Optimization of balking and reneging queue with vacation interruption under \(N\)-policy (Q896729)

Summary: This paper analyzes a finite buffer multiple working vacations queue with balking, reneging, and vacation interruption under \(N\)-policy. In the working vacation, a customer is served at a lower rate and at the instants of a service completion; if there are at least \(N\) customers in the queue, the vacation is interrupted and the server switches to regular busy period otherwise continues the vacation. Using Markov process and recursive technique, we derive the stationary system length distributions at arbitrary epoch. Various performance measures and some special models of the system are presented. Cost analysis is carried out using particle swarm optimization and quadratic fit search method. Finally, some numerical results showing the effect of model parameters on key performance measures of the system are presented.