Transient solution for a finite capacity M/Ga’,b/1 vacation system with Bernoulli schedules

In this paper, the authors consider a single server queueing system with Poisson input, general batch service and a waiting room of finite capacity. Whenever there are less than ‘a’ customers in the system, the server goes for vacation for a random length of time. When vacation is completed and at least ‘a’ customers are present, a batch is taken for service. When a batch has just been served and if there are at least ‘a’ customers in the system, server accepts the batch with probability p or commences a vacation of random duration with probability 1-p. Using the theory of regenerative process, the authors derive explicit expressions for the time dependent system size probabilities at arbitrary epochs.