Transience of Multiclass Queueing Networks Via Fluid Limit Models

Abstract

This paper treats transience for queueing network models by considering an associated duid model. If starting from any initial condition the euid model explodes at a linear rate, then the associated queueing network with i.i.d. service times and a renewal arrival process explodes faster than any fractional power. There has been much recent i n terest in understanding the dynamics of queueing networks , and in particular their stability properties. Numerous techniques have been developed for veriication of stability or ergodicity using a variety of methods. Of interest to us in the present paper is the recent approach based upon a auid approximation. Rybko and Stolyar r15] h a ve recently examined the stability properties of a particular example by studying the properties of the associated duid approximation. Dupuis and Williams obtained results of this kind for reeected Brownian motion n8], and these ideas were subsequently generalized in Dai i3] and Dai and Meyn n4]. These results show h o w to demonstrate the stability of the stochastic system by establishing the stability of a auid approximation. In this paper we establish a converse result to obtain criteria for transience for stochastic queueing networks based upon a auid model.