Modelling and simulations of multilane traffic flow by kinetic theory methods

Bonzani, Ida; Cumin, Liliana M. Gramani

doi:10.1016/j.camwa.2008.05.033

Cited by 15 publications

(8 citation statements)

References 12 publications

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“…Therefore, the overall state of the system is described by a discrete probability distribution over groups of vehicles with velocity within a certain range. The model [68] has also been generalized to the case of multilane flow [31].…”

Section: Modeling Granular Flowsmentioning

confidence: 99%

On the Modeling of Traffic and Crowds: A Survey of Models, Speculations, and Perspectives

Bellomo¹,

Dogbe²

2011

SIAM Rev.

389

284

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This paper presents a review and critical analysis of the mathematical literature concerning the modeling of vehicular traffic and crowd phenomena. The survey of models deals with the representation scales and the mathematical frameworks that are used for the modeling approach. The paper also considers the challenging objective of modeling complex systems consisting of large systems of individuals interacting in a nonlinear manner, where one of the modeling difficulties is the fact that these systems are difficult to model at a global level when based only on the description of the dynamics of individual elements. The review is concluded with a critical analysis focused on research perspectives that consider the development of a unified modeling strategy.

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Section: Modeling Granular Flowsmentioning

confidence: 99%

On the Modeling of Traffic and Crowds: A Survey of Models, Speculations, and Perspectives

Bellomo¹,

Dogbe²

2011

SIAM Rev.

389

284

View full text Add to dashboard Cite

show abstract

“…[13,14] where both the acceleration and the slowing down interactions are modeled with a Vlasov-type relaxation towards a desired speed. Kinetic theory is also used to model multilane traffic flow [12,19,20,25,3], flows on networks [8], inhomogeneous space problems with non local interactions [18], control problems [15] and safety aspects in vehicular traffic [9]. For a review on kinetic traffic models, see [21].…”

Section: Introductionmentioning

confidence: 99%

Analysis of a multi-population kinetic model for traffic flow

Puppo

Semplice

Tosin

et al. 2017

Communications in Mathematical Sciences

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In this work we extend a recent kinetic traffic model [G. Puppo, M. Semplice, A. Tosin, G. Visconti, Kinet. Relat. Models, in press, 2016] to the case of more than one class of vehicles, each of which is characterized by few different microscopic features. We consider a Boltzmann-like framework with only binary interactions, which take place among vehicles belonging to the various classes. Our approach differs from the multi-population kinetic model proposed in [G. Puppo, M. Semplice, A. Tosin, G. Visconti, Commun. Math. Sci., 14:643-669, 2016] because here we assume continuous velocity spaces and we introduce a parameter describing the physical velocity jump performed by a vehicle that increases its speed after an interaction. The model is discretized in order to investigate numerically the structure of the resulting fundamental diagrams and the system of equations is analyzed by studying well posedness. Moreover, we compute the equilibria of the discretized model and we show that the exact asymptotic kinetic distributions can be obtained with a small number of velocities in the grid. Finally, we introduce a new probability law in order to attenuate the sharp capacity drop occurring in the diagrams of traffic

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“…Some of them (e.g., context sensitivity, desired velocity, desired space headway, and desired time headway, anticipation) are applicable for microscopic traffic flow modelling of CAVs. It is clear that the efficiency of CAVs is different based on the type of vehicles, and each commuter sets their personalized trade-offs when commuting with AVs [70]. Such differences lead to various intelligent driving systems requiring their associated car-following models for AV-incorporated traffic.…”

Section: Introductionmentioning

confidence: 99%

“…To the best knowledge of the authors, however, kinematics-based car-following models made substantial contributions to traffic flow modelling, but there are still some contradictions and conceptual weaknesses in their capability of describing the car following behavior in traffic flow. Besides, the aforementioned models are not developed based on kinematic theories for active particles, while vehicles are active particles whose mechanical properties play an essential role in traffic flow behavior [70][71][72]. In addition, driving behavior was only considered in these models to provide fast and efficient simulation, and models did not effectively consider Daganzo's remark [73].…”

Section: Introductionmentioning

confidence: 99%

Integrated-Hybrid Framework for Connected and Autonomous Vehicles Microscopic Traffic Flow Modelling

Jafaripournimchahi

Cai

Wang

et al. 2022

Journal of Advanced Transportation

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In this study, a novel traffic flow modeling framework is proposed considering the impact of driving system and vehicle mechanical behavior as two different units on the traffic flow. To precisely model the behavior of Connected and Autonomous (CA) vehicles, three submodels are proposed as a novel microscopic traffic flow framework, named Integrated-Hybrid (IH) model. Focusing on the realization of the car following behavior of CA vehicles, the driving system (vehicle control system) and the vehicle mechanical system are modeled separately and linked by throttle and brake actuators model. The IH model constitutes the key part of the Full Velocity Difference (FVD) model considering the mechanical capability of vehicles and dynamic collision avoidance strategies to ensure the safety of following distance between two consecutive vehicles. Linear stability conditions are derived for each model and developing methodology for each submodel is discussed. Our simulations revealed that the IH model successfully generates velocity and acceleration profiles during car following maneuvers and throttle angle/brake information in connected vehicles environment can effectively improve traffic flow stability. The vehicles’ departure and arrival process while passing through a signal-lane with a traffic light considering the anticipation driving behavior and throttle angle/brake information of direct leading vehicle was explored. Our numerical results demonstrated that the IH model can capture the velocity fluctuations, delay times, and kinematic waves efficiently in traffic flow.

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Modelling and simulations of multilane traffic flow by kinetic theory methods

Cited by 15 publications

References 12 publications

On the Modeling of Traffic and Crowds: A Survey of Models, Speculations, and Perspectives

On the Modeling of Traffic and Crowds: A Survey of Models, Speculations, and Perspectives

Analysis of a multi-population kinetic model for traffic flow

Integrated-Hybrid Framework for Connected and Autonomous Vehicles Microscopic Traffic Flow Modelling

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