# Mean Value Analysis by Chain of Product Form Queueing Networks

## Abstract

We develop a new computational algorithm for closed multichain product form queueing networks. For networks that consist of only single server fixed rate and infinite server service centers, the algorithm 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 wellknown mean value analysis (MVA) algorithm and MVAC has quite different computational and storage costs than MVA. 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 new recursion involving normalizing constants that was recently derived by Conway and Georganas. That recursion formed the basis for their recursion by chain (RECAL) algorithm for computing the normalizing constant and from it the mean performance measures. Since MVAC does not compute the normalizing constant, it avoids the potential floating point underflow/overflow problems that would complicate the implementation of RECAL. Furthermore, the recursion used in MVAC is derived by purely probabilistic arguments which makes it pedagogically appealing. The computational and storage costs for MVAC are similar to those for RECAL. © 1989 IEEE