The fluid limit of the multiclass processor sharing queue

نویسندگان

  • Abdelghani Ben Tahar
  • Alain Jean-Marie
چکیده

Consider a single server queueing system with several classes of customers, each having its own renewal input process and its own general service times distribution. Upon completing service, customers may leave, or reenter the queue, possibly as customers of a different class. The server is operating under the egalitarian processor sharing discipline. Building on prior work by Gromoll et al. [12] and Puha et al. [16], we establish the convergence of a properly normalized state process to a fluid limit. We show the existence of a unique solution to this fluid limit model, both for a stable and an overloaded queue. We also describe the asymptotic behavior of the trajectories of the fluid limit. Key-words: Processor Sharing, Fluid Limit ∗ Laboratoire de Mathématiques Raphaël Salem UMR 6085 CNRS-Université de Rouen, Avenue de l’Université, BP.12, F76801 Saint-Étienne-du-Rouvray, [email protected]. Part of this work was performed while the author was a CNRS Postdoctoral fellow at LIRMM. † INRIA and LIRMM, CNRS/Université Montpellier 2, 161 Rue Ada, F-34392 Montpellier, [email protected]. La limite fluide de la file d’attente Processor Sharing multiclasse Résumé : Dans une file d’attente “Processor Sharing”, chaque client présent reçoit une part égale de la capacité de service du serveur. Nous étudions le comportement de cette file quand il y a plusieurs classes de clients, susceptibles de ré-entrer dans la file quand leur service se termine. Les différentes classes sont caractérisées par des distributions de temps de service et des probabilités de routage différentes. A partir des résultats de Gromoll et al. [12] et Puha et al. [16], nous montrons l’existence de cette limite fluide, nous calculons les solutions de cette limite et nous décrivons ses propriétés asymptotiques. Mots-clés : Limite fluide, Processor Sharing The Fluid Limit of the Multiclass Processor Sharing Queue 3

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عنوان ژورنال:
  • Queueing Syst.

دوره 71  شماره 

صفحات  -

تاریخ انتشار 2012