Private road networks with uncertain demand

Xinying Fu, Vincent A.C. van den Berg*, Erik T. Verhoef

*Corresponding author for this work

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We study the efficiency of private supply of roads under demand uncertainty and evaluate various regulatory policies. Due to demand uncertainty, capacity is decided before demand is known but tolls can be adjusted after demand is known. Policy implications can differ from those under deterministic demand. For instance, for serial links, the toll in the second-best zero-profit case is no longer equal to the marginal external congestion cost. In the first-best scenario, the capacity under uncertain demand is higher than that under deterministic demand of the same expected value, though self-financing still holds in expected terms. Regulation by perfect competitive auction cannot replicate the second-best zero-profit result and thus leads to a lower welfare, whereas without uncertainty, various forms of competitive auctions can attain this second-best optimum. For more complex networks, when private firms add capacity in turn, contrary to the case without demand uncertainty, some forms of auction perform better than others with demand uncertainty.

Original languageEnglish
Pages (from-to)57-68
Number of pages12
JournalResearch in Transportation Economics
Publication statusPublished - 2018


This research was supported by the project Private Roads in Mixed Private Public Networks (CHINA.12.203) of the NSFC-NWO Joint Research Projects 2012 EW: the Application of Operations Research in Urban Transport. We thanks participants at the 19th HKSTS conference, the ITEA conference in 2014 and 2016, and the Sino-Dutch Forum on Smart City for their valuable comments and helpful suggestions. Any remaining errors are ours.

FundersFunder number
Operations Research in Urban Transport


    • Auction
    • Private supply
    • Road network
    • Road pricing
    • Traffic congestion
    • Uncertain demand
    • Uncertainty


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