Steady-State Algorithmic Analysis of M/M/c Two-Priority Queues with Heterogeneous Rates

Abstract

An algorithm for steady-state analysis of M/M/c nonpreemptive two-priority queues with heterogeneous rates is presented. It is based on a computational analysis à la Neuts which exploits a partition of the full state space into blocks. Both M/G/1 and GI/M/1 paradigm block structures arise and are exploited in the analysis. The mean number of waiting customers and the mean delay for each priority class are calculated. This gives a partial solution to the “Probabilistic puzzler” posed by D. P. Heyman in the fall 1977 issue of Applied Probability Newsletter, and extends a result of A. Cobham [Operations Research 2 (2954), 70–76] to two-priority queues with unequal service rates. In addition, the probabilities of individual states are computed. The algorithm has been programmed and some examples computed for nonpreemptive systems with five servers.

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