Critical analysis and perspectives on the hydrodynamic approach for the mathematical theory of vehicular traffic

Bonzani, Ida; Cumin, Liliana M. Gramani

doi:10.1016/j.mcm.2009.03.007

Cited by 12 publications

(4 citation statements)

References 46 publications

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“…Hence, incorporating the dynamic information of both throttle and brake actuators into the traffic flow modelling is essential, even if its mathematical representation and development are more complicated. However, since previous models did not consider vehicles as active particles and have not been developed based on kinematic theories, some conceptual weaknesses in describing driving behaviour are inevitable [44][45][46].…”

Section: Car-following Modelsmentioning

confidence: 99%

A viscous continuum traffic flow model based on the cooperative car‐following behaviour of connected and autonomous vehicles

Jafaripournimchahi

Cai

Wang

et al. 2022

IET Intelligent Trans Sys

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Connected and Autonomous Vehicles (CAVs) can receive various information from surrounding vehicles through Vehicle‐to‐Everything (V2X) communication technologies and adjust their car‐following behaviour accordingly. Although several studies have evaluated the impact of CAVs on traffic flow stability in a small segment of networks, most approaches are focused on their specific applications considering the trajectory information, and there is a lack of studies analyzing the impact of CAVs on a large‐scale network. This paper proposes a novel viscous continuum traffic model considering the anticipation of space headway, the throttle angle, and brake torque information during cooperative car‐following. The methods employed to develop the new car‐following model and its counterpart continuum traffic model have been described. The linear and non‐linear stability analyses of the newly developed model have been conducted to obtain the critical stability factors in small perturbations. Numerical simulations have been carried out to investigate the effect of the anticipation, the throttle angle, and brake torque information on traffic stability, fuel consumption, and exhaust emissions. The numerical results reveal that the anticipation of space headway and the transmission of the throttle angle and brake torque information during cooperative car‐following manoeuvres can improve the traffic flow stability and reduce fuel consumption and emissions.

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Section: Car-following Modelsmentioning

confidence: 99%

A viscous continuum traffic flow model based on the cooperative car‐following behaviour of connected and autonomous vehicles

Jafaripournimchahi

Cai

Wang

et al. 2022

IET Intelligent Trans Sys

View full text Add to dashboard Cite

show abstract

“…The differences between these models will therefore be in the assumptions made in how the system acts. We point to Hoogendoorn and Bovy (2001) and Bonzani and Gramani (2009) for a critical review on the topic.…”

Section: E4-4 Jeremie Coullon and Yvo Pokernmentioning

confidence: 99%

Markov chain Monte Carlo for a hyperbolic Bayesian inverse problem in traffic flow modeling

Coullon

Pokern

2022

DCE

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As a Bayesian approach to fitting motorway traffic flow models remains rare in the literature, we empirically explore the sampling challenges this approach offers which have to do with the strong correlations and multimodality of the posterior distribution. In particular, we provide a unified statistical model to estimate using motorway data both boundary conditions and fundamental diagram parameters in a motorway traffic flow model due to Lighthill, Whitham, and Richards known as LWR. This allows us to provide a traffic flow density estimation method that is shown to be superior to two methods found in the traffic flow literature. To sample from this challenging posterior distribution, we use a state-of-the-art gradient-free function space sampler augmented with parallel tempering.

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“…The differences between these models will therefore be in the assumptions made in how the system acts. We point to [4] and [17] for a critical review on the topic.…”

Section: Lwrmentioning

confidence: 99%

MCMC for a hyperbolic Bayesian inverse problem in traffic flow modelling – ADDENDUM

Coullon¹,

Pokern²

2022

DCE

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As work on hyperbolic Bayesian inverse problems remains rare in the literature, we explore empirically the sampling challenges these offer which have to do with shock formation in the solution of the PDE. Furthermore, we provide a unified statistical model to estimate using motorway data both boundary conditions and fundamental diagram parameters in LWR, a well known motorway traffic flow model. This allows us to provide a traffic flow density estimation method that is shown to be superior to two methods found in the traffic flow literature. Finally, we highlight how Population Parallel Tempering -a modification of Parallel Tempering -is a scalable method that can increase the mixing speed of the sampler by a factor of 10.

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Critical analysis and perspectives on the hydrodynamic approach for the mathematical theory of vehicular traffic

Cited by 12 publications

References 46 publications

A viscous continuum traffic flow model based on the cooperative car‐following behaviour of connected and autonomous vehicles

A viscous continuum traffic flow model based on the cooperative car‐following behaviour of connected and autonomous vehicles

Markov chain Monte Carlo for a hyperbolic Bayesian inverse problem in traffic flow modeling

MCMC for a hyperbolic Bayesian inverse problem in traffic flow modelling – ADDENDUM

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