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

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Original languageEnglish
Pages (from-to)315-322
Journal / PublicationManufacturing and Service Operations Management
Issue number2
Online published28 Mar 2014
Publication statusPublished - Mar 2014
Externally publishedYes


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. © 2014 INFORMS.

Research Area(s)

  • Downs-Thomson paradox, Equilibrium arrival rates, Pricing and capacity decisions, Queuing system, Two-tier service system