Graphical Solution and Busy Period Analysis of a Queueing Model with Feedback and Reneging

Abstract

In the present paper, a busy period of feedback queueing model is studied. The busy period is, to begin with, the arrival of the customer to an idle system and to an end when the system next becomes idle. The customers arrive according to the Poisson process and are served by a single server according to an exponential distribution. Sometimes the customers get impatience and leave the queue without getting service with a fixed probability. The probability generating a function of a busy period by using Laplace transformation and the graphical solution of the problem is obtained. Few interesting cases are also derived to match our results with earlier published work.