Repairable Queue with Non-exponential Interarrival Time and Variable Breakdown Rates


Koh, Siew Khew and Chin, Ching Herny and Tan, Yi Fei and Pooi, Ah Hin and Goh, Yong Kheng and Lee, Min Cherng and Ng, Tan Ching (2018) Repairable Queue with Non-exponential Interarrival Time and Variable Breakdown Rates. International Journal of Engineering & Technology, 7 (2.15). pp. 76-80. ISSN 2227-524X

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This paper considers a single server queue in which the service time is exponentially distributed and the service station may breakdown according to a Poisson process with the rates γ and γ' in busy period and idle period respectively. Repair will be performed immediately following a breakdown. The repair time is assumed to have an exponential distribution. Let g(t) and G(t) be the probability density function and the cumulative distribution function of the interarrival time respectively. When t tends to infinity, the rate of g(t)/[1 – G(t)] will tend to a constant. A set of equations will be derived for the probabilities of the queue length and the states of the arrival, repair and service processes when the queue is in a stationary state. By solving these equations, numerical results for the stationary queue length distribution can be obtained.

Item Type: Article
Uncontrolled Keywords: Interarrival Time, Constant Asymptotic Rate, Stationary Queue Length Distribution, Repairable Queue
Subjects: Q Science > QC Physics > QC 1-75 General
Divisions: Faculty of Engineering (FOE)
Depositing User: Ms Rosnani Abd Wahab
Date Deposited: 16 Mar 2021 19:40
Last Modified: 16 Mar 2021 19:40


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