自私停车问题的连续版本

IF 0.4 Q4 MATHEMATICS

Vestnik St Petersburg University-Mathematics Pub Date : 2024-04-18 DOI:10.1134/s1063454124010023

S. M. Ananjevskii, A. P. Chen

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引用次数: 0

摘要

摘要研究了用长度较小的间隔随机填充长度较大的线段的新模型。考虑了问题的新表述。在该模型中，只有当被填充的线段长度至少为 2 时，才会在线段上放置单位间隔。要放置的区间位置受均匀分布定律的影响。根据待填充线段的长度，研究了放置间隔的平均数量的行为。得到了雷尼常数的精确表达式。

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A Continuous Version of the Selfish Parking Problem

Abstract

A new model of the random filling of a segment of large length with intervals of smaller length is studied. A new statement of the problem is considered. A model in which unit intervals are placed on a segment only if the segment being filled has a length of at least 2 is considered. The position of the interval to be placed is subject to a uniform distribution law. The behavior of the average number of intervals placed is studied depending on the length of the segment to be filled. An exact expression is obtained for the analog of Rényi’s constant.

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来源期刊

Vestnik St Petersburg University-Mathematics MATHEMATICS-

CiteScore

0.70

自引率

50.00%

发文量

期刊介绍： Vestnik St. Petersburg University, Mathematics is a journal that publishes original contributions in all areas of fundamental and applied mathematics. It is the prime outlet for the findings of scientists from the Faculty of Mathematics and Mechanics of St. Petersburg State University. Articles of the journal cover the major areas of fundamental and applied mathematics. The following are the main subject headings: Mathematical Analysis; Higher Algebra and Numbers Theory; Higher Geometry; Differential Equations; Mathematical Physics; Computational Mathematics and Numerical Analysis; Statistical Simulation; Theoretical Cybernetics; Game Theory; Operations Research; Theory of Probability and Mathematical Statistics, and Mathematical Problems of Mechanics and Astronomy.