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Macroscopic fundamental diagrams (MFDs) and related network traffic dynamics models have received both theoretical support and empirical validation with the emergence of new data collection technologies. However, the existence of…

Statistical Mechanics · Physics 2024-12-11 Alexander Hammerl , Ravi Seshadri , Thomas Kjær Rasmussen , Otto Anker Nielsen

A simple macroscopic model for the vehicular traffic flow with hysteresis is proposed. The model includes drivers' hysteresis behavior into the classical Lighthill-Whitham-Richard (LWR) model. One novelty of the model is how the hysteresis…

Analysis of PDEs · Mathematics 2018-11-02 Andrea Corli , Haitao Fan

Transportation departments take actions to manage traffic flow and reduce travel times based on estimated current and projected traffic conditions. Travel time estimates and forecasts require information on traffic density which are…

Applications · Statistics 2016-02-01 Nicholas Polson , Vadim Sokolov

We investigate the adaptation of the time headways in car-following models as a function of the local velocity variance, which is a measure of the inhomogeneity of traffic flow. We apply this mechanism to several car-following models and…

Physics and Society · Physics 2007-08-08 Martin Treiber , Arne Kesting , Dirk Helbing

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.…

Statistical Mechanics · Physics 2007-05-23 Boris S. Kerner

The dynamical properties of road traffic time series from North-Rhine Westphalian motorways are investigated. The article shows that road traffic dynamics is well described as a persistent stochastic process with two fixed points…

Data Analysis, Statistics and Probability · Physics 2007-05-23 Helge Siegel , Dennis Belomestnyi

This paper develops a computational framework based on a car-following model to study traffic instability and lane changes. Building upon Newell's classical first-order car-following model, we show that, both analytically and numerically,…

Optimization and Control · Mathematics 2025-01-07 Nicholas Mankowski , Hassan Mushtaq , Hanliang Guo

We study traffic flow on roads with a localized periodic inhomogeneity such as traffic signals, using a stochastic car-following model. We find that in cases of congestion, traffic flow can be optimized by controlling the inhomogeneity's…

Statistical Mechanics · Physics 2007-05-23 Elad Tomer , Leonid Safonov , Nilly Madar , Shlomo Havlin

Travel time on a route varies substantially by time of day and from day to day. It is critical to understand to what extent this variation is correlated with various factors, such as weather, incidents, events or travel demand level in the…

Applications · Statistics 2019-10-17 Shuguan Yang , Sean Qian

Existing methods for traffic signal design are either too simplistic to capture realistic traffic characteristics or too complicated to be mathematically tractable. In this study, we attempts to fill the gap by presenting a new method based…

Dynamical Systems · Mathematics 2015-10-06 Wen-Long Jin , Yifeng Yu

Nowadays, traffic monitoring systems have access to real time data, e.g. through GPS devices. We propose a new traffic model able to take into account these data and, hence, able to describe the effects of unpredictable accidents. The well…

Analysis of PDEs · Mathematics 2014-11-11 Rinaldo M. Colombo , Francesca Marcellini

This paper analyzes the use of variable speed limits to optimize travel time reliability for commuters. The investigation focuses on a traffic corridor with a bottleneck subject to the capacity drop phenomenon. The optimization criterion is…

Optimization and Control · Mathematics 2025-09-16 Alexander Hammerl , Ravi Seshadri , Thomas Kjær Rasmussen , Otto Anker Nielsen

To improve the routing decisions of individual drivers and the management policies designed by traffic operators, one needs reliable estimates of travel time distributions. Since congestion caused by both recurrent patterns (e.g., rush…

Physics and Society · Physics 2022-10-13 Nikki Levering , Marko Boon , Michel Mandjes

While macroscopic models for single or multi-lane traffic flow are well established, these models are not applicable to the dynamics and characteristics of disordered traffic which is characterized by widely different types of vehicles and…

Physics and Society · Physics 2023-10-27 Shrey Agrawal , Venkatesan Kanagaraj , Martin Treiber

Traffic congestion represents a complex urban phenomenon that has been the subject of extensive research employing various modeling techniques grounded in the principles of physics and molecular theory. Although factors such as road design,…

Theoretical Economics · Economics 2025-10-07 Shawn Berry

Monitoring and control of traffic networks represent alternative, inexpensive strategies to minimize traffic congestion. As the number of traffic sensors is naturally constrained by budgetary requirements, real-time estimation of traffic…

Systems and Control · Computer Science 2019-11-12 Sebastian A. Nugroho , Ahmad F. Taha , Christian Claudel

The causal connection between congestions and velocity changes at different locations induces various statistical features, which we identify and measure in detail. We carry out an empirical analysis of large-scale traffic data on a local…

Physics and Society · Physics 2024-10-10 Shanshan Wang , Michael Schreckenberg , Thomas Guhr

This paper analyzes the car following behavioral stochasticity based on two sets of field experimental trajectory data by measuring the wave travel time series of vehicle n. The analysis shows that (i) No matter the speed of leading vehicle…

Adaptation and Self-Organizing Systems · Physics 2019-11-06 Junfang Tian , Chenqiang Zhu , Danjue Chen , Rui Jiang , Guanying Wang , Ziyou Gao

In this article, we investigate theoretical and numerical properties of the first-order Lighthill-Whitham-Richards (LWR) traffic flow model with time delay. Since standard results from the literature are not directly applicable to the…

Numerical Analysis · Mathematics 2020-03-30 Simone Göttlich , Elisa Iacomini , Thomas Jung

By analyzing empirical time headway distributions of traffic flow, a hypothesis about the underlying stochastic process can be drawn. The results found lead to the assumption that the headways $T_i$ of individual vehicles follow a linear…

Other Condensed Matter · Physics 2007-05-23 Peter Wagner
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