Analysis of single server finite queueing model with reneging

Abstract

The present investigation deals with the analysis of Markovian queueing model with finite capacity and finite population wherein the server works in fast and slow random environments, depending on the status of service system, with exponential distributed time parameters. On arrival of the customer in slow mode, the exponential distributed time may be fixed. Due to the impatient behaviour (reneging), the customer may leave the queue after some time of joining the system if the server does not change its state before expiry of the timer. To discuss the behaviour of the queue length distribution and to obtain the transient solution, Runge-Kutta method of the fourth order is used. Various performance measures are determined in terms of transient probabilities of the system states. The numerical illustrations are facilitated to validate the tractability of performance measures as far as computational aspect is concerned.