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

摘要

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 a 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 (1954), 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. (Author)