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The Fluid Limit of the Multiclass Processor Sharing Queue

Abdelghani Ben Tahar 1 Alain Jean-Marie 2, 3 
2 MAESTRO - Models for the performance analysis and the control of networks
CRISAM - Inria Sophia Antipolis - Méditerranée
3 LIRMM/HE - Hors Équipe
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : 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. (Ann. Appl. Probab., 2002) and Puha et al. (Math. Ops. Res., 2006), we establish the convergence of a properly normalized state process to a fluid limit characterized by a system of algebraic and integral equations. We show the existence of a unique solution to this system of equations, both for a stable and an overloaded queue. We also describe the asymptotic behavior of the trajectories of the fluid limit.
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Submitted on : Tuesday, September 17, 2013 - 4:48:22 PM
Last modification on : Friday, August 5, 2022 - 10:45:57 AM

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Abdelghani Ben Tahar, Alain Jean-Marie. The Fluid Limit of the Multiclass Processor Sharing Queue. Queueing Systems, Springer Verlag, 2012, 71 (4), pp.347-404. ⟨10.1007/s11134-012-9287-9⟩. ⟨hal-00862877⟩



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