Calculating joint queue length distributions in product form queueing networks

Abstract

We develop a new computational algorithm called Distribution Analysis by Chain (DAC) which computes joint queue length distributions for product form queuening networks with single server fixed rate, infinite server and queue dependent service centers. Joint distributions are essential in problems such as the calculation of avaliability measures using queueing network models. The algorith is efficient since the cost to evaluate joint queue length probabilities is of the same order as the number of these probabilities. This contrasts with the cost of evaluating these probabilities using previous algorithms. The DAC algorithm also computes mean queue lengths and throughputs more efficiently than the recently proposed RECAL and MVAC algorithms. Furthermore, the algorithm is numerically stable and its recursion is surprisingly simple.