Impatient customer queue with Bernoulli schedule vacation interruption

This paper deals with an infinite buffer M/M/1 queue with working vacations and Bernoulli schedule vacation interruption wherein the customers balk with a probability. Whenever the system becomes empty, the server takes a working vacation during which service is provided with a lower rate and if there are customers at a service completion instant, vacation is interrupted and the server resumes a normal working period with probability q or continues the vacation with probability 1−q. The service times during working vacation and vacation times are assumed to be exponentially distributed. During a working vacation customers may renege due to impatience. The closed form expressions of the steady-state probabilities and the performance measures of the model are obtained using generating functions. Various numerical results are presented to show the effect of the model parameters on the system performance measures.