An analysis of the M $$^X$$ X /M/1 queue with multiple working vacations by GI/M/1 type Markov process

Abstract

In this paper, we analyze an M/M/1 queue with batch arrival and multiple working vacations. We describe the queueing model by a special GI/M/1 type Markov process with infinite phases, and by the matrix analytic method, we not only give the stationary queue length distribution of the model, but also obtain the exact number of vacations completed by the server.