The optimal control of an Mx/G/1 unreliable server queue with two phases of service and Bernoulli vacation schedule

This paper deals with an M-X/G/1 Bernoulli vacation queue with two phases of service and unreliable server under N-policy. While the server is working with any phase of service, it may break down at any instant and the service channel becomes unavailable. The breakdown period is followed by a delay period. If no customer arrives when the server is unavailable, the server becomes idle in the system until the queue size builds up to a threshold value N(>= 1). As soon as the queue size becomes at least N, the server immediately begins to serve the waiting customers in two successive phases of service. The first phase of service is followed by a second phase, after the completion of which, the server may take a vacation or may remain in the system to serve the next unit, if any. We derive the queue size distribution at a random epoch and at a departure epoch, as well as various system performance measures. Finally, we derive a simple procedure to obtain the optimal stationary policy under a linear cost structure. (C) 2011 Elsevier Ltd. All rights reserved.