Dynamic Traffic Assignment for Electric Vehicles

TL;DR

This paper develops a theoretical framework and computational methods for dynamic traffic assignment tailored to electric vehicles, considering their unique range and recharging constraints, and demonstrates the existence of energy-feasible equilibria.

Contribution

It introduces a novel walk-based model for electric vehicle traffic flows, proves the existence of energy-feasible dynamic equilibria, and provides a fixed-point algorithm for computing these equilibria.

Findings

Existence of energy-feasible dynamic equilibrium established.

A fixed-point algorithm effectively computes equilibria.

Application to real-world instances shows complex travel time and energy interactions.

Abstract

We initiate the study of dynamic traffic assignment for electrical vehicles addressing the specific challenges such as range limitations and the possibility of battery recharge at predefined charging locations. We pose the dynamic equilibrium problem within the deterministic queueing model of Vickrey and as our main result, we establish the existence of an energy-feasible dynamic equilibrium. There are three key modeling-ingredients for obtaining this existence result: * We introduce a walk-based definition of dynamic traffic flows which allows for cyclic routing behavior as a result of recharging events en route. * We use abstract convex feasibility sets in an appropriate function space to model the energy-feasibility of used walks. * We introduce the concept of capacitated dynamic equilibrium walk-flows which generalize the former unrestricted dynamic equilibrium path-flows. Viewed in this framework, we show the existence of an energy-feasible dynamic equilibrium by applying an infinite dimensional variational inequality, which in turn requires a careful analysis of continuity properties of the network loading as a result of injecting flow into walks. We complement our theoretical results by a computational study in which we design a fixed-point algorithm computing energy-feasible dynamic equilibria. We apply the algorithm to standard real-world instances from the traffic assignment community illustrating the complex interplay of resulting travel times, energy consumption and prices paid at equilibrium.