Open Access

Lukas Graf, Tobias Harks, Prashant Palkar

• 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. As our main result, we establish the existence of energy-feasible dynamic equilibria within networks using the deterministic queuing model of Vickrey for the flow dynamics on edges. There are three key modeling-ingredients for obtaining this existence result: 1. We introduce a walk-based definition of dynamic traffic flows which allows for cyclic routing behavior as a result of recharging events en route. 2. We use abstract convex feasibility sets in an appropriate function space to model the energy-feasibility of used walks. 3. 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 anWe 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. As our main result, we establish the existence of energy-feasible dynamic equilibria within networks using the deterministic queuing model of Vickrey for the flow dynamics on edges. There are three key modeling-ingredients for obtaining this existence result: 1. We introduce a walk-based definition of dynamic traffic flows which allows for cyclic routing behavior as a result of recharging events en route. 2. We use abstract convex feasibility sets in an appropriate function space to model the energy-feasibility of used walks. 3. 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. The study demonstrates that battery constraints have a significant impact on the resulting travel times and energy consumption profiles compared to conventional fuel-based vehicles. We further show that our algorithm computes (approximate) equilibria for small and medium sized instances in acceptable running times but struggles for larger instances.…