A note on the stability of multiclass Markovian queueing networks

摘要

In this paper we show that in a multiclass Markovian network with unit rateservers, the condition that the average load $\rho$ at every server is lessthan 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 formultidimensional discrete-time Markov chains over countable state spaces due toRosberg (JAP, Vol.~17, No.~3, 1980) and a monotonicity argument to establishthis assertion.