Stability of Single Class Queueing Networks

Abstract

The stability of queueing networks is a fundamental problem in modern communications and computer networks. Stability (or recurrence) is known under various independence or ergodic conditions on the service and interarrival time processes if the “fluid or mean approximation” is asymptotically stable. The basic property of stability should be robust to variations in the data. Perturbed Liapunov function methods are exploited to give effective criteria for the recurrence under very broad conditions on the “driving processes” if the fluid approximation is asymptotically stable. In particular, stationarity is not required, and the data can be correlated. Various single class models are considered. For the problem of stability in heavy traffic, where one is concerned with a sequence of queues, both the standard network model and a more general form of the Skorohod problem type are dealt with and recurrence, uniformly in the heavy traffic parameter, is shown. The results can be extend ed to account for many of the features of queueing networks, such as batch arrivals and processing or server breakdown. While we concentrate on the single class network, analogous results can be obtained for multiclass systems.