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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)

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    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.

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    File URL: http://www.bbk.ac.uk/ems/research/wp/PDF/BWPEF0407.pdf
    File Function: First version, 2004
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    Bibliographic Info

    Paper provided by Birkbeck, Department of Economics, Mathematics & Statistics in its series Birkbeck Working Papers in Economics and Finance with number 0407.

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    Date of creation: Nov 2004
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    Handle: RePEc:bbk:bbkefp:0407

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    Related research

    Keywords: QUEUES; STATE DEPENDENT SERVICE RATE; NON-COOPERATIVE GAME; NASH EQUILIBRIUM; SIMULATION;

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    1. 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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