Conditional stochastic decompositions in the M/M/c queue with server vacations

Abstract

We consider the M/M/c queue with server multiple vacations, where each of the c servers leaves for a vacation of an exponentially distributed duration when it finds no waiting units in line. If the server returns to an empty waiting line, it immediately takes another vacation. This paper is concerned with the upper triangular structure of the rate matrix R and the determination of the stationary distributions of queue length and waiting time. The emphasis is on obtaining the conditional stochastic decompositions of the stationary queue length and waiting time conditioned by the event , where denotes the event that all of the c servers are busy