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By using a probabilistic equivalence between the M/G/1 queue with multiple server ’ vacations and the M/M/c system, we derive the Laplace-Stieltjes transform of the waiting time Wk, of a class-k customer in the non-preemptive priority M/M/c queue where all customers have the same mean service time. We also calculate the first two moments of Wk.
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Kella et al. (1985) studied this question.
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