Product Form and Local Balance in Queueing Networks

Abstract

A new property of queueing discipline, station balance, seems to explain why some disciplines yield product form solutions for queues and networks using nonexponential service disciplines and other disciplines do not. A queueing discipline satisfies station balance if rates at which customers receive service at each position of the queue are proportional to the probability that a customer arrives at that position. Station and local balance in queues and networks of queues are investigated. In addition to characterizing local balance and product form, the results of the paper generalize previous results on local balance to arbitrary differentiable service distribution functions.