INVESTIGADORES
FERRARI pablo Augusto
artículos
Título:
Slow-to-Start Traffic Model: Traffic Saturation and Scaling Limits
Autor/es:
FERRARI, PABLO A.; ROLLA, LEONARDO T.
Revista:
JOURNAL OF STATISTICAL PHYSICS
Editorial:
SPRINGER
Referencias:
Lugar: Munich; Año: 2020 vol. 180 p. 935 - 953
ISSN:
0022-4715
Resumen:
We consider a one-dimensional traffic model with a slow-to-start rule. The initial position ofthe cars in R is a Poisson process of parameter λ. Cars have speed 0 or 1 and travel in thesame direction. At time zero the speed of all cars is 0; each car waits a mean-one exponentialtime to switch speed from 0 to 1 and stops when it collides with a stopped car. When thecar is no longer blocked, it waits a new exponential time to assume speed one, and so on.We study the saturated regime λ > 1 and the critical regime λ = 1, showing that in bothregimes all cars collide infinitely often and each car has asymptotic mean velocity 1/λ. Inthe saturated regime the moving cars form a point process whose intensity tends to 1. Theremaining cars condensate in a set of points whose intensity tends to zero as 1/√t.We studythe scaling limit of the traffic jam evolution in terms of a collection of coalescing Brownianmotions.