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An approximation method for tandem queues with blocking. (English) Zbl 0643.90026
We propose an approximate analysis of open systems of tandom queues with blocking caused by finite buffers between servers. Our approach relies on the use of marginal probability distributions (“state equivalence”) coupled with an approximate evaluation of the conditional probabilities introduced through the equivalence. The method iterates over consecutive pairs of servers using the solution of a two-queue system as a building block. It produces performance measures for individual servers as well as an approximation to joint queue-length probability distributions for pairs of neighboring stations. Experience indicates that the number of iterations required for the method grows moderately with the number of nodes in the network. We give examples to demonstrate the accuracy and the convergence properties of the proposed approximation.

MSC:
90B22 Queues and service in operations research
60K25 Queueing theory (aspects of probability theory)
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