  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.
