Marginal cost pricing for system optimal traffic assignment with recourse under supply-side uncertainty

• Published in: Transportation research. Part B: methodological Vol. 110; pp. 104 - 121
• Main Authors: Rambha, Tarun, Boyles, Stephen D., Unnikrishnan, Avinash, Stone, Peter
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.04.2018; Elsevier Science Ltd
• Subjects: Bottlenecks; Computational geometry; Convexity; Delay; Equilibrium with recourse; Marginal cost pricing; Online shortest paths; Optimization; Parameter uncertainty; Policies; Pricing; Shortest-path problems; Studies; Supply chains; Supply-side uncertainty; Transportation; Transportation networks; Travel time; Variation; Weather; Equilibrium with recourse; Marginal cost pricing; Supply-side uncertainty; Online shortest paths
• ISSN: 0191-2615; 1879-2367
• DOI: 10.1016/j.trb.2018.02.008

•Supply-side uncertainty is modeled using probabilistic link performance functions.•Travelers select links en route using adaptive routing policies.•An equilibrium model is formulated assuming users minimize their expected costs.•State-dependent marginal cost tolls are shown to lead to a system optimum.•Suboptimality of static tolls is demonstrated using the Sioux Falls test network. Transportation networks are often subject to fluctuations in supply-side parameters such as capacity and free-flow travel time due to factors such as incidents, poor weather, and bottlenecks. In such scenarios, assuming that network arcs exist in a finite number of states with different delay functions with different probabilities, a marginal cost pricing scheme that leads to a socially optimal outcome is proposed. The suggested framework makes the behavioral assumption that travelers do not just choose paths but follow routing policies that respond to en route information. Specifically, it is assumed that travelers are fully-rational and that they compute the optimal online shortest path assuming full-reset. However, such policies may involve cycling, which is unrealistic in practice. Hence, a network transformation that helps restrict cycles up to a certain length is devised and the problem is reformulated as a convex optimization problem with symmetric delay functions. The results of numerical tests on the Sioux Falls test network are presented using the Frank–Wolfe algorithm.