Mean value analysis by chain of product form queueing networks

Abstract

A computational algorithm is developed for closed multichain product-form queueing networks. For networks that consist of only single-server fixed rate and infinite-server service centers, it involves only mean performance measures. The algorithm, called mean value analysis by chain (MVAC), is based on a recursion that is quite different in form from the recursion used in the well-known mean value analysis (MVA) algorithm and has quite different computational and storage costs. For networks with few service centers and many chains, MVAC typically has much lower costs than MVA, although it becomes more costly than MVA as the number of service centers increases. The MVAC recursion is similar in structure to a recursion involving normalizing constants that was derived by A.E. Conway and N.D. Georganas (1986). That recursion formed the basis for their recursion by chain (RECAL) algorithm for computing the normalizing constant and from it the mean performance measures. The computational and storage costs for MVAC are shown to be similar to those for RECAL. >