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

M.ReniSagaya Raj; B.Chandrasekar; S. Anand Gnanaselvam

doi:https://doi.org/10.14445/22315373/IJMTT-V7P506

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 7 | Number 1 | Year 2014 | Article Id. IJMTT-V7P506 | DOI : https://doi.org/10.14445/22315373/IJMTT-V7P506

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

M.ReniSagaya Raj , B.Chandrasekar , S. Anand Gnanaselvam

Citation :

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 Mathematics Trends and Technology (IJMTT), vol. 7, no. 1, pp. 42-49, 2014. Crossref, https://doi.org/10.14445/22315373/IJMTT-V7P506

Abstract

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.

Keywords

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

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