@MISC{Šeba08parkingin, author = {Petr Šeba}, title = {Parking in the city}, year = {2008} }

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Abstract

We show that the spacing distribution between parked cars can be obtained as a solution of certain linear distributional fixed point equation. The results are compared with the data measured on the streets of Hradec Kralove. We also discuss a relation of this results to the random matrix theory. Our aim is to describe the spacing distribution between cars parked parallel to the curb somewhere in the center of a city. We will assume that the street is long enough to enable a parallel parking of many cars. Moreover we assume that there are no driveways or side streets in the segment of interest and that the street is free of any kind of marked parking lots or park meters. So the drivers are not biased to park at some particular positions. On the contrary: they are free to park the car anywhere provided they find and empty space to do it. In additions we assume that there are not cars parked permanently on the street (i.e. we assume that the majority of the cars leaves the street during the night). The standard way to describe such random parking is the continuous version of the random sequential adsorption model known also as the "random car parking problem "- see [1], [2] for review. It is a well studied process where the cars are parked without overlapping onto randomly chosen positions. All cars have the same length l0 and all parking attempts are regarded as independent. Assume that the street has a length L>> l0. The particular parking attempt goes as follows: choose a random position x on the street. If the interval (x − l0/2, x + l0/2) is free park the car with its middle at x. If