The nature of the on-street parking search

Parking occupancy in a delineated area is defined by three major parameters – the rate of car arrivals, the dwell time of already parked cars, and the willingness of drivers to continue their search for a vacant parking spot. We investigate a series of theoretical and numeric models, both deterministic and stochastic, that describe parking dynamics in an 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 a parking system – the average fraction of cars among the arrivals that will find parking in the area, the average number of cars that cruise for parking, and the average cruising time. Stochastic models make it possible to estimate the distributions of these characteristics as well as the parameters defined by the distribution PDF, like the fraction of the arriving cars that find parking in less than t minutes. The results are robust to the distribution of drivers' dwell and renege times and can be directly applied to assess the real-world parking dynamics.