Calculating joint queue-length distributions in product-form queuing networks

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Abstract
A new computational algorithm called distribution analysis by chain (DAC) is developed. This algorithm computes joint queue-length distributions for product-form queuing networks with single-server fixed rate, infinite server, and queue-dependent service centers. Joint distributions are essential in problems such as the calculation of availability measures using queuing network models. The algorithm 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.