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

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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.

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Authors and Affiliations

  1. Department of Applied Mathematics, National Chung-Hsing University, Taichung, Taiwan, ROC

    K.-H. Wang

  2. Department of Industrial Engineering and Management, National Chiao Tung University, Hsin Chu, Taiwan, ROC

    C.-C. Kuo & W. L. Pearn

Authors
  1. K.-H. Wang
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  2. C.-C. Kuo
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  3. W. L. Pearn
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Correspondence to K.-H. Wang.

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Communicated by Y.C. Ho.

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Wang, KH., Kuo, CC. & Pearn, W.L. Optimal Control of an M/G/1/K Queueing System with Combined F Policy and Startup Time. J Optim Theory Appl 135, 285–299 (2007). https://doi.org/10.1007/s10957-007-9253-6

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  • DOI: https://doi.org/10.1007/s10957-007-9253-6

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