  Electric vehicle charging facilities offer electric charge and parking to
users for a fee. Both parking availability and electric charge capacity are
constrained resources, and as the demand for charging facilities grows with
increasing electric vehicle adoption, so too does the potential for exceeding
these resource limitations. In this paper, we study how prices set by the
charging facility impact the likelihood that resource constraints are exceeded.
Specifically, we present probabilistic bounds on the number of charging spots
and the total power supply needed at a facility based on the characteristics of
the arriving vehicles. We assume the charging facility either offers a set of
distinct and fixed charging rates to each user or allows the user to decide a
charging deadline, from which a charging rate is determined. Users arrive
randomly, requiring a random amount of charge. Additionally, each user has a
random impatience factor that quantifies their value of time, and a random
desired time to stay at a particular location. Assuming rational user behavior,
and with knowledge of the probability distribution of the random parameters, we
present high-confidence bounds on the total number of vehicles parked at the
station and the aggregate power use of all vehicles actively charging. We
demonstrate how these bounds can be used by a charging facility to determine
appropriate prices and investigate through a Monte-Carlo simulation case study
the tightness of the bounds.
