Performance analysis of finite buffer discrete-time queue with bulk service

Abstract

Discrete-time queues are extensively used in modelling the ATM environment at the cell level. In this paper, we model a single-server queue with finite buffer space in a discrete-time environment where the services are performed in batches of maximum size ‘b’ with a minimum threshold value ‘a’. The analytic analysis of the model is carried out for the both arrival first (AF) and departure first (DF) management policies and distributions of buffer content at various epochs have been obtained. The system performance measures such as average buffer content, average delay and probability of blocking are discussed. A comparative study of AF and DF management policies on certain performance measures is also presented. Scope and purpose B-ISDN and in particular ATM networks are designed in order to transfer and switch all type of information services such as voice, data and video communications. As these systems operate on a discrete-time basis, many classical results of queuing theory which are used in performance analysis cannot be applied and hence require a fresh investigation. The purpose of this paper is to analyse a discrete-time finite buffer queue with general bulk service rule which may be useful to system designers and other practitioners involved in investigating the performance of communication systems based on B-ISDN.