The ``parking'' problem for segments of different length
type: Item
instance of: scholarly article
title: The ``parking'' problem for segments of different length
zbMATH Open document ID: 0927.60011
DOI: 10.1007/BF02365212
author: S. M. Anan'evskij
published in: Journal of Mathematical Sciences (New York)
publication date: 1999-07-13T00:00:00Z
review text: \textit{A. Rényi} has considered the parking problem for a segment \([0,x]\) by intervals of length 1 [Publ. Math. Inst. Hung. Acad. Sci. 3, 109-127 (1958; Zbl 0105.11903)]. In the present paper a modified parking problem is considered. Intervals of two different lengths (1 or 2) fill the segment \([0,x]\). Let \(N_x\) be the number of the accommodated intervals on \([0,x]\). The main result is the following theorem: There exists \(\lim_{x\to \infty} EN_x/x=\gamma>0\) (\(E\) stands for expectation). Moreover, \(EN_x = \gamma x + {3 \over 2} \gamma - 1 + O\left(\left(c/x\right)^{x -3/2}\right)\), \(x\to \infty\), where \(c\) is a positive constant. See also \textit{A. Dvoretzky} and \textit{H. Robbins} [ibid., Ser. A 9, 209-225 (1964; Zbl 0251.60023)].
Mathematics Subject Classification ID: 60D05
zbMATH DE Number: 1300645
zbMATH Keywords: parking problem
reviewed by: Viktor Ohanyan
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02365212
OpenAlex ID: W1983398325
description: scientific article; zbMATH DE number 1300645