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The Morning Commute Problem with Coarse Toll and Nonidentical Commuters


Research Report

Sustainable Transportation Center

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Suggested Citation:
Xiao, Feng Evan, Zhen Sean Qian, Hongjun Michael Zhang (2010) The Morning Commute Problem with Coarse Toll and Nonidentical Commuters. Institute of Transportation Studies, University of California, Davis, Research Report UCD-ITS-RR-10-42

This paper studies the morning commute problem under a flat peak-period toll within the context of heterogeneous commuters. All the possible queuing profiles resulting from different choices of toll level and charging time interval are examined. The optimal toll patterns were derived from minimizing the total travel cost of all commuters, excluding toll cost, and we proved that at the optimum there will be no queue or capacity waste at the bottleneck at both the starting and ending points of the charging time interval. Moreover, the optimal coarse toll scheme is pareto-improving. Different from the homogeneous case, which can be regarded as a special case of the heterogeneous case, price discrimination occurs when commuters have different values of time. We find that commuters in the middle pack of the value-of-time distribution are more easily to be hurt by higher toll charges and the optimal solution depends on the units in which the system cost is measured. Numerical examples are provided to demonstrate and compare the resulting equilibrium flow patterns under different objectives.