Finding a parking slot is a serious issue in contemporary urban mobility. It is estimated that the average driver in the U.S., U.K. and Germany wastes 17, 44 and 41 hours a year respectively searching for parking, at an estimated annual cost of 72.7 billion dollars, 23.3 billion pounds and 40.4 billion euros in these countries. Despite the importance of the topic (30% of cars might be cruising for parking in many large cities) and the central role given to parking policies, surprisingly little is known about the basic laws governing the search time.

In this work, we present a set of analytical and computational approaches to investigate the role of the drivers' perception of the 'attractiveness' of parking spots, in determining the occupancy of on-street parking spots in busy downtown districts. Under this concept of attractiveness, we subsume the various factors governing the selection of a place to park, including its distance to the destination, cost, and intrinsic characteristics. We implement this idea in a stochastic agent-based model and simulate it numerically to investigate the cruising phenomenon in the central district of Lyon.

We also demonstrate the effect of modulating spot attractiveness on the on-street parking spot occupancies and the time spend cruising for parking. As a matter of fact, the occupancy in such a model is exactly solvable and we develop an analytic formula to do so. We verify the accuracy of our results by comparing with occupancies generated through in-silico experiments.