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This paper studies a two-level modification of the M/M/1 queuing model where the rate of arrival and the service capacity are subject to Poisson alternations. The ensuing “two-dimensional” problem is analyzed by using partial-generating-function techniques, which appear to be essential in the present context. The steady-state probabilities and the expected queue are evaluated, and numerous special and extreme cases are analyzed in detail.
Yechiali et al. (Tue,) studied this question.