ASYMPTOTIC PROPERTIES OF QUEUING-NETWORKS

A new approach to the analysis of asymptotic properties of closed queu ing networks with both constant service rates and, in certain cases, l oad-dependent service rates is developed. The method is based on a dec omposition of the generating function of the normalising constant into simpler node functions which are easily inverted term by term. An exa ct closed form is obtained for the normalising constant in some cases and an approximation, based on an integral formula, in others. These r esults are applied to model a large computer system with terminals, wh ich is also used to illustrate the main properties of the normalising constant and the system throughput function as the population increase s. The authors' method is compared with others in terms of both accura cy and efficiency. Finally, it is indicated how multiclass networks ca n be handled, essentially by reduction to a collection of single class networks.