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Strategic bidding in an accumulating priority queue: equilibrium analysis

Author

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  • Moshe Haviv

    (The Hebrew University of Jerusalem)

  • Liron Ravner

    (The Hebrew University of Jerusalem)

Abstract

We study the strategic purchasing of priorities in a time-dependent accumulating priority M/G/1 queue. We formulate a non-cooperative game in which customers purchase priority coefficients with the goal of reducing waiting costs in exchange. The priority of each customer in the queue is a linear function of the individual waiting time, with the purchased coefficient being the slope. The unique pure Nash equilibrium is solved explicitly for the case with homogeneous customers. A general characterisation of the Nash equilibrium is provided for the heterogeneous case. It is shown that both avoid the crowd and follow the crowd behaviors are prevalent, within class types and between them. We further present a pricing mechanism that ensures the order of the accumulating priority rates in equilibrium follows a $$C\mu $$ C μ type rule and improves overall efficiency.

Suggested Citation

  • Moshe Haviv & Liron Ravner, 2016. "Strategic bidding in an accumulating priority queue: equilibrium analysis," Annals of Operations Research, Springer, vol. 244(2), pages 505-523, September.
    • Handle: RePEc:spr:annopr:v:244:y:2016:i:2:d:10.1007_s10479-016-2141-4
    DOI: 10.1007/s10479-016-2141-4
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    References listed on IDEAS

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    1. Philipp Afèche & Haim Mendelson, 2004. "Pricing and Priority Auctions in Queueing Systems with a Generalized Delay Cost Structure," Management Science, INFORMS, vol. 50(7), pages 869-882, July.
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    Cited by:

    1. Moshe Haviv & Eyal Winter, 2020. "An optimal mechanism charging for priority in a queue," Papers 2002.06533, arXiv.org.
    2. Vasco F. Alves, 2021. "Endogenous queue number determination in G/M/s systems," 4OR, Springer, vol. 19(1), pages 113-126, March.
    3. Roei Engel & Refael Hassin, 2017. "Customer equilibrium in a single-server system with virtual and system queues," Queueing Systems: Theory and Applications, Springer, vol. 87(1), pages 161-180, October.
    4. Moshe, Shir & Oz, Binyamin, 2023. "Charging more for priority via two-part tariff for accumulating priorities," European Journal of Operational Research, Elsevier, vol. 304(2), pages 652-660.
    5. Na Li & David A. Stanford & Peter Taylor & Ilze Ziedins, 2017. "Nonlinear Accumulating Priority Queues with Equivalent Linear Proxies," Operations Research, INFORMS, vol. 65(6), pages 1712-1721, December.

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