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The emergence of congestion is a critical phenomenon in transport systems. Transport is organized along pathways abstracted by links, which connect different nodes as regions to form the network. The modeling of traffic has so far mainly…

Physics and Society · Physics 2023-03-23 Zhidong He

Mitigating traffic congestion on urban roads, with paramount importance in urban development and reduction of energy consumption and air pollution, depends on our ability to foresee road usage and traffic conditions pertaining to the…

Physics and Society · Physics 2018-04-27 Jingyuan Wang , Yu Mao , Jing Li , Chao Li , Zhang Xiong , Wen-Xu Wang

While many classical traffic models treat the spatial extension of streets continuously or by discretization into cells of a certain length, we will subdivide roads into comparatively long homogeneous road sections of constant capacity with…

Statistical Mechanics · Physics 2009-11-10 Dirk Helbing

This article present a method of mutual transformation between count model and composition model. Offer the mathematical view of classical radio and log-radio in compositional data analysis and expand the idea of mixture model of counts…

Statistics Theory · Mathematics 2025-09-12 Guanyi Wu

Traffic congestion at urban-scale levels occurs when road network supply is insufficient compared with demand. Therefore, the relationship between supply and demand has been extensively investigated in the literature. Especially the impact…

Applications · Statistics 2023-10-26 Kota Nagasaki , Toru Seo

We calculate the distribution of the distance headways (i.e., the instantaneous gap between successive vehicles) as well as the distribution of instantaneous distance between successive jams in the Nagel-Schreckenberg (NS) model of…

Statistical Mechanics · Physics 2015-06-25 Debashish Chowdhury , Kingshuk Ghosh , Arnab Majumdar , Shishir Sinha , R. B. Stinchcombe

Day-to-day traffic dynamics are widely used to model flow evolution due to travelers' learning and adjustment behavior, yet empirical analysis of these models often relies on descriptive calibration with limited inferential content. This…

Optimization and Control · Mathematics 2026-05-05 Minghui Wu , Yafeng Yin , Jerome P. Lynch , Zhichen Liu

From the macroscopic viewpoint for describing the acceleration behavior of drivers, this letter presents a weighted probabilistic cellular automaton model (the WP model, for short) by introducing a kind of random acceleration probabilistic…

Physics and Society · Physics 2009-11-13 X. L. Li , H. Kuang , T. Song , S. Q. Dai , Z. P. Li

As a dynamical complex system, traffic is characterized by a transition from free flow to congestions, which is mostly studied in highways. However, despite its importance in developing congestion mitigation strategies, the understanding of…

Physics and Society · Physics 2015-12-02 Feilong Wang , Daqing Li , Xiaoyun Xu , Ruoqian Wu , Shlomo Havlin

We present a detailed analysis of single-vehicle data which sheds some light on the microscopic interaction of the vehicles. Besides the analysis of free flow and synchronized traffic the data sets especially provide information about wide…

Statistical Mechanics · Physics 2009-11-07 Wolfgang Knospe , Ludger Santen , Andreas Schadschneider , Michael Schreckenberg

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

Inter-city highway transportation is significant for urban life. As one of the key functions in intelligent transportation system (ITS), traffic evaluation always plays significant role nowadays, and daily traffic flow prediction still…

Machine Learning · Computer Science 2023-08-11 Weilong Ding , Tianpu Zhang , Jianwu Wang , Zhuofeng Zhao

We study the emergence of congestion patterns in urban networks by modeling vehicular interaction by means of a simple traffic rule and by using a set of measures inspired by the standard Betweenness Centrality (BC). We consider a…

Physics and Society · Physics 2022-07-25 Marco Cogoni , Giovanni Busonera , Francesco Versaci

Traffic prediction is a fundamental task in many real applications, which aims to predict the future traffic volume in any region of a city. In essence, traffic volume in a region is the aggregation of traffic flows from/to the region.…

Signal Processing · Electrical Eng. & Systems 2019-06-04 Xian Zhou , Yanyan Shen , Linpeng Huang

This paper is concerned with a fluidodynamic model for traffic flow. More precisely, we consider a single conservation law, deduced from conservation of the number of cars, defined on a road network that is a collection of roads with…

Analysis of PDEs · Mathematics 2007-05-23 G. M. Coclite , B. Piccoli

Three-way data can be conveniently modelled by using matrix variate distributions. Although there has been a lot of work for the matrix variate normal distribution, there is little work in the area of matrix skew distributions. Three matrix…

Methodology · Statistics 2018-08-15 Michael P. B. Gallaugher , Paul D. McNicholas

A macroscopic model-based approach for estimation of the traffic state, specifically of the (total) density and flow of vehicles, is developed for the case of "mixed" traffic, i.e., traffic comprising both ordinary and connected vehicles.…

Optimization and Control · Mathematics 2015-04-28 Nikolaos Bekiaris-Liberis , Claudio Roncoli , Markos Papageorgiou

The ability of existing headway distributions to accurately reflect the diverse behaviors and characteristics in heterogeneous traffic (different types of vehicles) and mixed traffic (human-driven vehicles with autonomous vehicles) is…

Applications · Statistics 2025-11-06 Natchaphon Leungbootnak , Zihao Li , Zihang Wei , Dominique Lord , Yunlong Zhang

This paper develops a data-driven toolkit for traffic forecasting using high-resolution (a.k.a. event-based) traffic data. This is the raw data obtained from fixed sensors in urban roads. Time series of such raw data exhibit heavy…

Signal Processing · Electrical Eng. & Systems 2021-01-01 Wenqing Li , Chuhan Yang , Saif Eddin Jabari

In the setting of a recently developed cellular stochastic traffic flow model, it has shown that the joint per-cell vehicle densities, as a function of time, can be accurately approximated by a Gaussian process, which has the attractive…

Optimization and Control · Mathematics 2020-07-16 Michel Mandjes , Jaap Storm