• PERFORMANCE MEASURES OF VARIANT WORKING VACATIONS ON BATCH ARRIVAL QUEUE WITH RENEGING

Abstract

This paper analyzes a batch arrival infinite-buffer single server queueing system with variant working vacations wherein customers arrive according to a Poisson process. As soon as the system becomes empty, the server takes working vacation. The service times during regular busy period, working vacation period and vacation times are assumed to be exponentially distributed and are mutually independent. During working vacations the customer may renege and the reneging time follows exponential distribution. We derive the probability generating function of the steady-state probabilities and obtain the closed form expressions of the system size when the server is in different states. In addition, we obtain some other performance measures and discuss their monotonicity. A cost model is formulated to determine the optimal service rate during working vacation and regular busy period.