A Recursive Algorithm for State Dependent GI/M/1/N Queue with Bernoulli-Schedule Vacation

Abstract

In this paper, we study a renewal input working vacations queue with state dependent services and Bernoulli-schedule vacations. The model is analyzed with single and multiple working vacations. The server goes for exponential working vacation whenever the queue is empty and the vacation rate is state dependent. At the instant of a service completion, the vacation is interrupted and the server resumes a regular busy period with probability 1 − q (if there are customers in the queue), or continues the vacation with probability q (0 ≤ q ≤ 1). We provide a recursive algorithm using the supplementary variable technique to numerically compute the stationary queue length distribution of the system. Finally, using some numerical results, we present the parameter effect on the various performance measures.