  With the rapid growth in the demand for plug-in electric vehicles (EVs), the
corresponding charging infrastructures are expanding. These charging stations
are located at various places and with different congestion levels. EV drivers
face an important decision in choosing which charging station to go to in order
to reduce their overall time costs. However, existing literature either assumes
a flat charging rate and hence overlooks the physical characteristics of an EV
battery where charging rate is typically reduced as the battery charges, or
ignores the effect of other drivers on an EV's decision making process. In this
paper, we consider both the predetermined exogenous wait cost and the
endogenous congestion induced by other drivers' strategic decisions, and
propose a differential equation based approach to find the optimal strategies.
We analytically characterize the equilibrium strategies and find that
co-located EVs may make different decisions depending on the charging rate
and/or remaining battery levels. Through numerical experiments, we investigate
the impact of charging rate characteristics, modeling parameters and the
consideration of endogenous congestion levels on the optimal charging
decisions. Finally, we conduct numerical studies on real-world data and find
that some EV users with slower charging rates may benefit from the
participation of fast-charging EVs.
