Abstract
We consider a queueing system consisting of multiple identical servers and a common queue. The service time follows an exponential distribution and the batch arrival process is governed by a semi-Markov process (SMP). Our analysis is based on the theory of piecewise Markov process. We derive the distributions of the queue size and the waiting time. When the sojourn time of SMP follows an exponential distribution all the unknown constants contained in the generating function of queue size can be determined through the zeros of the denominator for this generating function. A numerical example is shown.
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