A note on the stability of multiclass Markovian queueing networks

Details A note on the stability of multiclass Markovian queueing networks A note on the stability of multiclass Markovian queueing networks

2010-06-22

arxiv.org/abs/1006.4387v1

Computer Science

Networking and Internet Architecture

Submitted to Journal of Applied Probability

Scientific paper

In this paper we show that in a multiclass Markovian network with unit rate servers, the condition that the average load $\rho$ at every server is less than unity is indeed sufficient for the stability or positive recurrence for \emph{any} work conserving scheduling policy and \emph{class-independent} routing. We use a variation of the positive recurrence criterion for multidimensional discrete-time Markov chains over countable state spaces due to Rosberg (JAP, Vol.~17, No.~3, 1980) and a monotonicity argument to establish this assertion.

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