Control Policies of an M/G/1 Queueing System with a Removable and Non-reliable Server

This paper considers a single non-reliable server in the ordinary M/G/1 queueing system whose arrivals form a Poisson process and service times are generally distributed. We also study a single removable and non-reliable server in the controllable M/G/1 queueing systems operating under the N policy, the T policy and the Min( N , T ) policy. It is assumed that the server breaks down according to a Poisson process and the repair time has a general distribution. In three control policies, we show that the probability that the server is busy in the steady-state is equal to the traffic intensity. It is shown that the optimal N policy and the optimal Min( N , T ) policy are always superior to the optimal T policy. Sensitivity analysis is also investigated.