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Queueing Systems

, Volume 71, Issue 4, pp 347–404 | Cite as

The fluid limit of the multiclass processor sharing queue

  • Abdelghani Ben Tahar
  • Alain Jean-MarieEmail author
Article

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 re-enter 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. 12:797–859, 2002) and Puha et al. (Math. Oper. Res. 31(2):316–350, 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.

Keywords

Fluid limit Fluid model Measure valued process Multiclass networks Processor sharing 

Mathematics Subject Classification (2000)

68M20 90B22 

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.FST-SettatUniv. Hassan ISettatMorocco
  2. 2.INRIA and LIRMMUMR 5506 CNRS—Univ. Montpellier 2MontpellierFrance

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