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 in modeling and performance analysis of telecommunication networks based on asynchronous transfer mode (ATM) environment. This paper analyzes a finite buffer single server batch service (a, b) queue with general input and Markovian service process (MSP). 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 capacity d (a d < b) of the batch being served is attained whichever occurs first. Using the embedded Markov chain technique and the supplementary variable technique we obtain the steady state queue length distributions at pre- arrival and arbitrary epochs. The primary focus is on the various performance measures of the steady state distribution of the batch service, special cases and also on numerical illustrations.