Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

Asymptotics in Knuth's parking problem for caravans

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Code(s) de Classification MSC:

Résumé: 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 lot to park. Extending a recent work by Chassaing and Louchard [9], we relate the asymptotics for the sizes of blocks formed by occupied lots with the dynamics of the additive coalescent. According to the behavior of the caravan's size tail distribution, several qualitatively different versions of eternal additive coalescent are involved.

Mots Clés: Parking problem ; additive coalescent ; bridges with exchangeable increments

Date: 2004-05-25

Prépublication numéro: PMA-917