Transient solution for a finite capacity M/G a,b /1 queueing system with vacations to the server

In this paper we consider a single server queueing system with Poisson input, general service and a waiting room that allows only a maximum of b customers to wait at any time. A minimum of a customers are required to start a service and the server goes for a vacation whenever he finds less than a customers in the waiting room after a service. If the server returns from a vacation to find less than a customers waiting, he begins another vacation immediately. Using the theory of regenerative processes we derive expressions for the time dependent system size probabilities at arbitrary epochs.