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The Bernoulli Feedback Queue with Balking: Stochastic Order Results and Equilibrium Joining Rules

Author

Listed:
  • E. J. Collins
  • A. C. Brooms

    (Department of Economics, Mathematics & Statistics, Birkbeck)

Abstract

We consider customer joining behaviour for a system that consists of a FCFS queue with Bernoulli feedback. A consequence of the feedback characteristic is that the sojourn time of a customer already in the system depends on the joining decisions taken by future arrivals to the system. By establishing stochastic order results for coupled versions of the system, we prove the existence, and uniqueness, of Nash equilibrium joining policies, and show that these are characterized by (possibly randomized) threshold rules. We contrast the Nash rule with the socially optimizing joining rule that minimizes the long-term expected average sojourn time (or cost) per customer. The latter rule is characterized by a nonrandomized threshold, and we show that the Nash rule admits at least as many customers into the system as the socially optimizing one.

Suggested Citation

  • E. J. Collins & A. C. Brooms, 2005. "The Bernoulli Feedback Queue with Balking: Stochastic Order Results and Equilibrium Joining Rules," Birkbeck Working Papers in Economics and Finance 0517, Birkbeck, Department of Economics, Mathematics & Statistics.
    • Handle: RePEc:bbk:bbkefp:0517
    as

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    File URL: https://eprints.bbk.ac.uk/id/eprint/26971
    File Function: First version, 2005
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    References listed on IDEAS

    as
    1. Uri Yechiali, 1971. "On Optimal Balking Rules and Toll Charges in the GI / M /1 Queuing Process," Operations Research, INFORMS, vol. 19(2), pages 349-370, April.
    2. Eitan Altman & Nahum Shimkin, 1998. "Individual Equilibrium and Learning in Processor Sharing Systems," Operations Research, INFORMS, vol. 46(6), pages 776-784, December.
    3. Naor, P, 1969. "The Regulation of Queue Size by Levying Tolls," Econometrica, Econometric Society, vol. 37(1), pages 15-24, January.
    Full references (including those not matched with items on IDEAS)

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