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We consider a one-dimensional traffic model with a slow-to-start rule. Theinitial position of the cars in $\mathbb R$ is a Poisson process of parameter$\lambda$. Cars have speed 0 or 1 and travel in the same direction. At timezero the speed of all cars is 0; each car waits an exponential time to switchspeed 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 emergence of condensation for the saturated regime$\lambda>1$ and the critical regime $\lambda=1$, showing that in both regimesall cars collide infinitely often and each car has asymptotic mean velocity$1/\lambda$. In the saturated regime the moving cars form a point process whoseintensity tends to 1. The remaining cars condensate in a set of points whoseintensity tends to zero as $1/\sqrt t$. We study the scaling limit of thetraffic jam evolution in terms of a collection of coalescing Brownian motions.

Slow-to-Start Traffic Model: Condensation, Saturation and Scaling Limits