The mathematics of product form queuing networks

Markov processes that have a product form solution have become an important computer performance modeling tool. The fact that such a simple solution exists for seemingly complex Markov processes is surprising 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 companion results, such as the arrival 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