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

  • Authors

    • Koh Siew Khew
    • Chin Ching Herny
    • Tan Yi Fei
    • Pooi Ah Hin
    • Goh Yong Kheng
    • Lee Min Cherng
    • Ng Tan Ching
    2018-04-06
    https://doi.org/10.14419/ijet.v7i2.15.11218
  • Interarrival Time, Constant Asymptotic Rate, Stationary Queue Length Distribution, Repairable Queue.

  • Abstract

    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.

     

  • References

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  • How to Cite

    Siew Khew, K., Ching Herny, C., Yi Fei, T., Ah Hin, P., Yong Kheng, G., Min Cherng, L., & Tan Ching, N. (2018). Repairable Queue with Non-exponential Interarrival Time and Variable Breakdown Rates. International Journal of Engineering & Technology, 7(2.15), 76-80. https://doi.org/10.14419/ijet.v7i2.15.11218

    Received date: 2018-04-06

    Accepted date: 2018-04-06

    Published date: 2018-04-06