Stability of Multiclass Jackson-Type Networks

#### S.G. Foss, A.N. Rybko

1996, v.2, Issue 3, 461-486

ABSTRACT

This paper deals with the stability study of multiclass open queueing networks under the FIFO (first in first out) discipline. It is known that the natural traffic intensity condition $\rho < 1$ is necessary, but not sufficient for stability of these networks. We introduce a Jackson-type property for the transition probabilities of multiclass networks and show that if a network satisfies this property, then the traffic intensity condition characterises its stability region. Our approach is based on the analysis of the corresponding fluid network.

Keywords: open multiclass queueing network,fluid limit,stability,Jackson-type property,Markov chain