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hal-00710225, version 1

A retrial system with two input streams and two orbit queues

Konstantin Avrachenkov (, http://www-sop.inria.fr/mistral/personnel/K.Avrachenkov/me.html) a, 1, Philippe Nain (, http://www-sop.inria.fr/maestro/personnel/Philippe.Nain/) b, 1, Uri Yechiali () c, 2

N° RR-7999 (2012)

Abstract: Two independent Poisson streams of jobs flow into a single-server service system having a limited common buffer that can hold at most one job. If a type-i job (i=1,2) finds the server busy, it is blocked and routed to a separate type-i retrial (orbit) queue that attempts to re-dispatch its jobs at its specific Poisson rate. This creates a system with three dependent queues. Such a queueing system serves as a model for two competing job streams in a carrier sensing multiple access system. We study the queueing system using multi-dimensional probability generating functions, and derive its necessary and sufficient stability conditions while solving a boundary value problem. Various performance measures are calculated and numerical results are presented.

  • a –  INRIA
  • b –  INRIA Sophia Antipolis - Mediterranee
  • c –  Tel Aviv University
  • 1:  MAESTRO (INRIA Sophia Antipolis)
  • INRIA – Université Montpellier II - Sciences et techniques
  • 2:  Department of Statistics and Operations Research [Tel Aviv]
  • Tel Aviv University
  • Collaboration : Tel Aviv University
  • Domain : Computer Science/Networking and Telecommunication
  • Keywords : Retrial queues – Riemann-Hilbert boundary value problem – Carrier sensing multiple access system
  • Internal note : RR-7999
 
  • hal-00710225, version 1
  • http://hal.inria.fr/hal-00710225
  • oai:hal.inria.fr:hal-00710225
  • From: Konstantin Avrachenkov <>
  • Submitted on: Wednesday, 20 June 2012 12:35:53
  • Updated on: Friday, 22 June 2012 08:36:32