Analysis of Discrete-Time Single Server Queue with Balking and Multiple Working Vacations

This paper analyzes a discrete-time single server queueing system with balking and multiple working vacations. The arriving customers balk (that is, do not join the queue) with a probability. The inter-arrival times of customers are assumed to be independent and geometrically distributed. The server works at a different rate rather than completely stopping service during vacations. The service times during a service period, service times during a vacation period and vacation times are assumed to be geometrically distributed. We obtain the closed form expressions for the steady-state probabilities at arbitrary and outside observer's observation epochs. Computational experiences with a variety of numerical results are discussed in the form of tables and graphs. Moreover, some queueing models discussed in the literature are derived as special cases of our model.