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Strategic customer behavior in an M/M/1 feedback queue

Author

Listed:
  • Mark Fackrell

    (The University of Melbourne)

  • Peter Taylor

    (The University of Melbourne)

  • Jiesen Wang

    (The University of Melbourne)

Abstract

We investigate the behavior of equilibria in an M/M/1 feedback queue where price- and time-sensitive customers are homogeneous with respect to service valuation and cost per unit time of waiting. Upon arrival, customers can observe the number of customers in the system and then decide to join or to balk. Customers are served in order of arrival. After being served, each customer either successfully completes the service and departs the system with probability q, or the service fails and the customer immediately joins the end of the queue to wait to be served again until she successfully completes it. We analyze this decision problem as a noncooperative game among the customers. We show that there exists a unique symmetric Nash equilibrium threshold strategy. We then prove that the symmetric Nash equilibrium threshold strategy is evolutionarily stable. Moreover, if we relax the strategy restrictions by allowing customers to renege, in the new Nash equilibrium, customers have a greater incentive to join. However, this does not necessarily increase the equilibrium expected payoff, and for some parameter values, it decreases it.

Suggested Citation

  • Mark Fackrell & Peter Taylor & Jiesen Wang, 2021. "Strategic customer behavior in an M/M/1 feedback queue," Queueing Systems: Theory and Applications, Springer, vol. 97(3), pages 223-259, April.
    • Handle: RePEc:spr:queues:v:97:y:2021:i:3:d:10.1007_s11134-021-09693-z
    DOI: 10.1007/s11134-021-09693-z
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    References listed on IDEAS

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    1. Refael Hassin, 1996. "On the Advantage of Being the First Server," Management Science, INFORMS, vol. 42(4), pages 618-623, 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. Refael Hassin & Moshe Haviv, 1997. "Equilibrium Threshold Strategies: The Case of Queues with Priorities," Operations Research, INFORMS, vol. 45(6), pages 966-973, December.
    4. Ralph L. Disney, 1981. "A note on sojourn times in M/G/1 queues with instantaneous, bernoulli feedback," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 28(4), pages 679-684, December.
    5. Ralph L. Disney & Donald C. McNickle & Burton Simon, 1980. "The M/G/1 queue with instantaneous bernoulli feedback," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 27(4), pages 635-644, December.
    6. Gallay, Olivier & Hongler, Max-Olivier, 2009. "Circulation of autonomous agents in production and service networks," International Journal of Production Economics, Elsevier, vol. 120(2), pages 378-388, August.
    7. Naor, P, 1969. "The Regulation of Queue Size by Levying Tolls," Econometrica, Econometric Society, vol. 37(1), pages 15-24, January.
    8. A C Brooms & E J Collins, 2013. "Stochastic Order Results and Equilibrium Joining Rules for the Bernoulli Feedback Queue," Birkbeck Working Papers in Economics and Finance 1305, Birkbeck, Department of Economics, Mathematics & Statistics.
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    Cited by:

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