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In Part I of this paper series, several macroscopic traffic model elements for mathematically describing freeway networks equipped with managed lane facilities were proposed. These modeling techniques seek to capture at the macroscopic the…

Systems and Control · Electrical Eng. & Systems 2019-08-28 Matthew A. Wright , Roberto Horowitz , Alex A. Kurzhanskiy

Kinetic models for vehicular traffic are reviewed and considered from the point of view of deriving macroscopic equations. A derivation of the associated macroscopic traffic flow equations leads to different types of equations: in certain…

Numerical Analysis · Mathematics 2015-03-13 Raul Borsche , Axel Klar , Mark Kimathi

We introduce a general formulation for an implicit equation-free method in the setting of slow-fast systems. First, we give a rigorous convergence result for equation-free analysis showing that the implicitly defined coarse-level time…

Dynamical Systems · Mathematics 2015-08-03 Christian Marschler , Jan Sieber , Rainer Berkemer , Atsushi Kawamoto , Jens Starke

The rapid development of autonomous vehicles (AVs) holds vast potential for transportation systems through improved safety, efficiency, and access to mobility. However, the progression of these impacts, as AVs are adopted, is not well…

Artificial Intelligence · Computer Science 2022-01-03 Cathy Wu , Aboudy Kreidieh , Kanaad Parvate , Eugene Vinitsky , Alexandre M Bayen

Optimal transport has recently been brought forward as a tool for modeling and efficiently solving a variety of flow problems, such as origin-destination problems and multi-commodity flow problems. Although the framework has shown to be…

Optimization and Control · Mathematics 2025-07-29 Anqi Dong , Karl Henrik Johansson , Johan Karlsson

We present a macroscopic model of mixed multi-lane freeway traffic that can be easily calibrated to empirical traffic data, as is shown for Dutch highway data. The model is derived from a gas-kinetic level of description, including effects…

Statistical Mechanics · Physics 2009-10-31 Vladimir Shvetsov , Dirk Helbing

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

Traffic flow forecasting aims to predict future traffic flows based on the historical traffic conditions and the road network. It is an important problem in intelligent transportation systems, with a plethora of methods been proposed.…

Machine Learning · Computer Science 2025-08-04 Yusheng Zhao , Xiao Luo , Haomin Wen , Zhiping Xiao , Wei Ju , Ming Zhang

A new single lane car following model of traffic flow is presented. The model is inertial and free of collisions. It demonstrates experimentally observed features of traffic flow such as the existence of three regimes: free, fluctuative…

Disordered Systems and Neural Networks · Physics 2009-10-31 Elad Tomer , Leonid Safonov , Shlomo Havlin

A macroscopic model is proposed to depict the traffic dynamics involved in urban traffic systems. The link dynamics are described based on the cell-transmission model and bounded by the link capacities, while the flow dynamics are proposed…

Optimization and Control · Mathematics 2020-02-25 Yicheng Zhang

We generalize the phase transition model studied in [R. Colombo. Hyperbolic phase transition in traffic flow.\ SIAM J.\ Appl.\ Math., 63(2):708-721, 2002], that describes the evolution of vehicular traffic along a one-lane road. Two…

Analysis of PDEs · Mathematics 2018-02-14 Edda Dal Santo , Massimiliano D. Rosini , Nikodem Dymski , Mohamed Benyahia

We study the derivation of second order macroscopic traffic models from kinetic descriptions. In particular, we recover the celebrated Aw-Rascle model as the hydrodynamic limit of an Enskog-type kinetic equation out of a precise…

Statistical Mechanics · Physics 2020-01-24 Giacomo Dimarco , Andrea Tosin

Traffic waves, the spatiotemporal propagation of congestion, are a key feature of traffic flow. As Adaptive Cruise Control (ACC) systems gain widespread adoption and show promise for improving both efficiency and safety, understanding how…

Analysis of PDEs · Mathematics 2026-02-03 Zihao Li , Quyuan Lin , Fan Pu , Soyoung Ahn , Yunlong Zhang , Jiwan Jiang , Yang Zhou

This paper presents a new class of one-dimensional (1D) traffic models with look-ahead rules that take into account of two effects: nonlocal slow-down effect and right-skewed non-concave asymmetry in the fundamental diagram. The proposed 1D…

Cellular Automata and Lattice Gases · Physics 2020-01-29 Yi Sun , Changhui Tan

This paper presents a mesoscopic traffic flow model that explicitly describes the spatio-temporal evolution of the probability distributions of vehicle trajectories. The dynamics are represented by a sequence of factor graphs, which enable…

Machine Learning · Statistics 2019-09-25 Saif Eddin Jabari , Deepthi Mary Dilip , DianChao Lin , Bilal Thonnam Thodi

A statistical predictive model in which a high-dimensional time-series regenerates at the end of each day is used to model road traffic. Due to the regeneration, prediction is based on a daily modeling using a vector autoregressive model…

Statistics Theory · Mathematics 2021-01-27 Mohammed Bouchouia , François Portier

Traffic prediction is necessary not only for management departments to dispatch vehicles but also for drivers to avoid congested roads. Many traffic forecasting methods based on deep learning have been proposed in recent years, and their…

Machine Learning · Computer Science 2020-05-12 Jichen Wang , Weiguo Zhu , Yongqi Sun , Chunzi Tian

We propose a macroscopic traffic network flow model suitable for analysis as a dynamical system, and we qualitatively analyze equilibrium flows as well as convergence. Flows at a junction are determined by downstream supply of capacity as…

Systems and Control · Computer Science 2015-05-25 Samuel Coogan , Murat Arcak

The Lorentz mirror model provides a clean setting to study macroscopic transport generated solely by quenched environmental randomness. We introduce a hierarchical version whose distribution of left--right crossings satisfies an exact…

Statistical Mechanics · Physics 2026-03-05 Raphael Lefevere , Hal Tasaki

Many headway-based car-following models describe longitudinal adaptation through linear relaxation laws, which can produce unrealistically large accelerations and limit the physical consistency of microscopic traffic dynamics. Motivated by…

Systems and Control · Electrical Eng. & Systems 2026-05-13 Nizhum Rahman , Trachette L. Jackson