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Optimal Control of a Single-Server Queue with Balking and Reneging


  • Joseph D. Blackburn

    (University of Chicago)


We consider the problem of controlling a single-server queue by turning the server on and off. In addition to a Poisson arrival process and general service-time distribution, provisions for balking and reneging are included in the models, yielding a variety of applications. Stationary optimal policies which maximize expected discounted reward over an infinite horizon are shown to have a simple critical-number characterization. Algorithms for computing the critical numbers are described.

Suggested Citation

  • Joseph D. Blackburn, 1972. "Optimal Control of a Single-Server Queue with Balking and Reneging," Management Science, INFORMS, vol. 19(3), pages 297-313, November.
  • Handle: RePEc:inm:ormnsc:v:19:y:1972:i:3:p:297-313

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    Cited by:

    1. de Lange, Robert & Samoilovich, Ilya & van der Rhee, Bo, 2013. "Virtual queuing at airport security lanes," European Journal of Operational Research, Elsevier, vol. 225(1), pages 153-165.
    2. Boronico, Jess S. & Siegel, Philip H., 1998. "Capacity planning for toll roadways incorporating consumer wait time costs," Transportation Research Part A: Policy and Practice, Elsevier, vol. 32(4), pages 297-310, May.

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