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A coupled PDE-ODE model for bounded acceleration in macroscopic traffic flow models

IFAC-PapersOnLine 2018年第9期51卷 37-42页

作者： Laurent-Brouty, Nicolas Costeseque, Guillaume Goatin, Paola Université Côte d'Azur CNRS LJAD Inria France Ecole des Ponts ParisTech Champs-sur-Marne France

In this paper, we propose a new mathematical model accounting for the boundedness of traffic acceleration at a macroscopic scale. Our model is built on a first order macroscopic PDE model coupled with an ODE describing the trajectory of the leader of a platoon accelerating at a given constant rate. We use Wave Front Tracking techniques to construct approximate solutions to the Initial Value Problem. We present some numerical examples including the case of successive traffic signals on an arterial road and we compare the solution to our model with the solution given by the classical LWR equation in order to evaluate the impact of bounded acceleration. © 2018

关键词： traffic control Initial value problems Ordinary differential equations traffic signals Wavefronts Approximate solution Arterial roads Boundedness Constant rate First order macroscopic scale macroscopic traffic flow model New mathematical model

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A coupled PDE-ODE model for bounded acceleration in macroscopic traffic flow models

A coupled PDE-ODE model for bounded acceleration in macrosco...

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15th International-Federation-of-Automatic-Control (IFAC) Symposium on Control in Transportation Systems (CTS)

作者： Laurent-Brouty, Nicolas Costeseque, Guillaume Goatin, Paola Univ Cote dAzur INRIA CNRS LJAD Nice France Ecole Ponts ParisTech Champs Sur Marne France

关键词： Bounded acceleration macroscopic traffic flow model PDE-ODE coupling wave front tracking scheme

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First order multi-lane traffic flow model - an incentive based macroscopic model to represent lane change dynamics

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TRANSPORTMETRICA B-TRANSPORT DYNAMICS 2019年第1期7卷 1758-1779页

作者： Nagalur Subraveti, Hari Hara Sharan Knoop, Victor L. van Arem, Bart Delft Univ Technol Fac Civil Engn & Geosci Dept Transport & Planning Delft Netherlands

Unbalanced lane usage on motorways might lead to the reduction in capacity of the motorway. Lane-level traffic management present new opportunities to balance the lane-flow distribution and help reduce congestion. In order to come up with efficient traffic management strategies on a lane-level, there is a need for accurate lane-specific traffic state estimation models. This paper presents a first-order lane-level traffic flow model. The proposed model differs from the existing models in the following areas: (i) incentive-based motivation for lane changes and consideration of downstream conditions (ii) transfer of lateral flows among cells. The model is tested against real-world data. It is observed that the model is able to capture the lane-level dynamics in terms of the lane flow distribution. The model results are compared to a linear regression model and results show that the developed model performs better than the regression model on the test sections.

关键词： Lane-level macroscopic traffic flow model cell transmission model incentives lane flow distribution

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Estimation of stochastic link capacity and link performance function including uncertainty of driver's behaviour

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TRANSPORTMETRICA A-TRANSPORT SCIENCE 2025年第1期21卷 27-49页

作者： Kato, Teppei Uchida, Kenetsu Tani, Ryuichi Munehiro, Kazunori Nagaoka Univ Technol Grad Sch Engn Niigata Japan Hokkaido Univ Grad Sch Engn Sapporo Hokkaido Japan Civil Engn Res Inst Cold RegionPWRI Sapporo Hokkaido Japan

Recently, user equilibrium models with uncertainty were proposed to describe stochastic travel time in road networks. The accurate estimation of a stochastic link capacity is important for such models. This study develops a method for estimating a stochastic link capacity by considering the uncertainty of the driver's behaviour. We postulate that the stochastic link capacity follows a lognormal distribution. The characteristics of the lognormal distribution suit real traffic observation, e.g. nonnegativity, asymmetricity, and long-tailed. Furthermore, the estimated link capacity can derive the analytical likelihood function for the link performance function. Then, the link performance function can be estimated analytically by explicitly considering the source of uncertainty. The proposed methods can contribute to the estimation of stochastic link capacity and the link performance function for the user equilibrium model with stochastic travel time. A numerical calculation demonstrates the proposed method using real traffic observations in Sapporo, Japan.

