A Variational Formulation for Higher Order Macroscopic Traffic Flow Models of the GSOM Family

Lebacque, Jean-Patrick; Khoshyaran, Megan M.

doi:10.1016/j.sbspro.2013.05.021

Cited by 20 publications

(30 citation statements)

References 16 publications

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“…The bi-dimensional traffic flow model can be interfaced with a GSOM model ( [6]) of the main motorways and arteries. In this perspective the bi-dimensional model will mainly describe dense networks of secondary roads.…”

Section: Recommendationsmentioning

confidence: 99%

Reactive Dynamic Assignment for a Bi-dimensional Traffic Flow Model

Sossoe

Lebacque²

2016

Advances in Intelligent Systems and Computing

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Abstract. This paper develops a graph-theoretic framework for large scale bi-dimensional transport networks and provides new insight into the dynamic traffic assignment. Reactive dynamic assignment are deployed to handle the traffic contingencies, traffic uncertainties and traffic congestion. New shortest paths problem in large networks is defined and routes cost calculation is provided. Since mathematical modelling of traffic flow is a keystone in the theory of traffic flow management, and then in the traffic assignment, it is convenient to elaborate a good model of assignment for large scale networks relying on an appropriate model of flow related to very large networks. That is the zone-based optimization of traffic flow model on networks developed by [8], completed and improved by [9].

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Section: Recommendationsmentioning

confidence: 99%

Reactive Dynamic Assignment for a Bi-dimensional Traffic Flow Model

Sossoe

Lebacque²

2016

Advances in Intelligent Systems and Computing

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“…While methods of data assimilation have been only developed for first order models up to now, this work presents a new algorithm to reconstruct traffic states from both Eulerian and Lagrangian data. We take advantage of a very recent article [34] in which a variational principle has been proved for models of the GSOM family.…”

Section: Motivationmentioning

confidence: 99%

“…For this reason we have focused on developing variational methods for GSOM models. Guided by the ideas developed for the LWR model, variational formulations have been recently developed and proved for models of the GSOM family in both Eulerian [41] and Lagrangian frameworks [34].…”

Section: Variational Formulation Of the Gsom Familymentioning

confidence: 99%

“…Unlike the paper of Lebacque and Khoshyaran [34] which will be discussed just after, these models are expressed from the Eulerian viewpoint as a system of two conservation laws (the first one for the conservation of vehicles and the second one for the behavioral motion of traffic flow around an equilibrium state)…”

Section: Eulerian Settingmentioning

confidence: 99%

“…In [34], the authors prove the existence of a variational principle for the GSOM models family. In a first step, the article gives the Hamilton-Jacobi formulation of GSOM models.…”

Section: Lagrangian Settingmentioning

confidence: 99%

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A variational formulation for higher order macroscopic traffic flow models: Numerical investigation

Costeseque

Lebacque²

2014

Transportation Research Part B: Methodological

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This paper deals with numerical methods providing semi-analytic solutions to a wide class of macroscopic traffic flow models for piecewise affine initial and boundary conditions. In a very recent paper, a variational principle has been proved for models of the Generic Second Order Modeling (GSOM) family, yielding an adequate framework for effective numerical methods. Any model of the GSOM family can be recast into its Lagrangian form as a Hamilton-Jacobi equation (HJ) for which the solution is interpreted as the position of vehicles. This solution can be computed thanks to Lax-Hopf like formulas and a generalization of the inf-morphism property. The efficiency of this computational method is illustrated through a numerical example and finally a discussion about future developments is provided.Keywords: Traffic flow, Hamilton-Jacobi equation, Lax-Hopf algorithm, Lagrangian. Introduction General backgroundMacroscopic traffic flow modeling. In order to get a realistic estimation of the real-time traffic states on networks, traffic operators and managers need macroscopic traffic flow models. These models must be simple, robust, allowing to get solutions at a low computational cost. The main macroscopic models are based on conservation laws or hyperbolic systems (see [30,19] for a review). The seminal LWR model (for Lighthill-Whitham and Richards) was proposed in [42,51] as a single conservation law with unknown the vehicles density. This model based on a first order Partial Differential Equation (PDE) is very simple and robust but it fails to recapture some empirical features of traffic. In particular, it does not allow to take into account non-equilibrium traffic states mainly in congested situation. More sophisticated models referred to as higher order models were developed to encompass kinematic constraints of real vehicles or also the wide variety of driver behaviors, even at the macroscopic level. In this paper we deal with models of the Generic Second Order Modeling (GSOM) family. Even if these models are more complicated to deal with, they permit to reproduce traffic instabilities (such as the so-called stop-and-go waves, the hysteresis phenomenon or capacity drop) which move at the traffic speed and differ from kinematic waves [53] Traffic flow monitoring. Before the wide propagation of internet handsets, traffic monitoring has mainly been built on dedicated infrastructure which imply quite important installation and maintenance costs. Traffic flow monitoring and management has been deeply modified with the development of new technologies in mobile sensing aiming to provide a quite important quantity of floating car data. Traffic flow models are needed to be well suited such that managers could use both Eulerian and Lagrangian data for improving traffic state estimation. The term Eulerian refers to "classical" fixed equipment giving records of occupancy or flow of vehicles on a freeway section. This kind of measurements come from e.g. fixed inductive loop detectors, Radio Frequency Identification (R...

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