The optimal control of an [formula omitted] unreliable server queue with two phases of service and Bernoulli vacation schedule

Abstract

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.