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A single server Poisson input queue with a second optional channel. (English) Zbl 1011.60072
Summary: Consider an M/G/1 queue such that over and above the first ‘essential service’ having a general service time distribution, a unit may need a second ‘optional service’ with another independent general service time. A unit may depart from the system either after the first essential service with probability $$(1-r)$$ or at the end of the first service may immediately go for a second service with probability $$r$$ ($$0\leq r\leq 1$$). This is a generalization of a recent paper by Madan.

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