Related papers: Fundamental theorems of traffic flow

This paper presents a more complete version than hitherto published of our explanation of a transition from regular to irregular motions and more generally of the nature of a certain kind of deterministic chaos. To this end we introduced a…

We investigate both experimentally and theoretically the traffic of particles flowing in microfluidic obstacle networks. We show that the traffic dynamics is a non-linear process: the particle current does not scale with the particle…

A nucleation model for the breakdown phenomenon in freeway free traffic flow at an on-ramp bottleneck is presented. This model, which can explain empirical results on the breakdown phenomenon, is based on assumptions of three-phase traffic…

This paper studies a stochastic model that describes the evolution of vehicle densities in a road network. It is consistent with the class of (deterministic) kinematic wave models, which describe traffic flows on the basis of conservation…

The ability to predict traffic flow over time for crowded areas during rush hours is increasingly important as it can help authorities make informed decisions for congestion mitigation or scheduling of infrastructure development in an area.…

This paper is concerned with the study of a model case of first order Hamilton-Jacobi equations posed on a "junction", that is to say the union of a finite number of half-lines with a unique common point. The main result is a comparison…

We study a minimal model of traffic flows in complex networks, simple enough to get analytical results, but with a very rich phenomenology, presenting continuous, discontinuous as well as hybrid phase transitions between a free-flow phase…

It is shown that the branch of the empirical fundamental diagram for congested traffic strongly depends both on the type of the congested pattern at a freeway bottleneck and on the freeway location where the fundamental diagram is measured.…

We have revealed physical features of autonomous driving in the framework of the three-phase traffic theory for which there is no fixed time headway to the preceding vehicle. A comparison with the classical model approach to autonomous…

Traffic flow data collected by an induction loop detector on the highway close to Koeln-Nord are investigated with respect to their dynamics including the stochastic content. In particular we present a new method, with which the flow…

The capacity of a street segment quantifies the maximal density of vehicles before congestion arises. Here we show in a simple mathematical model that fluctuations in the instantaneous number of vehicles entering a street segment are…

The central points of communication network flow has often been identified using graph theoretical centrality measures. In real networks, the state of traffic density arises from an interplay between the dynamics of the flow and the…

We consider transport networks with nodes scattered at random in a large domain. At certain local rates, the nodes generate traffic flowing according to some navigation scheme in a given direction. In the thermodynamic limit of a growing…

The characteristic features of traffic breakdown near on-ramp are analyzed. To describe this phenomenon the probabilistic description regarding the jam emergence as the formation of a large car cluster on highway inside the synchronized…

We critically discuss the concept of ``synchronized flow'' from a historical, empirical, and theoretical perspective. Problems related to the measurement of vehicle data are highlighted, and questionable interpretations are identified.…

Rectified flow (Liu et al., 2022; Liu, 2022; Wu et al., 2023) is a method for defining a transport map between two distributions, and enjoys popularity in machine learning, although theoretical results supporting the validity of these…

We present an economics-based method for deciding the optimal rates at which vehicles are allowed to enter a highway. The method exploits the naturally occuring fluctuations of traffic flow and is flexible enough to adapt in real time to…

Based on experimental traffic data obtained from German and US highways, we propose a novel two-dimensional first-order macroscopic traffic flow model. The goal is to reproduce a detailed description of traffic dynamics for the real road…

In this work, we derive first order continuum traffic flow models from a microscopic delayed follow-the-leader model. Those are applicable in the context of vehicular traffic flow as well as pedestrian traffic flow. The microscopic model is…

We show that keeping a constant lower limit on the net-time headway is the key mechanism behind the dynamics of pedestrian streams. There is a large variety in flow and speed as functions of density for empirical data of pedestrian streams,…