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An ɛ -Nash Equilibrium with High Probability for Strategic Customers in Heavy Traffic

Author

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  • Rami Atar

    (Department of Electrical Engineering, Technion–Israel Institute of Technology, Haifa 32000, Israel)

  • Subhamay Saha

    (Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati 781039, Assam, India)

Abstract

A multiclass queue with many servers is considered, where customers make a join-or-leave decision upon arrival based on queue length information, without knowing the state of other queues. A game theoretic formulation is proposed and analyzed, that takes advantage of a phenomenon unique to heavy traffic regimes, namely, Reiman’s snaphshot principle, by which waiting times are predicted with high precision by the information available upon arrival. The payoff considered is given as a random variable , which depends on the customer’s decision, accounting for waiting time in the queue and penalty for leaving. The notion of an equilibrium is only meaningful in an asymptotic framework, which is taken here to be the Halfin-Whitt heavy traffic regime. The main result is the identification of an ɛ -Nash equilibrium with probability approaching 1. On the way to proving this result, new diffusion limit results for systems with finite buffers are obtained.

Suggested Citation

  • Rami Atar & Subhamay Saha, 2017. "An ɛ -Nash Equilibrium with High Probability for Strategic Customers in Heavy Traffic," Mathematics of Operations Research, INFORMS, vol. 42(3), pages 626-647, August.
    • Handle: RePEc:inm:ormoor:v:42:y:2017:i:3:p:626-647
    DOI: 10.1287/moor.2016.0820
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    References listed on IDEAS

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    1. Itay Gurvich & Ward Whitt, 2009. "Queue-and-Idleness-Ratio Controls in Many-Server Service Systems," Mathematics of Operations Research, INFORMS, vol. 34(2), pages 363-396, May.
    2. Gad Allon & Itai Gurvich, 2010. "Pricing and Dimensioning Competing Large-Scale Service Providers," Manufacturing & Service Operations Management, INFORMS, vol. 12(3), pages 449-469, August.
    3. Athanasia Manou & Antonis Economou & Fikri Karaesmen, 2014. "Strategic Customers in a Transportation Station: When Is It Optimal to Wait?," Operations Research, INFORMS, vol. 62(4), pages 910-925, August.
    4. Ragavendran Gopalakrishnan & Sherwin Doroudi & Amy R. Ward & Adam Wierman, 2016. "Routing and Staffing When Servers Are Strategic," Operations Research, INFORMS, vol. 64(4), pages 1033-1050, August.
    5. Shlomo Halfin & Ward Whitt, 1981. "Heavy-Traffic Limits for Queues with Many Exponential Servers," Operations Research, INFORMS, vol. 29(3), pages 567-588, June.
    6. Naor, P, 1969. "The Regulation of Queue Size by Levying Tolls," Econometrica, Econometric Society, vol. 37(1), pages 15-24, January.
    7. Pengfei Guo & Refael Hassin, 2011. "Strategic Behavior and Social Optimization in Markovian Vacation Queues," Operations Research, INFORMS, vol. 59(4), pages 986-997, August.
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