Large bursts do not cause instability

Fluid models of queuing networks are among the simplest models to analyze, owing to the fact that calculus can be applied. At the same time, wider classes of network models are more flexible for modeling real traffic. It is thus useful to reduce questions about the more realistic models to questions about related fluid models. Such a reduction was achieved by J.G. Dai (1995), who showed that stability of a fluid model implies stability (in the sense of Harris recurrence) of related multiclass networks with random service and interarrival processes of renewal type. The purpose of this paper is to similarly reduce the question of stability for networks with input traffic satisfying deterministic constraints in the sense of R.I. Cruz (1991) to a question of stability for a fluid model. It is shown that the stability of networks with fluid traffic implies stability of networks with deterministically constrained traffic.