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The M/G/1 retrial queue with Bernoulli schedule. (English) Zbl 0706.60089
Summary: We consider an M/G/1 retrial queue with infinite waiting space in which arriving customers who find the server busy join either (a) the retrial group with probability p in order to seek service again after a random amount of time, or (b) the infinite waiting space with probability \(q(=1- p)\) where they wait to be served.
The joint generating function of the numbers of customers in the two groups is derived by using the supplementary variable method. It is shown that our results are consistent with known results when \(p=0\) or \(p=1\).

MSC:
60K25 Queueing theory (aspects of probability theory)
90B22 Queues and service in operations research
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