Document Zbl 1350.60097

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Service differentiation can in fact be formulated as a generalized resource allocation optimization towards the minimization of some important system characteristics. For complex scheduling policies, however, optimization can be a demanding task, due to the difficult analytical analysis of the system at hand. In this paper, we study the optimization problem in a queueing system with two traffic classes, a work-conserving parameterized scheduling policy, and an objective function that is a convex combination of either linear, convex or concave increasing functions of given performance measures of both classes. In case of linear and concave functions, we show that the optimum is always in an extreme value of the parameter. Furthermore, we prove that this is not necessarily the case for convex functions; in this case, a unique local minimum exists. This information greatly simplifies the optimization problem. We apply the framework to some interesting scheduling policies, such as Generalized Processor Sharing and semi-preemptive priority scheduling. We also show that the well-documented $c\mu $-rule is a special case of our framework.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6642808">Cited in <strong>4</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A60K25" title="MSC2020">60K25</a> </td> <td class="space"> Queueing theory (aspects of probability theory) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A49J55" title="MSC2020">49J55</a> </td> <td class="space"> Existence of optimal solutions to problems involving randomness </td> </tr><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%3A68M20" title="MSC2020">68M20</a> </td> <td class="space"> Performance evaluation, queueing, and scheduling in the context of computer systems </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aqueueing+systems">queueing systems</a>; <a href="/?q=ut%3Ascheduling">scheduling</a>; <a href="/?q=ut%3Aoptimization">optimization</a>; <a href="/?q=ut%3Ageneralized+processor+sharing">generalized processor sharing</a>; <a href="/?q=ut%3Astrict+priority">strict priority</a></div> <div class="software"> <h3>Software:</h3><a href="/software/14021">BRENT</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 1350.60097" data-ciurl="/ci/06642808" data-biburl="/bibtex/06642808.bib" data-amsurl="/amsrefs/06642808.bib" data-xmlurl="/xml/06642808.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06642808.pdf" title="Zbl 1350.60097 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/s10288-016-0312-4" aria-label="DOI for “On the optimization of two-class work-conserving parameterized scheduling policies”" title="10.1007/s10288-016-0312-4">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">Adan I, Boxma O, Resing J (2001) Queueing models with multiple waiting lines. 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