M/M/1 queueing system with non-reliable server and threshold-based recovery

|In this paper we consider an M=M=1 queueing system with non-reliable server. When the server is in normal state, the service error (or failure) occurs according to a Poisson process. In the error state, the server needs to be repaired at a repair facility with exponen- tial repair time according to the threshold policy. The repair starts only when the number of customers in the system reaches some prespeci¯ed threshold level q>=1. We perform a steady- state analysis of the continuous-time Markov chain describing the system behavior and calculate optimal threshold level to minimize the long-run average losses given by the cost structure.