Two-dimensional macroscopic model for large scale traffic networks

Mollier, Stephane; Monache, Maria Laura Delle; Canudas‐de‐Wit, Carlos; Seibold, Benjamin

doi:10.1016/j.trb.2019.02.016

Cited by 23 publications

(23 citation statements)

References 31 publications

(30 reference statements)

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“…In this section, we suggest an extension of the model introduced in [23], [25] including a space dependent flux function. This extension is even more relevant than in the one dimensional case for at least two reasons:…”

Section: Description Of 2d Lwr Modelmentioning

confidence: 99%

“…In this section, we recall the estimation method introduced in [23], [25]. We denote by q ∈ {1, .., Q} the different roads of the network.…”

Section: Velocity Direction Fieldmentioning

confidence: 99%

“…In [24], a flux direction per zone is defined using microsimulation on the network. In [23] and [25], the estimation of a continuous flux direction field is suggested. In [26], [27] authors considers a maximum speed that may depend on space, but these parameters are postulated instead of being extracted from the network.…”

Section: Introductionmentioning

confidence: 99%

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2D-LWR in large-scale network with space dependent fundamental diagram

Mollier

Monache

Canudas‐de‐Wit

2018

2018 21st International Conference on Intelligent Transportation Systems (ITSC)

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Traffic modeling of large-scale urban networks is a challenging task. In the literature, the network is mainly assumed to be homogeneous. However, in a large-scale scenario, it is unlikely that the traffic network characteristics-such as speed limit, number of lanes, or the network geometry-remain constant throughout the network. Therefore, we introduce a two dimensional macroscopic model for large-scale traffic networks where the fundamental diagram is space-dependent and varies with respect to the area considered. We simulate our model and compare the results with those obtained by microsimulation.

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Section: Description Of 2d Lwr Modelmentioning

confidence: 99%

“…In this section, we recall the estimation method introduced in [23], [25]. We denote by q ∈ {1, .., Q} the different roads of the network.…”

Section: Velocity Direction Fieldmentioning

confidence: 99%

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2D-LWR in large-scale network with space dependent fundamental diagram

Mollier

Monache

Canudas‐de‐Wit

2018

2018 21st International Conference on Intelligent Transportation Systems (ITSC)

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“…Recently, 2D models relying on the network, with space-dependent parameters have been developed [1], [2]. A method of validation using microsimulation is presented in [18]. However, all these models allow only the representation of a unique direction of flow.…”

Section: Introductionmentioning

confidence: 99%

“…These models have a unique flow direction and to the best of our knowledge the only extension to multiple direction is [19]. One way to accomodate the multiple directions of flow is to extend the existing model in [18] to a system of conservation laws. However, these systems of equations are not always hyperbolic as for the case of two populations of pedestrian evolving in opposite direction [12].…”

Section: Introductionmentioning

confidence: 99%

A decision support and planning mobility method for large scale traffic networks

Mollier

Monache

Canudas‐de‐Wit

2019

2019 18th European Control Conference (ECC)

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This paper presents a new planning and decisionmaking method in large scale traffic networks for predicting how traffic evolves in special events, emergencies and changes in the city mobility demands. The proposed method is based on a 2-D aggregated traffic model for large scale traffic networks [1], [2] which describes traffic evolution as a fluid in two space dimensions. We propose an extension of the model by including additional state density variables, each one associated to a particular layer describing vehicles evolving in different directions. The model is a 2D-PDE described by a system of conservation laws. For this specific case, the resulting PDE is not anymore hyperbolic as typically the LWR model but results in a hybrid hyperbolic-elliptic PDE depending on the density level. In this case, usual numerical schemes may be not valid and often lead to oscillation in the solution. Thus, we consider a high order numerical scheme to improve the numerical solution. Finally, the model is used to predict how the typical traffic evolution will be impacted in particular scenarios like special events or changes in demands. Comparative simulations are provided.

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Optimal observer‐based output feedback controller for traffic congestion with bottleneck

Guan

Zhang

Prieur

2021

Intl J Robust & Nonlinear

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This article designs an optimal observer-based output feedback control for traffic breakdown to dissolve traffic congestion using the backstepping method and optimization. The linearized Aw-Rascle-Zhang model is used to represent the congested traffic dynamics resulting from traffic breakdown. Based on the factors leading to traffic breakdown, we take into account the boundary conditions consisting of a boundary with a constant density and a speed drop at the upstream inlet of a bottleneck, and a boundary with a disturbance of inflow (high traffic demand) at the inlet of the road segment under consideration. To dissolve traffic congestion, a dynamic feedback controller is designed at the upstream boundary. By using the backstepping approach, an observer-based output feedback controller is computed to guarantee the integral input-to-state stability of the closed-loop system. By establishing an optimization problem and solving it, the optimal value of the considered class controller is obtained. The performance of the output feedback controller is also validated by numerical simulations.

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Two-dimensional macroscopic model for large scale traffic networks

Cited by 23 publications

References 31 publications

2D-LWR in large-scale network with space dependent fundamental diagram

2D-LWR in large-scale network with space dependent fundamental diagram

A decision support and planning mobility method for large scale traffic networks

Optimal observer‐based output feedback controller for traffic congestion with bottleneck

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