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Stochastic analysis of the departure and quasi-input processes in a versatile single-server queue. (English) Zbl 0858.60083
Summary: This paper is concerned with the stochastic analysis of the departure and quasi-input processes of a Markovian single-server queue with negative exponential arrivals and repeated attempts. Our queueing system is characterized by the phenomenon that a customer who finds the server busy upon arrival joins an orbit of unsatisfied customers. The orbiting customers form a queue such that only a customer selected according to a certain rule can reapply for service. The intervals separating two successive repeated attempts are exponentially distributed with rate $$\alpha + j\mu$$, when the orbit size is $$j\geq 1$$. Negative arrivals have the effect of killing some customer in the orbit, if one is present, and they have no effect otherwise. Since customers can leave the system without service, the structural form of type M/G/1 is not preserved. We study the Markov chain with transitions occurring at epochs of service completions or negative arrivals. Then we investigate the departure and quasi-input processes.

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