inria-00368246, version 2
The Fluid Limit of the Multiclass Processor Sharing Queue
Abdelghani Ben Tahar a, 1Alain Jean-Marie
2, 3
N° RR-6867 (2009)
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. and Puha et al., 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.
- a – Université de Rouen
- 1: Laboratoire de Mathématiques Raphaël Salem (LMRS)
- CNRS : UMR6085 – Université de Rouen
- 2: Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier (LIRMM)
- CNRS : UMR5506 – Université Montpellier II - Sciences et Techniques du Languedoc
- 3: MAESTRO (INRIA Sophia Antipolis)
- INRIA – Université Montpellier II - Sciences et Techniques du Languedoc
- Domain : Mathematics/Probability
Computer Science/Operations ResearchComputer Science/Performance and Reliability - Keywords : Processor sharing – Law of large number – fluid model – measure val ued process – multiclass networks
- Internal note : RR-6867
- Comment : This second version improves the presentation of results in Section 3 and in Appendix C.
- Available versions : v1 (2009-03-21) v2 (2009-04-21)
- inria-00368246, version 2
- http://hal.inria.fr/inria-00368246
- oai:hal.inria.fr:inria-00368246
- From: Alain Jean-Marie
- Submitted on: Tuesday, 21 April 2009 10:28:58
- Updated on: Monday, 31 August 2009 16:00:05
Associated documents
Export