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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

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…

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 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

In large-scale traffic optimization, models based on Macroscopic Fundamental Diagram (MFD) are recognized for their efficiency in broad network analyses. However, they fail to reflect variations in the individual traffic status of each road…

Machine Learning · Computer Science 2025-05-20 Zhixiong Jin , Dimitrios Tsitsokas , Nikolas Geroliminis , Ludovic Leclercq

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

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

Being widely adopted by the transportation and planning practitioners, the fundamental diagram (FD) is the primary tool used to relate the key macroscopic traffic variables of speed, flow, and density. We empirically analyze the relation…

Emerging Technologies · Computer Science 2025-01-14 Chao Zhang , Yechen Li , Neha Arora , Carolina Osorio

Despite the importance of urban traffic flows, there are only a few theoretical approaches to determine fundamental relationships between macroscopic traffic variables such as the traffic density, the utilization, the average velocity, and…

Physics and Society · Physics 2009-11-13 Dirk Helbing

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

The rapid urbanization and increasing traffic have serious social, economic, and environmental impact on metropolitan areas worldwide. It is of a great importance to understand the complex interplay of road networks and traffic conditions.…

Other Computer Science · Computer Science 2018-10-31 Weizi Li , Meilei Jiang , Yaoyu Chen , Ming C. Lin

Most traffic state forecast algorithms when applied to urban road networks consider only the links in close proximity to the target location. However, for longer-term forecasts also the traffic state of more distant links or regions of the…

Physics and Society · Physics 2020-09-18 Felix Rempe , Klaus Bogenberger

This paper presents two case studies where a macroscopic model-based approach for traffic state estimation, which we have recently developed, is employed and tested. The estimation methodology is developed for a "mixed" traffic scenario,…

Systems and Control · Computer Science 2015-09-22 Claudio Roncoli , Nikolaos Bekiaris-Liberis , Markos Papageorgiou

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

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

Effective modern transportation systems depend critically on accurate Signal Phase and Timing (SPaT) estimation. However, acquiring ground-truth SPaT information faces significant hurdles due to communication challenges with transportation…

Signal Processing · Electrical Eng. & Systems 2025-07-22 Mingcheng Liao , Zebang Feng , Miao Fan , Shengtong Xu , Haoyi Xiong

Besides the traditional data collection by stationary detectors, recent advances in wireless and sensor technologies have promoted new potentials for a vehicle-based data collection and local dissemination of information. By means of…

Other Computer Science · Computer Science 2010-12-22 Arne Kesting , Martin Treiber

Smartphones and other mobile devices are today pervasive across the globe. As an interesting side effect of the surge in mobile communications, mobile network operators can now easily collect a wealth of high-resolution data on the habits…

Networking and Internet Architecture · Computer Science 2016-10-25 Ghazaleh Khodabandelou , Vincent Gauthier , Mounim A. El-Yacoubi , Marco Fiore

Space-time visualizations of macroscopic or microscopic traffic variables is a qualitative tool used by traffic engineers to understand and analyze different aspects of road traffic dynamics. We present a deep learning method to learn the…

Machine Learning · Computer Science 2022-04-12 Bilal Thonnam Thodi , Zaid Saeed Khan , Saif Eddin Jabari , Monica Menendez

Accurate estimation of the traffic state over a network is essential since it is the starting point for designing and implementing any traffic management strategy. Hence, traffic operators and users of a transportation network can make…

Computers and Society · Computer Science 2022-01-04 Alexander Genser , Noel Hautle , Michail Makridis , Anastasios Kouvelas
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