  We consider a spatially distributed demand for electrical vehicle recharging,
that must be covered by a fixed set of charging stations. Arriving EVs receive
feedback on transport times to each station, and waiting times at congested
ones, based on which they make a selfish selection. This selection determines
total arrival rates in station queues, which are represented by a fluid state;
departure rates are modeled under the assumption that clients have a given
sojourn time in the system. The resulting differential equation system is
analyzed with tools of optimization. We characterize the equilibrium as the
solution to a specific convex program, which has connections to optimal
transport problems, and also with road traffic theory. In particular a price of
anarchy appears with respect to a social planner's allocation. From a dynamical
perspective, global convergence to equilibrium is established, with tools of
Lagrange duality and Lyapunov theory. An extension of the model that makes
customer demand elastic to observed delays is also presented, and analyzed with
extensions of the optimization machinery. Simulations to illustrate the global
behavior are presented, which also help validate the model beyond the fluid
approximation.
