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Analysis of discrete-time queues with correlated arrivals, negative customers and server interruption. (English) Zbl 1335.60175

Summary: This paper analyses a discrete-time infinite capacity queueing system with correlated arrival and negative customers served by a two-state Markovian server. Positive customers are generated according to the first order Markovian arrival process with geometrically distributed lengths of On periods and Off periods. Further, the geometrically distributed arrival of negative customers removes the positive customers, if any, and has no effect when the system is empty. The server state is a two-state Markov chain which alternates between good and bad states with geometrically distributed service times. Closed-form expressions for mean queue length, unfinished work and sojourn time distributions are obtained. Numerical illustrations are also presented.

MSC:

60K25 Queueing theory (aspects of probability theory)
90B22 Queues and service in operations research
68M20 Performance evaluation, queueing, and scheduling in the context of computer systems
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