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Optimal Control of an M/G/1/K Queueing System with Combined F Policy and Startup Time

Author

Listed:
  • K.-H. Wang

    (National Chung-Hsing University)

  • C.-C. Kuo

    (National Chiao Tung University)

  • W. L. Pearn

    (National Chiao Tung University)

Abstract

We investigate the optimal management problem of an M/G/1/K queueing system with combined F policy and an exponential startup time. The F policy queueing problem investigates the most common issue of controlling the arrival to a queueing system. We present a recursive method, using the supplementary variable technique and treating the supplementary variable as the remaining service time, to obtain the steady state probability distribution of the number of customers in the system. The method is illustrated analytically for exponential service time distribution. A cost model is established to determine the optimal management F policy at minimum cost. We use an efficient Maple computer program to calculate the optimal value of F and some system performance measures. Sensitivity analysis is also investigated.

Suggested Citation

  • K.-H. Wang & C.-C. Kuo & W. L. Pearn, 2007. "Optimal Control of an M/G/1/K Queueing System with Combined F Policy and Startup Time," Journal of Optimization Theory and Applications, Springer, vol. 135(2), pages 285-299, November.
    • Handle: RePEc:spr:joptap:v:135:y:2007:i:2:d:10.1007_s10957-007-9253-6
    DOI: 10.1007/s10957-007-9253-6
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    References listed on IDEAS

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    1. Kimura, Toshikazu, 1981. "Optimal control of an M/G/1 queuing system with removable server via diffusion approximation," European Journal of Operational Research, Elsevier, vol. 8(4), pages 390-398, December.
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    3. Jau-Chuan Ke, 2003. "The operating characteristic analysis on a general input queue with N policy and a startup time," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 57(2), pages 235-254, May.
    4. Ke, Jau-Chuan & Wang, Kuo-Hsiung, 2002. "A recursive method for the N policy G/M/1 queueing system with finite capacity," European Journal of Operational Research, Elsevier, vol. 142(3), pages 577-594, November.
    5. Teghem, J., 1987. "Optimal control of a removable server in an M/G/1 queue with finite capacity," European Journal of Operational Research, Elsevier, vol. 31(3), pages 358-367, September.
    6. Colin E. Bell, 1971. "Characterization and Computation of Optimal Policies for Operating an M / G /1 Queuing System with Removable Server," Operations Research, INFORMS, vol. 19(1), pages 208-218, February.
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    Cited by:

    1. Sanga, Sudeep Singh & Jain, Madhu, 2019. "Cost optimization and ANFIS computing for admission control of M/M/1/K queue with general retrial times and discouragement," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    2. Dong-Yuh Yang & Po-Kai Chang, 2015. "A parametric programming solution to the -policy queue with fuzzy parameters," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(4), pages 590-598, March.

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