ANALYSES OF AN M/M/N QUEUE WITH SERVERS VACATIONS

Consider an M/M/N queueing system. A server that completes service and finds no waiting customers leaves for a vacation whose length follows an exponential distribution. A server returning to an empty queue takes another vacation. In this paper, we present a matrix-geometric approach for modelling the system and propose algorithms for computing the stationary queue length distribution, the expected length of busy period, the mean waiting time, and the waiting time distribution. Two numerical examples are given at the end.