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

This paper presents the analysis of a renewal input finite buffer queue wherein the customers can decide either to join the queue with a probability or balk. The service process is Markovian service process ($MSP$) governed by an underlying $m$-state Markov chain. Employing the supplementary variable and imbedded 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.