ANALYSIS OF FINITE BUFFER RENEWAL INPUT QUEUE WITH BALKING AND MARKOVIAN SERVICE PROCESS

Subject Areas : International Journal of Mathematical Modelling & Computations

Vijaya Laxmi Pikkala ¹ ( )
Jyothsna Kanithi ² ( )

Received: 2016-04-15 Accepted : 2016-04-15 Published : 2015-03-21

Keywords: Finite buffer, Queue, Markovian service process, balking, Waiting-time,

Abstract :

This paper presents the analysis of a renewal input finite buffer queue wherein the customers can decide either tojoin the queue with a probability or balk. The service process is Markovian service process ($MSP$) governed by anunderlying $m$-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 thesystem 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.