# Rare-Event Properties of the Nagel-Schreckenberg Model

## TL;DR

This paper uses large-deviation simulations to analyze the distribution of traffic flow in the Nagel-Schreckenberg model, revealing rare traffic states and how flow distribution changes with car density.

## Contribution

It introduces a large-deviation approach to characterize rare traffic flow events in the Nagel-Schreckenberg model across a wide probability range.

## Key findings

- Flow distribution shape changes from free flow to congestion.
- Rare traffic situations can be characterized by correlations with jams and standing cars.
- Distribution spans over 140 decades in probability.

## Abstract

We have studied the distribution of traffic flow $q$ for the Nagel-Schreckenberg model by computer simulations. We applied a large-deviation approach, which allowed us to obtain the distribution $P(q)$ over more than one hundred decades in probability, down to probabilities like $10^{-140}$. This allowed us to characterize the flow distribution over a large range of the support and identify the characteristics of rare and even very rare traffic situations. We observe a change of the distribution shape when increasing the density of cars from the free flow to the congestion phase. Furthermore, we characterize typical and rare traffic situations by measuring correlations of $q$ to other quantities like density of standing cars or number and size of traffic jams.