  Parking occupancy in the area is defined by three major parameters - the rate
of cars arrivals, the dwell time of already parked cars, and the willingness of
drivers who are searching but yet did not find a vacant parking spot, to
continue their search. We investigate a series of theoretical and numeric
models, deterministic and stochastic, that describe parking dynamics in the
area as dependent on these parameters, over the entire spectrum of the demand
to supply ratio, focusing on the case when the demand is close to or above the
supply. We demonstrate that a simple deterministic model provides a good
analytical approximation for the major characteristics of the parking system -
the average fraction of cars among the arriving that will find parking in the
area, the average number of cars that cruise for parking, and average cruising
time. Stochastic models make it possible to estimate the distributions of these
characteristics as well as the parameters that are related to the variance of
these distributions, like the fraction of the arriving cars that find parking
in less than t minutes.
