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  DOI Prefix   10.20431


 

International Journal of Scientific and Innovative Mathematical Research
Volume 5, Issue 11, 2017, Page No: 32-51

Analysis of Mx/G(a,b)/1 Queueing System with Two Phases of Service Subject to Server Breakdown and Extended Bernoulli Vacations

G.Ayyappan,R.Supraja

1 Department of Mathematics, Pondicherry Engineering College, Pillaichavady, Puducherry, India.
2 Department of Mathematics, Pondicherry Engineering College, Pillaichavady, Puducherry, India.

Citation :G.Ayyappan,R.Supraja, Analysis of Mx/G(a,b)/1 Queueing System with Two Phases of Service Subject to Server Breakdown and Extended Bernoulli Vacations International Journal of Scientific and Innovative Mathematical Research 2017,5(11) : 32-51

Abstract

This paper deals with a batch arrival queueing system with a single server providing two phases of heterogeneous service to a batch of customers with dissimilar service rates. After attainment of two successive phases of service, the server takes the first type of Bernoulli vacation. At the end of Bernoulli vacation, the server has the option to take the second type of extended vacation. Although the server is functioning with any phase of service, it may breakdown at any moment and the service channel will break off for a short period of time. As a result of breakdown, a batch of customers in either phase of service is interrupted, the service channel sent to repair process immediately. The repair process presumed to be general distribution. We derive the probability generating function of the number of customers in the queue at a random epoch in transient and steady state conditions and also we obtained the queue size distribution at a departure epoch under the steady state conditions. Performance measures in the different states of the system, the mean queue size and the average waiting time in the queue are obtained explicitly. Some particular cases are determined. A numerical illustration is given.


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