Analysis of Queuing Model for Machine Repairing System with Bernoulli Vacation Schedule

 International Journal of Mathematical Trends and Technology (IJMTT) © 2014 by IJMTT Journal Volume-10 Number-2 Year of Publication : 2014 Authors : R.K. Shrivastava , Awadhesh Kumar Mishra 10.14445/22315373/IJMTT-V10P514

R.K. Shrivastava , Awadhesh Kumar Mishra. "Analysis of Queuing Model for Machine Repairing System with Bernoulli Vacation Schedule", International Journal of Mathematical Trends and Technology (IJMTT). V10:85-92 June 2014. ISSN:2231-5373. www.ijmttjournal.org. Published by Seventh Sense Research Group.

Abstract
In this paper, we consider a queueing model for machine repairing system with Bernoulli vacation schedule. The failure times, repair times and vacation times are all assumed to be exponentially distributed. In congestion, the server may increase the repair rate with pressure coefficient  to reduce the queue length. We assume that the server begins the working vacation when the system is empty. The server may go for a vacation of random length with probability p or may continue to repair the next (if available) failed machine with probability q = 1  p. The whole system is modelled as a finite state Markov Chain and its steady state distribution is obtained by matrix recursive approach.

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Keywords
Machine repair, Bernoulli vacation, pressure coefficient, Markov Chain, Matrix-recursive method.