Network equilibrium of electric vehicles with stochastic range anxiety

This paper discusses a new traffic assignment problem with stochastic distance constraints, as an emerging modeling tool for describing traffic networks that serve plug-in electric vehicles with limited driving ranges. The driving range of electric vehicles is subject to onboard battery capacities and electricity consumption states as well as network-wide battery-recharging opportunities, which inevitably raise the so-called “range anxiety” concern in the driving population. In addition to varying battery capacities and electricity consumption rates, the variation of driving distance limits perceived by individual drivers is also a reflection of their heterogeneous perception errors and risk-taking behaviors to battery depletion. This paper presents a convex programming model with a finite number of constraints for characterizing the proposed problem, based on the introduction of a new path flow variable called cumulative path flow rate. A linear approximation algorithm was further developed, encapsulating an efficient k-shortest path search procedure to perform the network loading. Numerical results obtained from conducting quantitative analyses on example networks clearly illustrate the applicability of the modeling and solution methods for the proposed problem and reveal the mechanism of stochastic distance limits impacting the network equilibrium.