Optimal Control of Mx/H2/1 Queue with a Removable and Non-Reliable

A single removable and non-reliable server in both an infinite and a finite queueing system with compound Poisson arrivals and two-type hyper-exponential distribution for the service times is considered in this paper. The server may be turned on at arrival epochs or off at service completion epochs. Breakdown and repair times of the server are assumed to followαnegative exponential distribution. Conditions for a stable queueing system, that is steady-state, are provided. Cost models for both system capacities are respectively developed to determine the optimal operating policy numerically at minimum cost. This paper provides the minimum expected cost and the optimal operating policy based on assumed numerical values given to the system parameters, as well as to the cost elements. Sensitivity analysis is also investigated