Asymptotics in Knuth's parking problem for caravans

Jean Bertoin (1) , Grégory Miermont (2)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay

We consider a generalized version of Knuth's parking problem, in which caravans consisting of a 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, 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 caravan's size tail distribution, several qualitatively different versions of eternal additive coalescent are involved.

Keywords: Parking problem; additive coalescent; bridges with exchangeable increments

Domains: Probability [math.PR]

Jean Bertoin, Grégory Miermont. Asymptotics in Knuth's parking problem for caravans. Random Structures and Algorithms, 2006, 29 (1), pp.38--55. ⟨10.1002/rsa.20092⟩. ⟨hal-00004229⟩