Analysis of a finite buffer general input queue with Markovian service process and accessible and non-accessible batch service

Abstract

Queues with Markovian service process ($MSP$) are mainly useful inmodeling and performance analysis of telecommunication networksbased on asynchronous transfer mode (ATM) environment. This paperanalyzes a finite buffer single server batch service ($a, b)$ queuewith general input and Markovian service process ($MSP$). Theserver accesses new arrivals even after service has started on anybatch of initial number $a$. This operation continues till the service time of the ongoing batch is completed or the maximumaccessible capacity $d ~(a\le d < b)$ of the batch being served isattained whichever occurs first. Using the embedded Markov chaintechnique and the supplementary variable technique we obtain thesteady state queue length distributions at pre-arrival and arbitraryepochs. The primary focus is on the various performance measures ofthe steady state distribution of the batch service, special casesand also on numerical illustrations.