Stability of Multiclass Jackson-Type Networks
1996, v.2, Issue 3, 461-486
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