An Approach to Analyzing the Behavior of Some Queueing Networks

Abstract

Several researchers have reported difficulties in analyzing the behavior of single queues and networks of queues. This is so even in the case of closed product-form networks, for which an exact solution and efficient solution algorithms are known. The difficulty arises because the exact solution could not, by itself, be used for such analysis as proving properties of the network, relating performance measures to one another, and characterizing some interesting behavior. This paper proposes an approach to surmounting such difficulties. The idea is to analyze an approximate solution based on Schweitzer's approximation, and interpret the results as approximate relationships among the exact performance measures. This approach is applied to three problems concerning the interaction among job classes, the mean arrival and variance of queue length, and thrashing. The reliability of the approach is tested by applying it to an optimal routing problem, for which the exact solution is known. The results are illustrated with problems drawn from computer systems.