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.
Bertoin, Jean