Macroscopic Models in Traffic Flow

Velasco, R. M.; Saavedra, Patricia

doi:10.1007/s12346-008-0014-1

Cited by 8 publications

(2 citation statements)

References 34 publications

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“…Such models are conventionally arrived at by integrating microscopic traffic flow models and converting the single-entity level characteristics to comparable system level characteristics. For example, macroscopic models investigated in researches, which were carried out by scientists Ngoduy (2013Ngoduy ( , 2012; Velasco, Saavedra (2008); Helbing et al (2001); Zhang et al (1997), etc. ;-Mesoscopic (kinetic) scale.…”

Section: Analysis Of Researches and Publicationsmentioning

confidence: 99%

Methods for numerical calculation of parameters pertaining to the microscopic following-the-leader model of traffic flow: using the fast spline transformation

et al. 2013

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As known in transport engineering, civil engineering, transport planning and mathematics, traffic flow is the study of interactions between vehicles, drivers and infrastructure (including highways, signage and traffic control devices), with the aim of understanding and developing an optimal road network with efficient movement of traffic and minimal traffic congestion problems. The presented paper discusses a small part of a traffic flow study -the development of the methodology for assessing the speed and acceleration of a car during the column movement followingthe-leader, based on a new mathematical method. Two methods -(1) the numerical calculation of the first derivative, i.e. speed of the car movement; (2) the numerical calculation of the second derivative, i.e. acceleration of the car movement -were developed, using the fast spline transformation. In the future, parameters obtained with the help of two new methods, can be used to solve complex transportation problems, such as: (1) control of traffic flows; (2) organisation of harmonised work of traffic lights; (3) analysis of psycho-physiological condition of a driver, etc. -leader model, fast spline transformation, numerical calculation. Reference to this paper should be made as follows: Kuzhel, N.; Bieliatynskyi, A.; Prentkovskis, O.; Klymenko, I.; Mikaliūnas, Š.; Kolganova, O.; Kornienko, S.; Shutko, V. 2013. Methods for numerical calculation of parameters pertaining to the microscopic following-the-leader model of traffic flow: using the fast spline transformation, Transport 28(4): 413-419. http://dx.

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Section: Analysis Of Researches and Publicationsmentioning

confidence: 99%

Methods for numerical calculation of parameters pertaining to the microscopic following-the-leader model of traffic flow: using the fast spline transformation

et al. 2013

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“…As a result it is obtained the viscous Burgers equation, which can be rewritten as a diffusion equation by means of the Cole-Hopf transformation [6] and the exact solution is then written in integral terms. When the density profile is compared with the one in the LWR model we can easily see that it is smoothed according to the value of the diffusion coefficient [7]. Recently, Jordan [8] has proposed a new model in which an equation for the density is constructed.…”

Section: Introductionmentioning

confidence: 99%

A first order model in traffic flow

Velasco

Saavedra

2007

Physica D: Nonlinear Phenomena

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Phase-space analysis for hydrodynamic traffic models

Saavedra

Velasco

2009

Phys. Rev. E

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This work is devoted to the study of steady states in two hydrodynamic traffic models. The first model to be analyzed is the Kerner-Konhäuser model and the second is called kinetic Navier-Stokes model. The study is made through an analysis in the phase space. Taking into account the analogy with the description of the one-particle motion, we can give a sensible meaning to the dynamical functions which determine the stability of the steady states. Lastly, we constructed the phase plane paths in several cases for both models.

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Macroscopic Models in Traffic Flow

Cited by 8 publications

References 34 publications

Methods for numerical calculation of parameters pertaining to the microscopic following-the-leader model of traffic flow: using the fast spline transformation

Methods for numerical calculation of parameters pertaining to the microscopic following-the-leader model of traffic flow: using the fast spline transformation

A first order model in traffic flow

Phase-space analysis for hydrodynamic traffic models

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