The Morning Commute Problem with Coarse Toll and Nonidentical Commuters

Abstract

This paper studies the morning commute problem under a flat peak-period toll (coarse toll) within the context of heterogeneous commuters. All the possible cumulative departure curves resulting from different choices of toll level and charging period are examined. The optimal toll schemes are then derived from minimizing the total travel cost of all commuters, excluding toll cost. We prove 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 period for the type of Value-Of-Time (VOT) distribution considered in the paper. 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 VOT. The optimal solution depends on the units in which the system cost is measured and we find that commuters in the middle pack of the VOT distribution are worse off by higher toll charges if the system cost is measured in money instead of time. A numerical example is provided at the end for demonstration.