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

Costeseque, Guillaume; Lebacque, Jean-Patrick

doi:10.1016/j.trb.2014.08.012

Cited by 32 publications

(13 citation statements)

References 56 publications

(84 reference statements)

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“…Another direction of research would be to numerically compare our method and the variational approach (see Costeseque and Lebacque (2014b)) adapted for junction modeling, which has not been done right now.…”

Section: Recent Models Likementioning

confidence: 99%

Lagrangian GSOM traffic flow models on junctions

Costeseque¹,

Lebacque²,

Khelifi³

2015

IFAC-PapersOnLine

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International audienceThis paper is concerned with the macroscopic modeling and simulation of traffic flow on junctions. More precisely, we deal with a generic class of second order models, known in the literature as the GSOM family. While classical approaches focus on the Eulerian point-of-view, here we recast the model using its Lagrangian coordinates and we treat the junction as a specific discontinuity in Lagrangian framework. We propose a complete numerical methodology based on a finite difference scheme for solving such a model and we provide a numerical example

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Section: Recent Models Likementioning

confidence: 99%

Lagrangian GSOM traffic flow models on junctions

Costeseque¹,

Lebacque²,

Khelifi³

2015

IFAC-PapersOnLine

Self Cite

View full text Add to dashboard Cite

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“…For example, Lebacque and Khoshyaran (2013) showed that generic second-order models admit a Hamilton-Jacobi and variational formulation as an optimal control problem. Costeseque and Lebacque (2014) numerically investigated the VT formulation for higher order traffic models. Additionally, the deterministic nature of VT was questioned and by the inclusion of stochastic shortest path algorithms new fields of application were made accessible.…”

Section: Introductionmentioning

confidence: 99%

On the application of variational theory on networks

Tilg¹,

Ambühl²,

Batista³

et al. 2020

Preprint

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The well-known Lighthill-Whitham-Richards (LWR) theory is the fundamental pillar for most macroscopic traffic models. In the past, many methods were developed to numerically derive solutions for LWR problems. Examples for such numerical solution schemes are the cell transmission model, the link transmission model, and the variational theory (VT) of traffic flow. So far, the latter framework found applications in the fields of traffic modelling, macroscopic fundamental diagram estimation, multi-modal traffic analyses, and data fusion. However, these studies apply VT only at the link or corridor level. To the best of our knowledge, there is no methodology yet to apply VT at the network level. We address this gap by developing a VT-based framework applicable to networks. Our model allows us to account for source terms (e.g. inflows and outflows at intersections) and the propagation of spillbacks between adjacent corridors consistent with kinematic wave theory. We show that the trajectories extracted from a microscopic simulation fit the predicted traffic states from our model for a simple intersection with both source terms and spillbacks. We also use this simple example to illustrate the accuracy of the proposed model. Additionally, we apply our model to the Sioux Falls network and again compare the results to those from a microscopic simulation. Our results indicate a close fit of traffic states, but with substantially lower computational cost. The developed methodology is useful for network-wide traffic state estimations in real-time, or other applications within a model-based optimization framework.

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“…al. [3]. However, the absence of traffic intensity or density information in FCD and sparsity of other sensors rules out most of these traffic flow models, which are based these quantities.…”

Section: Introductionmentioning

confidence: 99%

Traffic speed prediction using ensemble kalman filter and differential evolution

Rapant

2019

MATEC Web Conf.

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Importance of traffic state prediction steadily increases with growing volume of traffic. Ability to predict traffic speed in short to medium horizon (i.e. up to one hour) is one of the main tasks of every newly developed Intelligent Transportation System. There are two possible approaches to this prediction. The first is to utilize physical properties of the traffic flow to construct an exact or approximate numerical model. This approach is, however, almost impossible to implement on a larger scale given the difficulty to obtain enough traffic data to describe the starting and boundary conditions of the model. The other option is to use historical traffic data and relate information and patterns they contain to the current traffic state by application of some form of statistical or machine learning approach. We propose to use combination of Ensemble Kalman filter and Cell Transmission Model for this task. These models combine properties of physical model with ability to incorporate uncertainty of the traffic data.

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

Cited by 32 publications

References 56 publications

Lagrangian GSOM traffic flow models on junctions

Lagrangian GSOM traffic flow models on junctions

On the application of variational theory on networks

Traffic speed prediction using ensemble kalman filter and differential evolution

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