Balking and reneging in a vacation queueing model

Abstract

We study a single server queueing system in which arrivals follow a compound Poisson process and the service times of customers have exponential distribution. The system is subject to server vacations occuiring randomly in time and in addition the impatient customers resort to balking and reneging during the server's vacation period. The steady state probability generating functions for the system when the server is available or on vacation have been obtained explicitly as also the average number in the system. Various particular cases of interest have also been derived.