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Related papers: Biham-Middleton-Levine Traffic Model With Origin-D…

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Estimating dynamic Origin-Destination (OD) traffic flow is crucial for understanding traffic patterns and the traffic network. While dynamic origin-destination estimation (DODE) has been studied for decades as a useful tool for estimating…

Optimization and Control · Mathematics 2024-01-22 Han Yu , Suyanpeng Zhang , Sze-chuan Suen , Maged Dessouky , Fernando Ordonez

Origin-Destination Matrix (ODM) estimation is a classical problem in transport engineering aiming to recover flows from every Origin to every Destination from measured traffic counts and a priori model information. In addition to traffic…

Optimization and Control · Mathematics 2019-07-18 Gabriel Michau , Nelly Pustelnik , Pierre Borgnat , Patrice Abry , Alfredo Nantes , Ashish Bhaskar , Edward Chung

In the Biham-Middleton-Levine traffic model cars are placed with some density p on a two dimensional torus, and move according to a (simple) set of predefined rules. Computer simulations show this system exhibits many interesting phenomena:…

Probability · Mathematics 2007-09-11 Itai Benjamini , Ori Gurel-Gurevich , Roey Izkovsky

The Biham, Middleton and Levine (BML) model is extended to describe dynamic route choices between the residence and workplace in cities. The traffic dynamic in the city with a single workplace is studied from the velocity diagram, arrival…

Physics and Society · Physics 2015-06-05 Jun Fang , Jing Shi , Xi-Qun Chen , Zheng Qin

Initially a car is placed with probability p at each site of the two-dimensional integer lattice. Each car is equally likely to be East-facing or North-facing, and different sites receive independent assignments. At odd time steps, each…

Probability · Mathematics 2007-05-23 Omer Angel , Alexander E Holroyd , James B Martin

Estimation of origin-destination (OD) demand plays a key role in successful transportation studies. In this paper, we consider the estimation of time-varying day-to-day OD flows given data on traffic volumes in a transportation network for…

In this paper we propose a LWR-like model for traffic flow on networks which allows one to track several groups of drivers, each of them being characterized only by their destination in the network. The path actually followed to reach the…

Optimization and Control · Mathematics 2016-06-17 Emiliano Cristiani , Fabio S. Priuli

Estimating Origin-Destination (OD) travel demand is vital for effective urban planning and traffic management. Developing universally applicable OD estimation methodologies is significantly challenged by the pervasive scarcity of…

Emerging Technologies · Computer Science 2025-07-02 Chao Zhang , Neha Arora , Christopher Bian , Yechen Li , Willa Ng , Andrew Tomkins , Bin Yan , Janny Zhang , Carolina Osorio

We study a Follow-the-Leader (FtL) ODE model for traffic flow with rough road condition, and analyze stationary traveling wave profiles where the solutions of the FtL model trace along, near the jump in the road condition. We derive a…

Analysis of PDEs · Mathematics 2018-02-06 Wen Shen

By means of microscopic simulations we show that non-instantaneous adaptation of the driving behaviour to the traffic situation together with the conventional measurement method of flow-density data can explain the observed…

Statistical Mechanics · Physics 2009-11-10 Martin Treiber , Dirk Helbing

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

The study focuses on estimating and predicting time-varying origin to destination (OD) trip tables for a dynamic traffic assignment (DTA) model. A bi-level optimisation problem is formulated and solved to estimate OD flows from pre-existent…

Signal Processing · Electrical Eng. & Systems 2019-06-13 Sajjad Shafiei , Adriana-Simona Mihaita , Chen Cai

We present a traffic flow model consisting of a gluing between the Lighthill-Whitham and Richards macroscopic model with a first order microscopic follow the leader model. The basic analytical properties of this model are investigated.…

Analysis of PDEs · Mathematics 2015-06-18 Rinaldo M. Colombo , Francesca Marcellini

We perform a systematic analysis on the large-scale taxi trip data to uncover urban mobility and city dynamics in multimodal urban transportation environments. As a case study, we use the taxi origin-destination trip data and some…

Computation · Statistics 2018-12-27 Xiao-Feng Xie , Zunjing Jenipher Wang

High-resolution origin-destination (OD) tables are essential for a wide spectrum of transportation applications, from modeling traffic and signal timing optimization to congestion pricing and vehicle routing. However, outside a handful of…

Computers and Society · Computer Science 2026-05-06 Rishav Sen , Jose Paolo Talusan , Abhishek Dubey , Ayan Mukhopadhyay , Samitha Samaranayake , Aron Laszka

We consider several non-local models for traffic flow, including both microscopic ODE models and macroscopic PDE models. The ODE models describe the movement of individual cars, where each driver adjusts the speed according to the road…

Analysis of PDEs · Mathematics 2018-11-16 Johanna Ridder , Wen Shen

This contribution summarizes and explains various principles from physics which are used for the simulation of traffic flows in large street networks, the modeling of destination, transport mode, and route choice, or the simulation of urban…

Physics and Society · Physics 2015-06-17 Dirk Helbing , Kai Nagel

Natural phenomena frequently involve a very large number of interacting molecules moving in confined regions of space. Cellular transport by motor proteins is an example of such collective behavior. We derive a deterministic compartmental…

Subcellular Processes · Quantitative Biology 2017-11-01 Yoram Zarai , Michael Margaliot , Anatoly B. Kolomeisky

In recent years, with the advancements in information and communication technology, different emerging on-demand shared mobility services have been introduced as innovative solutions in the low-density areas, including on-demand transit…

Computers and Society · Computer Science 2021-10-05 Nael Alsaleh , Bilal Farooq

In the area of urban transportation networks, a growing number of day-to-day (DTD) traffic dynamic theories have been proposed to describe the network flow evolution, and an increasing amount of laboratory experiments have been conducted to…

Physics and Society · Physics 2023-03-08 Hang Qi , Ning Jia , Xiaobo Qu , Zhengbing He
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