关键词： Stochastic link capacity macroscopic traffic flow model link performance function user equilibrium travel time reliability

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macroscopic traffic flow modeling with physics regularized Gaussian process: A new insight into machine learning applications in transportation

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TRANSPORTATION RESEARCH PART B-METHODOLOGICAL 2021年 146卷 88-110页

作者： Yuan, Yun Zhang, Zhao Yang, Xianfeng Terry Zhe, Shandian Univ Utah Dept Civil & Environm Engn Salt Lake City UT 84112 USA Univ Utah Sch Comp Salt Lake City UT 84112 USA

Despite the wide implementation of machine learning (ML) technique in traffic flow modeling recently, those data-driven approaches often fall short of accuracy in the cases with a small or noisy training dataset. To address this issue, this study presents a new modeling framework, named physics regularized machine learning (PRML), to encode classical traffic flow models (referred as physics models) into the ML architecture and to regularize the ML training process. More specifically, leveraging the Gaussian process (GP) as the base model, a stochastic physics regularized Gaussian process (PRGP) model is developed and a Bayesian inference algorithm is used to estimate the mean and kernel of the PRGP. A physics regularizer, based on macroscopic traffic flow models, is also developed to augment the estimation via a shadow GP and an enhanced latent force model is used to encode physical knowledge into the stochastic process. Based on the posterior regularization inference framework, an efficient stochastic optimization algorithm is then developed to maximize the evidence lowerbound of the system likelihood. For model evaluations, this paper conducts empirical studies on a real-world dataset which is collected from a stretch of I-15 freeway, Utah. Results show the new PRGP model can outperform the previous compatible methods, such as calibrated traffic flow models and pure machine learning methods, in estimation precision and is more robust to the noisy training dataset. Despite the wide implementation of machine learning (ML) technique in traffic flow modeling recently, those data-driven approaches often fall short of accuracy in the cases with a small or noisy training dataset. To address this issue, this study presents a new modeling framework, named physics regularized machine learning (PRML), to encode classical traffic flow models (referred as physics models) into the ML architecture and to regularize the ML training process. More specifically, leveraging the Gauss

关键词： macroscopic traffic flow model Physics regularized machine learning Multivariate Gaussian process Posterior regularization inference

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Freeway traffic control using iterative learning control-based ramp metering and speed signaling

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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY 2007年第2期56卷 466-477页

作者： Hou, Zhongsheng Xu, Jian-Xin Zhong, Hongwei Beijing Jiaotong Univ Sch Elect & Informat Engn Adv Control Syst Lab Beijing 100044 Peoples R China Natl Univ Singapore Dept Elect & Comp Engn Singapore 117576 Singapore Beijing Jiaotong Univ Sch Traff & Transportat Beijing 100044 Peoples R China

In this paper, an iterative learning approach for the freeway density control under ramp metering and speed regulation is developed in a macroscopic level traffic environment. Rigorous analyses show that the proposed learning control schemes guarantee the asymptotic convergence of the traffic density to the desired one. The two major features of the learning-based density control are 1) less prior modeling knowledge required in the control system design and 2) the ability to reject exogenous traffic perturbations. The control schemes are applied to a freeway model, and simulation results confirm the efficacy of the proposed approach.

关键词： freeway ramp metering iterative learning control (ILC) macroscopic traffic flow model speed control traffic density control

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Characteristics of speed dispersion and its relationship to fundamental traffic flow parameters

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TRANSPORTATION PLANNING AND TECHNOLOGY 2014年第7期37卷 581-597页

作者： Chung, Chih-Lin Recker, Will W. Tamkang Univ Dept Transportat Management New Taipei City 25137 Taiwan Univ Calif Irvine Inst Transportat Studies Irvine CA 92697 USA

Speed dispersion is essential for transportation research but inaccessible to certain sensors that simply record density, mean speed, and/or flow. An alternative is to relate speed dispersion with these available parameters. This paper is compiled from nearly a quarter million observations on an urban freeway and a resulting data-set with two speed dispersion measures and the three fundamental parameters. Data are examined individually by lane and aggregately by direction. The first dispersion measure, coefficient of variation of speed, is found to be exponential with density, negative exponential with mean speed, and two-phase linear to flow. These empirical relationships are proven to be general for a variety of coefficient ranges under the above function forms. The second measure, standard deviation of speed, does not present any simple relationships to the fundamental parameters, and its maximum occurs at around a half to two-thirds of the free flow speed. Speed dispersion may be significantly different by lane.

