The wait in a GI/M/k queue is bounded above (stochastically) by the wait in an associated GI/M/1 queue. The analysis of the single server queue is considerably easier than that of the k-server queue, and also the bounds developed for single server queues by J. F. C. Kingman and Kneale T. Marshall can be applied.
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Shelby L. Brumelle (1973) studied this question.
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