Analysis of variant working vacations queue with reneging

Abstract

In this paper, we study a single server queueing system with variant working vacations wherein customers arrive according to a Poission process. The server takes variant working vacations as soon as the system becomes empty. The service time during regular busy period, working vacation period and vacation times are assumed to be exponentially distributed and are mutually independent. During working vacation customer may renege due to impatience which follows exponential distribution. The steady state probabilities of number in the system are obtained using matrix geometric method. Numerical investigations showing the effect of model parameters on different performance measures are shown through tables and graphs. An optimization of cost function is performed to find the optimal service rate that minimizes the cost function.