  The rise of electric vehicles (EVs) is unstoppable due to factors such as the
decreasing cost of batteries and various policy decisions. These vehicles need
to be charged and will therefore cause congestion in local distribution grids
in the future. Motivated by this, we consider a charging station with finitely
many parking spaces, in which electric vehicles arrive in order to get charged.
An EV has a random parking time and a random charging time. Both the charging
rate per vehicle and the charging rate possible for the station are assumed to
be limited. Thus, the charging rate of uncharged EVs depends on the number of
cars charging simultaneously. This model leads to a layered queueing network in
which parking spaces with EV chargers have a dual role, of a server (to cars)
and customers (to the grid). We are interested in the performance of the
aforementioned model, focusing on the fraction of vehicles that get fully
charged. To do so, we develop several bounds and asymptotic (fluid and
diffusion) approximations for the vector process, which describes the total
number of EVs and the number of not fully charged EVs in the charging station,
and we compare these bounds and approximations with numerical outcomes.
