Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# Self-Organized Criticality of Traffic Flow

Version 1 : Received: 3 August 2021 / Approved: 5 August 2021 / Online: 5 August 2021 (08:02:42 CEST)
Version 2 : Received: 8 September 2021 / Approved: 9 September 2021 / Online: 9 September 2021 (15:58:11 CEST)

How to cite: Laval, J. Self-Organized Criticality of Traffic Flow. Preprints 2021, 2021080125 (doi: 10.20944/preprints202108.0125.v1). Laval, J. Self-Organized Criticality of Traffic Flow. Preprints 2021, 2021080125 (doi: 10.20944/preprints202108.0125.v1).

## Abstract

This paper shows that the kinematic wave model exhibits self-organized criticality when initialized with random initial conditions around the critical density. This has several important implications for traffic flow in the capacity state, such as: \item jam sizes obey a power law distribution with exponents 1/2, implying that both the mean and variance diverge to infinity, \item self-organization is an intrinsic property of traffic flow models in general, independently of other random perturbations, \item this critical behavior is a consequence of the flow maximization objective of traffic flow models, which can be observed on a density range around the critical density that depends on the length of the segment, \item typical measures of performance are proportional to the area under a Brownian excursion, and therefore are given by different scalings of the Airy distribution, \item traffic in the time-space diagram forms self-affine fractals where the basic unit is a triangle, in the shape of the fundamental diagram, containing 3 traffic states: voids, capacity and jams.

## Keywords

traffic flow; kinematic wave model; self-organized criticality; fractals

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