A Study on a Single Server Batch Arrival General Bulk Service Queueing System

Abstract

Abstract

This paper deals with the transient and steady state behavior of a single server batch arrival bulk service queueing system. A batch of customers arrives according to a Poisson process, whereas the bulk service is rendered by a single server with a minimum batch size of ‘a’ and maximum of ‘b’. The service time follows a general distribution. Probability generating function of the distributions  and , under equilibrium has been derived by using the supplementary variable technique. The time dependent probability generating function has been obtained in terms of their Laplace transforms and the corresponding steady state results have been obtained explicitly. Expected number of customers in the queue and the expected waiting time are derived. Some particular cases are discussed.

Keywords: Batch arrival, bulk service, supplementary variable, imbedded Markov chain, mean queue length, mean waiting time

Cite this Article

Ayyappan G, Nirmala M, Supraja R. A Study on a Single Server Batch Arrival General Bulk Service Queueing System. Current Trends in Information Technology. 2017; 7(3): 1–8p.