Path-constrained traffic assignment: Modeling and computing network impacts of stochastic range anxiety

Abstract

It is notoriously known that range anxiety is one of the major barriers that hinder a wide adoption of plug-in electric vehicles, especially battery electric vehicles. Recent studies suggested that if the caused driving range limit makes any impact on travel behaviors, it more likely occurs on the tour or trip chain level than the trip level. To properly assess its impacts on travel choices and traffic congestion, this research is devoted to studying a new network equilibrium problem that implies activity location and travel path choices on the trip chain level subject to stochastic driving ranges. Convex optimization and variational inequality models are respectively constructed for characterizing the equilibrium conditions under both discretely and continuously distributed driving ranges. For deriving the equilibrium flow solutions for these problem cases, we suggested different adaptations of a well-known path-based algorithm—the projected gradient method.While the problem instance with a discrete number of driving ranges can be simply treated as a multi-class version of its deterministic counterpart, the one with continuous driving ranges poses a much more complicated situation. To overcome this arising modeling and algorithmic complication, we introduce a couple of newly defined variables, namely, path-indexed travel subdemand rate and traffic subflow rate, by which the demand and flow rates as well as their corresponding feasible path sets can be dynamically indexed in the solution process with reference to path lengths. An illustrative example with various types and forms of driving range distributions demonstrates the applicability of the proposed modeling and solution methods and various impacts of the heterogeneity of range anxiety on network flows and computational costs. The numerical analysis results from this example show that stochastic driving ranges confine network flows in a different way from deterministic or no driving ranges and the projected gradient procedure relying on dynamically indexed subdemand and subflow rates is generally preferable to its counterpart on pre-indexed ones for both the discrete and continuous driving range cases.