A single server queue with arrival rate dependent on server breakdowns

Abstract

Abstract This paper considers a single server queueing system that alternates stochastically between two states: operational and failed. When operational, the system functions as anM/Ek/1 queue. When the system is failed, no service takes place but customers continue to arrive according to a Poisson process; however, the arrival rate is different from that when the system is operational. The durations of the operating and failed periods are exponential with mean 1/cβ and Erlang with mean 1/cβ, respectively. Generating functions are used to derive the steady‐state quantitiesLandW, both of which, when viewed as functions ofc, decrease at a rate inversely proportional to c2. The paper includes an analysis of several special and extreme cases and an application to a production‐storage system.

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