Measures Of Effectiveness Of M/M/1 Queue with Balking And Probabilistically Modified Reneging

Abstract

In this paper, a peculiar behavior of a customer in the queue during differentiated vacations has been studied to amount further influence on the effectiveness measures of the queue under consideration. Reneging behavior of a customer has been probabilistically modified. To solve the complex problem, a group of methods of generating functions, continued fractions and a special generalized (namely, confluent) hypergeometric function has been used in this paper. Time dependent effectiveness measures--mean, variance, system throughput and delay time--have been obtained for the queueing model under discussion. This work intends to constitute an improvement over the model attempted by our previous  authors Vijayashree and Janani (28).