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 an M/E k /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/ c β and Erlang with mean 1/ c β, respectively. Generating functions are used to derive the steady‐state quantities L and W , both of which, when viewed as functions of c , decrease at a rate inversely proportional to c 2 . The paper includes an analysis of several special and extreme cases and an application to a production‐storage system.