The analysis of a finite-buffer general input queue with batch arrival and exponential multiple vacations

Vacation queueing models have wide range of application in several areas including computer-communication, and manufacturing systems. A finite-buffer single-server queue with renewal input and multiple exponential vacations has been analysed by Karaesmen and Gupta. In this paper we extend the analysis to cover the batch arrivals, i.e. we consider a batch arrival single-server queue with renewal input and multiple exponential vacations. Using the imbedded Markov chain and supplementary variable techniques we obtain steady-state distribution of number of customers in the system at pre-arrival and arbitrary epochs. The Laplace–Stieltjes transforms of the actual waiting-time distribution of the first-, arbitrary- and last-customer of a batch under First-Come-First-Serve discipline have been derived. Finally, we present useful performance measures of interest such as probability of blocking, average queue (system) length. Some tables and graphs showing the effect of model parameters on key performance measures are presented.