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Slow-to-Start Traffic Model: Traffic Saturation and Scaling Limits.
- Source :
-
Journal of Statistical Physics . Sep2020, Vol. 180 Issue 1-6, p935-953. 19p. - Publication Year :
- 2020
-
Abstract
- We consider a one-dimensional traffic model with a slow-to-start rule. The initial position of the cars in R is a Poisson process of parameter λ . Cars have speed 0 or 1 and travel in the same direction. At time zero the speed of all cars is 0; each car waits a mean-one exponential time to switch speed from 0 to 1 and stops when it collides with a stopped car. When the car 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 both regimes all cars collide infinitely often and each car has asymptotic mean velocity 1 / λ . In the saturated regime the moving cars form a point process whose intensity tends to 1. The remaining cars condensate in a set of points whose intensity tends to zero as 1 / t . We study the scaling limit of the traffic jam evolution in terms of a collection of coalescing Brownian motions. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00224715
- Volume :
- 180
- Issue :
- 1-6
- Database :
- Academic Search Index
- Journal :
- Journal of Statistical Physics
- Publication Type :
- Academic Journal
- Accession number :
- 144920373
- Full Text :
- https://doi.org/10.1007/s10955-020-02555-7