This paper considers an infinite buffer single server accessible and non-accessible batch service queue with single and multiple exponential vacations, which has a wide range of applications in several areas including manufacturing and communication systems. The inter-arrival times are general independent and identically distributed random variables and the service times are exponential. We provide a recursive method, using the supplementary variable technique and treating the remaining inter-arrival time as the supplementary variable, to develop the steady-state queue length distributions at pre-arrival and arbitrary epochs. Some numerical results are presented in the form of self explanatory tables and graphs. Moreover, some queueing models discussed in the literature are derived as special cases of our model.

batch service, vacations, accessible batch, non-accessible batch, queue, infinite buffer.