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.

26 pages, 10 figures, accepted at Transportation Research Part B: Methodological