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Asymptotics in Knuth's parking problem for caravans


Bertoin, Jean; Miermont, G (2006). Asymptotics in Knuth's parking problem for caravans. Random Structures & Algorithms, 29(1):38-55.

Abstract

We consider a generalized version of Knuth's parking problem, in which caravans consisting of a random number of cars arrive at random on the unit circle. Then each car turns clockwise until it finds a free space to park. Extending a recent work by Chassaing and Louchard [Random Struct Algor 21(1) (2002), 76–119], we relate the asymptotics for the sizes of blocks formed by occupied spots with the dynamics of the additive coalescent. According to the behavior of the caravans' size tail distribution, several qualitatively different versions of the eternal additive coalescent are involved.

Abstract

We consider a generalized version of Knuth's parking problem, in which caravans consisting of a random number of cars arrive at random on the unit circle. Then each car turns clockwise until it finds a free space to park. Extending a recent work by Chassaing and Louchard [Random Struct Algor 21(1) (2002), 76–119], we relate the asymptotics for the sizes of blocks formed by occupied spots with the dynamics of the additive coalescent. According to the behavior of the caravans' size tail distribution, several qualitatively different versions of the eternal additive coalescent are involved.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2006
Deposited On:29 May 2013 14:04
Last Modified:06 Nov 2017 10:10
Publisher:Wiley-Blackwell
ISSN:1098-2418
Free access at:Related URL. An embargo period may apply.
Publisher DOI:https://doi.org/10.1002/rsa.20092
Related URLs:http://www.ams.org/mathscinet-getitem?mr=2238028
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1102.60006
http://arxiv.org/abs/math/0502220

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