Burning cars in a parking lot - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Communications in Mathematical Physics Année : 2011

Burning cars in a parking lot

Résumé

Knuth's parking scheme is a model in computer science for hashing with linear probing. One may imagine a circular parking lot with n sites; cars arrive at each site with unit rate. When a car arrives at a vacant site, it parks there; otherwise it turns clockwise and parks at the first vacant site which is found. We incorporate fires into this model by throwing Molotov cocktails on each site at a smaller rate n (-alpha) , where 0 < alpha < 1 is a fixed parameter. When a car is hit by a Molotov cocktail, it burns and the fire propagates to the entire occupied interval which turns vacant. We show that with high probability when n -> a, the parking lot becomes saturated at a time close to 1 (i.e. as in the absence of fire) for alpha > 2/3, whereas for alpha < 2/3, the average occupation approaches 1 at time 1 but then quickly drops to 0 before the parking lot is ever saturated. Our study relies on asymptotics for the occupation of the parking lot without fires in certain regimes which may be of independent interest.

Dates et versions

hal-00705406 , version 1 (07-06-2012)

Identifiants

Citer

J. Bertoin. Burning cars in a parking lot. Communications in Mathematical Physics, 2011, 306 (1), pp.261-290. ⟨10.1007/s00220-011-1288-8⟩. ⟨hal-00705406⟩
182 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More