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On the Downs–Thomson Paradox in a Self-Financing Two-Tier Queuing System

Author

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  • Pengfei Guo

    (Faculty of Business, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong)

  • Robin Lindsey

    (Sauder School of Business, University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada)

  • Zhe George Zhang

    (Department of Decision Sciences, Western Washington University, Bellingham, Washington 98225; and Beedie School of Business, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada)

Abstract

We model a two-tier queuing system with free and toll service options as two parallel M / M /1 servers. We solve for the welfare-maximizing toll service capacity and toll subject to the constraint that the toll service cover its costs. If the free and toll services are both used in equilibrium, a larger free-service capacity implies longer expected waiting time for the free service and lower welfare: an analogue to the Downs–Thomson paradox in transportation economics. The paradox is caused by the presence of scale economies in the toll service combined with the requirement that it be self-financing.

Suggested Citation

  • Pengfei Guo & Robin Lindsey & Zhe George Zhang, 2014. "On the Downs–Thomson Paradox in a Self-Financing Two-Tier Queuing System," Manufacturing & Service Operations Management, INFORMS, vol. 16(2), pages 315-322, May.
    • Handle: RePEc:inm:ormsom:v:16:y:2014:i:2:p:315-322
    DOI: 10.1287/msom.2014.0476
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    References listed on IDEAS

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    1. Shaler Stidham, 1992. "Pricing and Capacity Decisions for a Service Facility: Stability and Multiple Local Optima," Management Science, INFORMS, vol. 38(8), pages 1121-1139, August.
    2. Naor, P, 1969. "The Regulation of Queue Size by Levying Tolls," Econometrica, Econometric Society, vol. 37(1), pages 15-24, January.
    3. Antonios Printezis & Apostolos Burnetas & Gopalakrishnan Mohan, 2009. "Pricing and capacity allocation under asymmetric information using Paris Metro Pricing," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 5(3), pages 265-279.
    4. Sanjeev Dewan & Haim Mendelson, 1990. "User Delay Costs and Internal Pricing for a Service Facility," Management Science, INFORMS, vol. 36(12), pages 1502-1517, December.
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    Cited by:

    1. Zhang, Zhe George & Yin, Xiaoling, 2021. "Information and pricing effects in two-tier public service systems," International Journal of Production Economics, Elsevier, vol. 231(C).
    2. Qian, Qu & Zhuang, Weifen, 2017. "Tax/subsidy and capacity decisions in a two-tier health system with welfare redistributive objective," European Journal of Operational Research, Elsevier, vol. 260(1), pages 140-151.
    3. Wang, Jian-Jun & Li, Zhong-Ping & Shi, Jim (Junmin) & Chang, Ai-Chih (Jasmine), 2021. "Hospital referral and capacity strategies in the two-tier healthcare systems," Omega, Elsevier, vol. 100(C).
    4. A. Wang & I. Ziedins, 2018. "Probabilistic selfish routing in parallel batch and single-server queues," Queueing Systems: Theory and Applications, Springer, vol. 88(3), pages 389-407, April.
    5. Li, Zhong-Ping & Chang, Aichih (Jasmine) & Zou, Zongbao, 2023. "Design mechanism to coordinate a hierarchical healthcare system: Patient subsidy vs. capacity investment," Omega, Elsevier, vol. 118(C).

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