  In this paper, we consider electric vehicle charging facilities that offer
various levels of service for varying prices such that rational users choose a
level of service that minimizes the total cost to themselves including an
opportunity cost that incorporates users' value of time. In this setting, we
study the sensitivity of the expected occupancy at the facility to
mischaracterizations of user profiles and uncharacterized heterogeneity. For
user profile mischaracterizations, we first provide a fundamental upper bound
for the difference between the expected occupancy under any two different
distributions on a user's impatience (i.e., value of time) that only depends on
the minimum and maximum charging rate offered by the charging facility. Next,
we consider the case when a user's impatience is a discrete random variable and
study the sensitivity of the expected occupancy to the probability masses and
attained values of the random variable. We show that the expected occupancy
varies linearly with respect to the probability masses and is piecewise
constant with respect to the attained values. Furthermore, we study the effects
on the expected occupancy from the occurrence of heterogeneous user
populations. In particular, we quantify the effect on the expected occupancy
from the existence of sub-populations that may only select a subset of the
offered service levels. Lastly, we quantify the variability of early departures
on the expected occupancy. These results demonstrate how the facility operator
might design prices such that the expected occupancy does not vary much under
small changes in the distribution of a user's impatience, variable and limited
user service needs, or uncharacterized early departure, quantities which are
generally difficult to characterize accurately from data. We further
demonstrate our results via examples.
