Derivation of a first order traffic flow model of Lighthill-Whitham-Richards type

Burger, Michael; Göttlich, Simone; Jung, Thomas

doi:10.1016/j.ifacol.2018.07.009

Cited by 13 publications

(16 citation statements)

References 14 publications

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“…Since the derivation of such macroscopic equations is not unique and straightforward, we present our approach below, following mainly the ideas presented in [4,19].…”

Section: Formal Derivation From Microscopic Equationsmentioning

confidence: 99%

Micro-Macro Limit of a Nonlocal Generalized Aw-Rascle Type Model

Chiarello¹,

Friedrich²,

Goatin³

et al. 2020

SIAM J. Appl. Math.

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We introduce a Follow-the-Leader approximation of a non-local generalized Aw-Rascle-Zhang (GARZ) model for traffic flow. We prove the convergence to weak solutions of the corresponding macroscopic equations deriving L ∞ and BV estimates. We also provide numerical simulations illustrating the micro-macro convergence and we investigate numerically the non-local to local limit for both the microscopic and macroscopic models.

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“…Since the derivation of such macroscopic equations is not unique and straightforward, we present our approach below, following mainly the ideas presented in [4,19].…”

Section: Formal Derivation From Microscopic Equationsmentioning

confidence: 99%

Micro-Macro Limit of a Nonlocal Generalized Aw-Rascle Type Model

Chiarello¹,

Friedrich²,

Goatin³

et al. 2020

SIAM J. Appl. Math.

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“…This equation can also be found in [13], [14] for the case τ = 0 and in [5] for τ > 0. The first row of (13) can be interpreted as a conservation law for the number of vehicles participating in traffic.…”

Section: B Delayed Lighthill-whitham-richards (Lwr) Modelmentioning

confidence: 64%

“…Note that both Eulerian models, (15) with (18) and (14) with (19), formulate a partial delay differential equation (PDDE) with constant time delay and state-dependent spatial delay. This spatial delay was neglected in the PDDE models of [4], [5]. Since state-dependent delays make the analysis of differential equations significantly more difficult [15], it is more useful to use Lagrangian framework for introducing delays.…”

Section: B Delayed Lighthill-whitham-richards (Lwr) Modelmentioning

confidence: 99%

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Lagrangian Models for Controlling Large-Scale Heterogeneous Traffic

Molnár

Upadhyay

Hopka

et al. 2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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Heterogeneous traffic with a mixture of humandriven and connected automated vehicles is discussed to study how the penetration rate and the control design of connected automated vehicles affect the traffic flow on a large scale. Continuum traffic models are constructed by incorporating time delays to take into account the reaction time of human drivers and the delays in the control loops of connected automated vehicles. It is shown that Lagrangian delayed continuum models are suitable for studying heterogeneity, introducing delay, and taking into account the on-board traffic data used by the controllers of connected automated vehicles. We show that these models possess realistic stability properties and are capable of capturing the large-scale dynamics of vehicle automationinduced and connectivity-induced heterogeneity.

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“…On the other hand, we want to keep the delay in the explicit form, and therefore avoid the diffusion approximation. The model derived in [9] will be studied in details in the following, investigating carefully its theoretical and numerical features.…”

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confidence: 99%