A continuous version of the selfish parking problem

Authors

  • Sergey M. Ananjevskii St. Petersburg State University, 7-9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation
  • Alexander P. Chen Western University, 1151, ul. Richmond, London, Ontario, Canada https://orcid.org/0009-0000-4315-397X

DOI:

https://doi.org/10.21638/spbu01.2024.104

Abstract

The work is devoted to the study of a new model of random filling of a segment of large length with intervals of smaller length. A new formulation of the problem is considered. We study a model in which unit intervals are placed on a segment only if the segment being filled has a length of at least 2. In this case, the position of the placed interval is subject to a uniform distribution law. The paper investigates the behavior of the average number of placed intervals depending on the length of the filled segment. An exact expression is obtained for the analog of the Renyi constant.

Keywords:

random filling of a segment, parking problem, asymptotic behavior of the expectation

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Published

2024-05-10

How to Cite

Ananjevskii, S. M., & Chen, A. P. (2024). A continuous version of the selfish parking problem. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 11(1), 84–95. https://doi.org/10.21638/spbu01.2024.104

Issue

Vol. 11 No. 1 (2024)

Section

Mathematics

License

Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.

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