On the downs-thomson paradox in a self-financing two-tier queuing system

Pengfei Guo, Robin Lindsey, Zhe George Zhang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

35 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)315-322
Number of pages8
JournalManufacturing and Service Operations Management
Issue number2
Publication statusPublished - 1 Jan 2014


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

ASJC Scopus subject areas

  • Strategy and Management
  • Management Science and Operations Research


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