Analysis of Finite Buffer Renewal Input Queue with Balking and Markovian Service Process

This paper presents the analysis of a finite buffer renewal input queue wherein the customers can decide either to join the queue with a probability or to balk. The service process is Markovian service process (MSP ) governed by an underlying m-state Markov chain. Employing the supplementary variable and embedded Markov chain techniques, the steady-state system length distributions at pre-arrival and arbitrary epochs are obtained. Based on the system length distributions, some performance measures of the model and waiting-time analysis are presented. Finally, numerical results are displayed to show the effect of model parameters on the key performance measures.