论文标题
缓慢启动的交通模型：凝结，饱和和缩放限制
Slow-to-Start Traffic Model: Condensation, Saturation and Scaling Limits
论文作者
论文摘要
我们考虑具有缓慢启动规则的一维流量模型。汽车在$ \ Mathbb r $中的初始位置是参数$λ$的泊松过程。汽车的速度为0或1，并沿相同的方向行驶。在零时，所有汽车的速度为0；每辆车都等待指数时间将速度从$ 0 $切换到$ 1 $，并且与停车车相撞时停止。当汽车不再被阻塞时，它会等待一个新的指数时间来假设速度速度，依此类推。我们研究了饱和体制$λ> 1 $的冷凝物的出现和关键体制$λ= 1 $，这表明在这两种制度中，所有汽车都经常碰撞，每辆车都有渐近平均速度$ 1/λ$。在饱和度方案中，移动的汽车形成了一个点过程，其强度趋于1。其余的汽车在一组点的强度倾向于零为$ 1/\ sqrt t $中凝结。我们研究了一系列聚集的布朗尼动议，研究了交通堵塞演变的缩放限制。
We consider a one-dimensional traffic model with a slow-to-start rule. The initial position of the cars in $\mathbb R$ 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 an 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 emergence of condensation for 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 $1/\sqrt t$. We study the scaling limit of the traffic jam evolution in terms of a collection of coalescing Brownian motions.
