Exact Finite-Length Theory of Uniform Car Parking: Spatial Laws, Absorption, and Aggregation

Abstract:The uniform car-parking process is the one-dimensional random sequential adsorption of unit cars on a segment of finite length $s$: cars arrive at uniformly random positions and park wherever they fit, until no gap admits another. This paper develops the exact finite-$s$ theory. The joint density of the parked positions is resolved into jamming cells, on each of which it is a rational function, and evaluated by a subset recursion in $O(2^n n)$ operations; the marginal and gap order statistics are obtained as hyperlogarithms whose weight is fixed by the number of coordinates integrated out; and the absorption count and the aggregate quantities are treated through the integral equation descending from Rényi.

Robotics (cs.RO); Data Structures and Algorithms (cs.DS); Symbolic Computation (cs.SC); Probability (math.PR); Rings and Algebras (math.RA)

arXiv:2608.22671 [cs.RO]

(or arXiv:2608.22671v1 [cs.RO] for this version)

https://doi.org/10.48550/arXiv.2608.22671 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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