Asymptotic properties of queuing networks

Abstract

A new approach to the analysis of asymptotic properties of closed queuing networks with both constant service rates and, in certain cases, load-dependent service rates is developed. The method is based on a decomposition of the generating function of the normalising constant into simpler node functions which are easily inverted term by term. An exact closed form is obtained for the normalising constant in some cases and an approximation, based on an integral formula, in others. These results are applied to model a large computer system with terminals, which is also used to illustrate the main properties of the normalising constant and the system throughput function as the population increases. The authors' method is compared with others in terms of both accuracy and efficiency. Finally, it is indicated how multiclass networks can be handled, essentially by reduction to a collection of single class networks.