关键词： speed dispersion coefficient of variation of speed standard deviation of speed macroscopic traffic flow model

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A HETEROGENEOUS MULTICLASS traffic flow model WITH CREEPING

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SIAM JOURNAL ON APPLIED MATHEMATICS 2015年第2期75卷 813-835页

作者： Fan, Shimao Work, Daniel B. Univ Illinois Sci Lab Urbana IL 61801 USA Univ Illinois Dept Civil & Environm Engn Urbana IL 61801 USA

A heterogeneous traffic model with two vehicle classes is developed to capture overtaking and creeping in highly heterogeneous traffic flows. Creeping is a special case of overtaking that occurs when small vehicles continue to advance in congestion even though larger vehicles have completely stopped. To motivate the new model, it is shown that a two class homogeneous multiclass model is equivalent to a class of second order models originally proposed by Aw, Rascle, and Zhang (ARZ). Based on the properties of the ARZ model, homogeneous models do not allow overtaking or creeping. The new creeping model is a phase transition model which applies a system of conservation laws in the noncreeping phase and a system equivalent to a scalar model in the creeping phase. The solution to the Riemann problem is obtained by investigating the elementary waves, particularly for the cases when one vehicle class is absent, as well as in the presence of a phase transition. Based on the proposed Riemann solver, the solution to the Cauchy problem is constructed using wavefront tracking. Numerical tests are carried out using a Godunov scheme to illustrate the creeping phenomenon. Source code for the numerical simulations is available at https://***/shimaof/heterogeneous-traffic-model.

关键词： hyperbolic system of conservation laws macroscopic traffic flow model heterogeneous flow multiclass traffic model phase transition Riemann solver

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Continuum modeling of freeway traffic flows:State-of-the-art,challenges and future directions in the era of connected and automated vehicles

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Communications in Transportation Research 2023年第1期3卷 187-211页

作者： Saeed Mohammadian Zuduo Zheng Md.Mazharul Haque Ashish Bhaskar School of Civil and Environmental Engineering Queensland University of TechnologyBrisbane4000Australia School of Civil Engineering The University of QueenslandBrisbane4072Australia

Connected and automated vehicles(CAVs)are expected to reshape traffic flow dynamics and present new challenges and opportunities for traffic flow *** numerous studies have proposed optimal modeling and control strategies for CAVs with various objectives(e.g.,traffic efficiency and safety),there are uncertainties about the flow dynamics of CAVs in real-world *** uncertainties are especially amplified for mixed traffic flows,consisting of CAVs and human-driven vehicles,where the implications can be significant from the continuum-modeling perspective,which aims to capture macroscopic traffic flow dynamics based on hyperbolic systems of partial differential *** paper aims to highlight and discuss some essential problems in continuum modeling of real-world freeway traffic flows in the era of *** first provide a select review of some existing continuum models for conventional human-driven traffic as well as the recent attempts for incorporating CAVs into the continuum-modeling *** applicable,we provide new insights about the properties of existing models and revisit their implications for traffic flows of CAVs using recent empirical observations with CAVs and the previous discussions and debates in the *** paper then discusses some major problems inherent to continuum modeling of real-world(mixed)CAV traffic flows modeling by distinguishing between two major research directions:(a)modeling for explaining purposes,where making reproducible inferences about the physical aspects of macroscopic properties is of the primary interest,and(b)modeling for practical purposes,in which the focus is on the reliable predictions for operation and *** paper proposes some potential solutions in each research direction and recommends some future research topics.

关键词： Continuum model macroscopic traffic flow model traffic flow Connected and automated vehicles Autonomous vehicles Automated vehicles

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Dynamic traffic diversion model based on dynamic traffic demand estimation and prediction

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IET INTELLIGENT TRANSPORT SYSTEMS 2018年第9期12卷 1123-1130页

作者： Jiao Peng-peng Li Yi-gang Li Dong-yue Beijing Univ Civil Engn & Architecture Sch Civil & Transportat Engn 1 Zhanlanguan Rd Beijing Peoples R China

traffic diversion is an effective measure to solve the incidental traffic congestion in urban expressway traffic system. By adopting the macroscopic traffic flow model METANET, this study analyses the state change of traffic flow on the road network and establishes the dynamic traffic diversion model, inducing the redistribution of traffic demand. Considering the changes in the amount of origin-destination (O-D) demand, diversion rate is introduced into the basic theory of dynamic O-D model, and then established a dynamic traffic flow model based on dynamic demand change. The genetic algorithm is used to solve the non-linearity problem of the objective function in the traffic diversion model. This study sets up five cases for numerical analyses, and gets the optimal diversion scheme.

关键词： road traffic genetic algorithms numerical analysis dynamic traffic diversion model dynamic traffic demand estimation dynamic traffic demand prediction incidental traffic congestion urban expressway traffic system macroscopic traffic flow model METANET state change analysis road network traffic demand redistribution origin-destination demand O-D demand diversion rate dynamic O-D model dynamic traffic flow model dynamic demand change genetic algorithm nonlinearity problem numerical analysis optimal diversion scheme

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