The Mathematics of Product form Queuing Networks

Abstract

Markov processes that have a product form solution have become an important computer performance modeling tool. The fact that such a simple solutlon exists for seemingly complex Markov processes M surprlsmg at first encounter and can be established by showing that balance equations are satisfied. In this article we attempt to provide insight as to why such a solution form exists and demonstrate that product form and compamon results, such as the arrwal theorem and Norton�s theorem, are consequences of four properties satisfied by queues that satisfy partial balance Notions of reverse processes, reversibility, and quasireversibility are developed to establish the four properties. © 1993, ACM. All rights reserved.