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

• 成果类型: Article
• 署名作者: Guo, Pengfei; Lindsey, Robin; Zhang, Zhe George
• 署名单位: Hong Kong Polytechnic University; University of British Columbia; Western Washington University; Simon Fraser University
• 刊物名称: M&SOM-MANUFACTURING & SERVICE OPERATIONS MANAGEMENT
• ISSN/ISSBN: 1523-4614
• DOI: 10.1287/msom.2014.0476
• 发表日期: 2014
• 页码: 315-322
• 关键词: queuing system; two-tier service system; equilibrium arrival rates; pricing and capacity decisions; Downs-Thomson paradox

摘要

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.