The discrete-time \(Geo/Geo/1\) queue with negative customers and disasters. (English) Zbl 1107.90330

Summary: The arrival of a negative customer to a queueing system causes one ordinary customer to be removed (or killed) if any is present. The arrival of a disaster, on the other hand, kills all the customers in the system if any. In this paper, we extend the queueing theory on negative arrivals and disasters to the discrete-time \(Geo/Geo/1\) queueing system. Specifically, we find the ergodicity condition and give explicit formulae for the stationary distribution. We also provide some numerical results to illustrate the effect of the parameters on several performance characteristics.


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