On Downs–Thomson paradox in two-tier service systems with a fast pass and revenue-based capacity investment

Abstract

A two-tier service system consists of free and toll channels with its toll revenue reinvested in service capacity. In this study, we develop two models with revenue reinvestment in either the free or the toll system. Similar to the congestion problem in an urban transportation network, we investigate whether the Downs–Thomson paradox occurs in the cases where an additional free service capacity is increased. Based on the relations between the major performance measures (such as the customer waiting time, toll system revenue, and total social cost) and the key system parameters and decision variables (such as the traffic intensity, proportion of revenue invested in capacity expansion, toll system price, and service cost of the free or toll system), we find that the Downs–Thomson paradox in terms of total social cost may exist. The findings provide managerial insights if an additional budget is invested to expand the free service capacity.

Keywords:

• Queueing
• two-tier service systems
• Downs–Thomson paradox
• total social cost
• capacity expansion

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The first author acknowledges the financial support by Natural Sciences and Engineering Research Council of Canada [grant number RGPIN197319].