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.