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On the Nash equilibria for the FCFS queueing system with load-increasing service rate

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  • A.C. Brooms

    (Department of Economics, Mathematics & Statistics, Birkbeck)

Abstract

We consider a service system (Qs) that operates according to the FCFS discipline, and in which the service rate is an increasing function of the queue length. Customers arrive sequentially to the system and decide whether or not to join, using decision rules based upon the queue length on arrival to (Qs) . Each customer is interested in selecting a rule that meets a certain optimality criterion with regards to their expected sojourn time in the system; as a consequence, the decision rules of other customers need to be taken into account. Within a particular class of decision rules for an associated infinite player game, the structure of the Nash equilibrium routing policies is characterized. We prove that within this class, there exist a finite number of Nash equilibria, and that at least one of these is non-randomized. Finally, we explore the extent to which the Nash equilibria are characteristic of customer joining behaviour under a learning rule based on system-wide data with the aid of simulation experiments.

Suggested Citation

  • A.C. Brooms, 2004. "On the Nash equilibria for the FCFS queueing system with load-increasing service rate," Birkbeck Working Papers in Economics and Finance 0407, Birkbeck, Department of Economics, Mathematics & Statistics.
    • Handle: RePEc:bbk:bbkefp:0407
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    File URL: https://eprints.bbk.ac.uk/id/eprint/27109
    File Function: First version, 2004
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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.
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