A Study on the Queue Length of the State-Dependent of an Unreliable Machine

International Journal of Mathematical Trends and Technology (IJMTT)          
© 2014 by IJMTT Journal
Volume-7 Number-1                          
Year of Publication : 2014
Authors : M.ReniSagaya Raj , B.Chandrasekar , S. Anand Gnanaselvam


M.ReniSagaya Raj , B.Chandrasekar , S. Anand Gnanaselvam. "A Study on the Queue Length of the State-Dependent of an Unreliable Machine", International Journal of Mathematical Trends and Technology (IJMTT). V7:42-49 March 2014. ISSN:2231-5373. www.ijmttjournal.org. Published by Seventh Sense Research Group.

In this paper, we consider a state-dependent queueing system in which the machine is subject to random breakdowns. Jobs arrive at the system randomly following a Poisson process with state-dependent rates. Service times and repair times are exponentially distributed. The machine may fail to operate with probability depending on the number of jobs completed since the last repair. The main result of this paper is the matrix-geometric solution of the steady-state queue length from which many performance measurements such as mean queue length, machine utilization are obtained.


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Laplace transform, Markov chain, Matrix-geometric, Phase-type distribution, Steady-state probability.