Renewal input infinite buffer batch service queue with single exponential working vacation and accessibility to batches

Abstract

This paper considers an infinite buffer single server batch service queue with single exponential working vacation policy. The inter-arrival times are generally independent and identically distributed random variables and the service times are exponential. The server accesses new arrivals even after service has started on any batch of initial number a. This operation continues till the service time of the ongoing batch is completed or the maximum accessible limit d of the batch being served is attained whichever occurs first. The supplementary variable technique and the recursive method are used to develop the steady-state queue length distributions at pre-arrival and arbitrary epochs. Some performance measures and numerical results are discussed. Keywords: accessible batch; non-accessible batch; supplementary variable; batch service; single vacation; working vacation.