Optimization of Balking and Reneging Queue with Vacation Interruption under -Policy

This paper analyzes a finite buffer multiple working vacations queue with balking, reneging, and vacation interruption under -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 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. 1. Introduction Performance modeling of queueing systems with balking and reneging has attracted many researchers owing to their wide applications in real life congestion problems such as impatient telephone switchboard customers, hospital emergency rooms handling critical patients and perishable goods storage in inventory systems. Balking and reneging are a common phenomena in queues; as a consequence, the customers either decide not to join the queue or depart after joining the queue without getting service due to impatience. Modeling balking and reneging is worthwhile because one obtains new managerial insights. The lost revenues due to balking and reneging in various industries can be enormous. While making decision for the number of servers needed in the service system to meet time-varying demand, the balking and reneging probabilities can be used to estimate the amount of lost business in more practical consideration for the managers as given in Liao [1]. Impatience is the most prominent characteristic as individuals always feel anxious and impatient during waiting for service in real life. The customer's impatient acts should be involved in the study of queueing system to model real situations exactly. Intermittent operation of a service can be economically appealing whenever full time service would result in significant server idle time or would preclude the use of the server in some other productive capacity. On the other hand, having the server inoperative for periods of time may increase the probability of customer losses due to balking and reneging. An queue with customers balking and reneging has been discussed in Haight [2] and Haight [3], respectively. The combined impact of balking and reneging with finite capacity in an queue has