi.org/10.1023/A:1026060405346" class="nowrap">doi:10.1023/A:1026060405346</a></td> </tr><tr> <td>[13]</td> <td class="space">Harrison, J.M.: Dynamic scheduling of a multiclass queue: discount optimality. IEEE Trans. Autom. Control 23(2), 270–282 (1975) · <a href="/0321.60073" class="nowrap">Zbl 0321.60073</a></td> </tr><tr> <td>[14]</td> <td class="space">Harrison, J.M., Zeevi, A.: Dynamic scheduling of a multiclass queue in the Halfin–Whitt heavy traffic regime. Oper. Res. 52(2), 243–257 (2004) · <a href="/1165.90474" class="nowrap">Zbl 1165.90474</a> · <a href="https://doi.org/10.1287/opre.1030.0084" class="nowrap">doi:10.1287/opre.1030.0084</a></td> </tr><tr> <td>[15]</td> <td class="space">Klimov, G.P.: Time-sharing service systems I. Theory Probab. Appl. 19, 532–551 (1974) · <a href="/0378.60102" class="nowrap">Zbl 0378.60102</a> · <a href="https://doi.org/10.1137/1119060" class="nowrap">doi:10.1137/1119060</a></td> </tr><tr> <td>[16]</td> <td class="space">Mandelbaum, A., Stolyar, A.L.: Scheduling flexible servers with convex delay costs: heavy-traffic optimality of the generalized c{$\mu$}-rule. Oper. Res. 52(6), 836–855 (2004) · <a href="/1165.90402" class="nowrap">Zbl 1165.90402</a> · <a href="https://doi.org/10.1287/opre.1040.0152" class="nowrap">doi:10.1287/opre.1040.0152</a></td> </tr><tr> <td>[17]</td> <td class="space">Pinedo, M.: Stochastic scheduling with release dates and due dates. Oper. Res. 31, 559–572 (1983) · <a href="/0523.90046" class="nowrap">Zbl 0523.90046</a> · <a href="https://doi.org/10.1287/opre.31.3.559" class="nowrap">doi:10.1287/opre.31.3.559</a></td> </tr><tr> <td>[18]</td> <td class="space">Righter, R.: Scheduling. In: Shaked, M., Shanthikumar, J.G. (eds.) Stochastic Orders. Academic Press, San Diego (1994)</td> </tr><tr> <td>[19]</td> <td class="space">Smith, W.E.: Various optimizers for single-stage production. Nav. Res. Logist. Q. 3, 59–66 (1956) · <a href="https://doi.org/10.1002/nav.3800030106" class="nowrap">doi:10.1002/nav.3800030106</a></td> </tr><tr> <td>[20]</td> <td class="space">van Mieghem, J.A.: Dynamic scheduling with convex delay costs: the generalized c{$\mu$} rule. Ann. Appl. Probab. 5(3), 808–833 (1995) · <a href="/0843.90047" class="nowrap">Zbl 0843.90047</a></td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching. </div> </div></article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> © 2025 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms & Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; </script> <script src="/static/scripts.js?v=20240926"> </script> <script src="https://static.zbmath.org/contrib/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { preferredFont: "TeX", availableFonts: [ "STIX", "TeX" ], linebreaks: { automatic: true }, EqnChunk: (MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { Macros: { Aut: "\\operatorname{Aut}", Hom: "\\operatorname{Hom}" }, noUndefined: { attributes: { mathcolor: "#039", //"red", mathbackground: "white", //"#FFEEEE", mathsize: "90%" } } }, messageStyle: "none" }); </script> <script type="text/javascript"> $(document).ready(function() { $("#MathInput").stop(true, true).keyup(function() { $.ajax({ url: "/mwsq/", type: "POST", data: { query : $("#MathInput").val() }, dataType: "text" }) .done(function(xml) { $("#MathPreview").html(xml); $(window).resize(); }); }); var press = jQuery.Event("keyup"); press.ctrlKey = false; press.which = 40; $("#MathInput").trigger(press); }); </script> <div id="new_tab_icon" style="display: none"> <span class="glyphicon glyphicon-new-window" aria-hidden="true"></span><span class="sr-only">(opens in new tab)</span></div> </body> </html>

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