Analysis of Loss Networks with Routing

Nelson Antunes; Christine Fricker; Philippe Robert; Danielle Tibi

inria-00000959, version 2

Analysis of Loss Networks with Routing

Nelson Antunes () ¹, Christine Fricker () ², Philippe Robert () ², Danielle Tibi ³

Annals of Applied Probability (2005)

Abstract: This paper analyzes stochastic networks consisting of finite capacity nodes with different classes of requests which move according to some routing policy. The Markov processes describing these networks do not have, in general, reversibility properties so that the explicit expression of their invariant distribution is not known. A heavy traffic limit regime is considered: the arrival rates of calls as well as the capacities of the nodes are proportional to a factor going to infinity. It is proved that, in the limit, the associated rescaled Markov process converges to a deterministic dynamical system with a unique equilibrium point characterized by a non-standard fixed point equation.

1: Faculdade de Ciências e Tecnologia (FCT)
Universidade do Algarve
2: RAP (INRIA Paris - Rocquencourt)
INRIA : PARIS - ROCQUENCOURT
3: Laboratoire de Probabilités et Modèles Aléatoires (LPMA)
CNRS : UMR7599 – Université Pierre et Marie Curie [UPMC] - Paris VI – Université Paris VII - Paris Diderot

inria-00000959, version 2
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From: Philippe Robert <>
Submitted on: Friday, 13 January 2006 08:03:54
Updated on: Wednesday, 26 April 2006 18:46:07

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arXiv: cs.NI/0512088

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