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.

  • 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

    1. [1] Avi-Itzhak B & Naor P (1963), “Some queuing problems with the service station subject to breakdownâ€, Operations Research, Vol. 11, No. 3, pp. 303-322.

      [2] Fischer MJ (1977), “An Approximation to Queueing Systems with Interruptionsâ€, Management Science, Vol. 24, No. 3, pp. 338-344.

      [3] Gray WJ, Wang PP & Scott M (2000), “A vacation queueing model with service breakdownsâ€, Applied Mathematical Modelling, Vol. 24, No. 5-6, pp. 391-400.

      [4] Koh SK, Pooi AH & Tan YF, “Repairable Queue with Non-exponential Service Time and Variable Breakdown Rates†in International Conference on Mathematics, Engineering & Industrial Applications, Gurney Resort Hotel & Residences, Penang, 2014.

      [5] Koh SK (2013), “Maintenance of Deteriorating Non-Exponential Single Server Queueâ€, PhD Thesis, University of Malaya.

      [6] Li H & Zhu Y (1994), “A New Approach to G/G/1 Queues with Generalized. Setup Time and Exhaustive Serviceâ€, Journal of Applied Probability, Vol. 31, No. 4, pp. 1083-1097.

      [7] Sheng-li LV, Jing-bo L & De-quan Y, “The M/M/1 repairable queueing system with variable breakdown rates (Published Conference Proceedings style),†in Proc. 21th Annu. IEEE Conf. Chinese Control and Decision Conference, Guilin, China, 2009, pp. 2635-2637

      [8] Sheng-li LV & Jing-bo L, Discrete Dynamics in Nature and Society, Vol. 2013, pp. 1-10, 2013.

      [9] Vinod B & Altiok T (1986), “Approximating Unreliable Queueing Networks Under the Assumption of Exponentialityâ€, The Journal of the Operational Research Society, Vol. 37, No. 3, pp. 309-316.

      [10] White HC & Christie LS (1958), “Queueing with preemptive priorities or with breakdownsâ€, Operations Research, Vol. 6, pp. 79-95.

      [11] Yang XL & Alfa AS (2009), “A class of multi-server queueing system with server failuresâ€, Computers & Industrial Engineering, Vol. 56, No. 1, pp. 33-43.

  • Downloads

  • 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