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The macroscopic fundamental diagram (MFD) is a large scale description of the traffic in a urban area and relates the average car flow to the average car density. This MFD has been observed empirically in several cities but how its…

Physics and Society · Physics 2026-01-14 Erwan Taillanter , Andreas Schadschneider , Marc Barthelemy

This study develops a dynamic fundamental diagram (FD) framework tailored to mixed traffic environments comprising automated vehicles (AVs) and human-driven vehicles (HDVs). Describing function analysis is employed to derive approximate…

Systems and Control · Electrical Eng. & Systems 2026-04-29 Jiwan Jiang , Soyoung Ahn

Using a stochastic cellular automaton model for urban traffic flow, we study and compare Macroscopic Fundamental Diagrams (MFDs) of arterial road networks governed by different types of adaptive traffic signal systems, under various…

Cellular Automata and Lattice Gases · Physics 2013-02-19 Lele Zhang , Timothy M. Garoni , Jan de Gier

Macroscopic traffic flow is stochastic, but the physics-informed deep learning methods currently used in transportation literature embed deterministic PDEs and produce point-valued outputs; the stochasticity of the governing dynamics plays…

Systems and Control · Electrical Eng. & Systems 2026-03-11 Wuping Xin

Traditional DTA models of large cities suffer from prohibitive computation times and calibration/validation can become major challenges faced by practitioners. The empirical evidence in 2008 in support of the existence of a Macroscopic…

Analysis of PDEs · Mathematics 2018-12-04 Rafegh Aghamohammadi , Jorge A. Laval

Urbanization leads to an increase of traffic in cities. The Macroscopic Fundamental Diagram (MFD) suggests to describe urban traffic at a zonal level, in order to measure and control traffic. However, for a proper estimation, all data needs…

Physics and Society · Physics 2020-02-14 Victor L. Knoop , Marianthi Mermygka , Hans van Lint

Dynamic network-level models directly addressing ride-sourcing services can support the development of efficient strategies for both congestion alleviation and promotion of more sustainable mobility. Recent developments presented models…

Physics and Society · Physics 2023-01-25 Caio Vitor Beojone , Nikolas Geroliminis

Stochastic vegetation-water dynamical systems play a pivotal role in ecological stability, biodiversity, water resource management, and adaptation to climate change. This research proposes a machine learning-based method for analyzing rare…

Dynamical Systems · Mathematics 2024-02-29 Yang Li , Shenglan Yuan , Shengyuan Xu

Normalizing flows transform a simple base distribution into a complex target distribution and have proved to be powerful models for data generation and density estimation. In this work, we propose a novel type of normalizing flow driven by…

Machine Learning · Computer Science 2021-07-14 Ruizhi Deng , Bo Chang , Marcus A. Brubaker , Greg Mori , Andreas Lehrmann

Urban congestions cause inefficient movement of vehicles and exacerbate greenhouse gas emissions and urban air pollution. Macroscopic emission fundamental diagram (eMFD)captures an orderly relationship among emission and aggregated traffic…

In this work, we propose an alternative stochastic model for the fundamental diagram of traffic flow with minimal number of parameters. Our approach is based on a mesoscopic viewpoint of the traffic system in terms of the dynamics of…

Physics and Society · Physics 2016-02-23 Adriano Francisco Siqueira , Carlos Jose Todero Peixoto , Chen Wu , Wei-Liang Qian

The Macroscopic Fundamental Diagram is a popular tool used to describe traffic dynamics in an aggregated way, with applications ranging from traffic control to incident analysis. However, estimating the MFD for a given network requires…

Machine Learning · Computer Science 2026-05-12 Amalie Roark , Serio Agriesti , Francisco Camara Pereira , Guido Cantelmo

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…

Probability · Mathematics 2021-02-11 Michel Mandjes , Jaap Storm

The fundamental diagram (FD), also known as the flow--density relation, is one of the most fundamental concepts in the traffic flow theory. It describes the relation between equilibrated flow, density, and speed in traffic flow.…

Fluid Dynamics · Physics 2019-02-12 Toru Seo , Yutaka Kawasaki , Takahiko Kusakabe , Yasuo Asakura

Strongly nonlinear flows, which commonly arise in geophysical and engineering turbulence, are characterized by persistent and intermittent energy transfer between various spatial and temporal scales. These systems are difficult to model and…

Dynamical Systems · Mathematics 2022-01-25 Hassan Arbabi , Themistoklis Sapsis

A method is developed to estimate the properties of a global hydrodynamic instability in turbulent flows from measurement data of the limit-cycle oscillations. For this purpose, the flow dynamics are separated in deterministic contributions…

Fluid Dynamics · Physics 2021-04-21 Moritz Sieber , C. Oliver Paschereit , Kilian Oberleithner

In recent works, we have proposed a stochastic cellular automaton model of traffic flow connecting two exactly solvable stochastic processes, i.e., the Asymmetric Simple Exclusion Process and the Zero Range Process, with an additional…

Statistical Mechanics · Physics 2009-05-19 Masahiro Kanai , Katsuhiro Nishinari , Tetsuji Tokihiro

We develop an approach to learn an interpretable semi-parametric model of a latent continuous-time stochastic dynamical system, assuming noisy high-dimensional outputs sampled at uneven times. The dynamics are described by a nonlinear…

Machine Learning · Statistics 2019-02-13 Lea Duncker , Gergo Bohner , Julien Boussard , Maneesh Sahani

As urbanization advances, cities are expanding, leading to a more decentralized urban structure and longer average commuting durations. The construction of an urban expressway system emerges as a critical strategy to tackle this challenge.…

Systems and Control · Electrical Eng. & Systems 2024-06-14 Yunran Di , Weihua Zhang , Haotian Shi , Heng Ding , Jinbiao Huo , Bin Ran

This paper presents a macroscopic fundamental diagram model with volume-delay relationship (MFD-VD) for road traffic networks, by exploring two new data sources: license plate cameras (LPCs) and road congestion indices (RCIs). We derive a…

Physics and Society · Physics 2024-02-09 Ke Han , Tao Huang , Wenbo Fan , Qian Ge , Shihui Dong , Xuting Wang
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