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Parking plays a central role in transport policies and has wide-rangingconsequences: While the average time spent searching for parking exceeds dozensof hours per driver every year in many Western cities, the associated cruisingtraffic generates major externalities, by emitting pollutants and contributingto congestion. However, the laws governing the parking search time remainopaque in many regards, which hinders any general understanding of the problemand its determinants. Here, we frame the problem of parking search in a verygeneric, but mathematically compact formulation which puts the focus on therole of the street network and the unequal attractiveness of parking spaces.This problem is solved in two independent ways, valid in any street network andfor a wide range of drivers' behaviours. Numerically, this is done by means ofa computationally efficient and versatile agent-based model. Analytically, weleverage the machinery of Statistical Physics and Graph Theory to derive ageneric mean-field relation giving the parking search time as a function of theoccupancy of parking spaces; an expression for the latter is obtained in thestationary regime. We show that these theoretical results are applicable in toynetworks as well as in complex, realistic cases such as the large-scale streetnetwork of the city of Lyon, France. Taken as a whole, these findings clarifythe parameters that directly control the search time and provide transportengineers with a quantitative grasp of the parking problem. Besides, theyestablish formal connections between the parking issue in realistic settingsand physical problems.

Parking search in the physical world: Calculating the search time by leveraging physical and graph theoretical methods