Analysis of infinite buffer general bulk service queue with state dependent balking

Abstract

This paper investigates the effect of impatient phenomena of the arriving customers in a bulk service queue, where inputs are flowing into the system according to the Poisson process and are served in groups according to the 'general bulk service' (GBS) rule. The service time of a group of customers follows exponential distribution. On arrival, a customer decides whether to join or balk the system, based on the observation of the system size and status of the server, i.e., whether server is busy or idle. The steady state joint probability distribution of the number of customers in the queue as well as with the server is obtained by using the probability generating function method, which is based on the roots of the characteristic equations formed using probability generating function for steady state joint probabilities. Finally, various performance measures, such as, average queue length, average waiting time, probability that the server is busy, average queue length when server is busy, etc., have been obtained. The paper ends with several numerical discussions to demonstrate the effect of certain model parameters on the key performance measures.