%0 Book Section %1 statphys23_0159 %A Rodriguez, A.R. Mendez %A Belmont, R.M. Velasco %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K flow hydrodynamic model statphys23 topic-11 traffic %T Alternative model for traffic flow %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=159 %X In this work we present the construction of an alternative macroscopic model for traffic flow. We are interested in a model of three dynamic equations describing traffic flow. The macroscopic model is obtained by the usual methods of Kinetic Theory, from the Paveri-Fontana equation 1. The obtained macroscopic model is a hierarchy of equations for the moments of the distribution function involved. In order to close the model we need to know the solution distribution function of the Paveri- Fontana equation. We find the homogeneous and steady state solution of the kinetic Paveri-Fontana equation via a simple model between the average desired velocity and instantaneous velocity 2. By means of a maximization procedure of the informational entropy and Grad's method 3 it is obtained an approximated solution for the Paveri-Fontana equation in terms of the macroscopic variables density $\rho$, average velocity $V$ and velocity variance $\Theta$. In order to obtain a distribution function in terms of the spatial derivatives of the macroscopic variables we consider a relaxation behavior of the distribution function. With the distribution function obtained we compute the third moment of the distribution which provides us the clousure of the macroscopic model. Once the model is closed we solve numericaly and analyse the solution finding some interesting caracteristics present in real traffic. References:\\ 1) S. L. Paveri-Fontana,Transp. Res 9, 1975,(225-235)\\ 2) R. M. Velasco and Marques, Jr, Willson,Phys. Rev. E 72, 2005, (046102)\\ 3) H. Grad,CPAM 2, 1949,(331-407)

@incollection{statphys23_0159, abstract = {In this work we present the construction of an alternative macroscopic model for traffic flow. We are interested in a model of three dynamic equations describing traffic flow. The macroscopic model is obtained by the usual methods of Kinetic Theory, from the Paveri-Fontana equation [1]. The obtained macroscopic model is a hierarchy of equations for the moments of the distribution function involved. In order to close the model we need to know the solution distribution function of the Paveri- Fontana equation. We find the homogeneous and steady state solution of the kinetic Paveri-Fontana equation via a simple model between the average desired velocity and instantaneous velocity [2]. By means of a maximization procedure of the informational entropy and Grad's method [3] it is obtained an approximated solution for the Paveri-Fontana equation in terms of the macroscopic variables density $\rho$, average velocity $V$ and velocity variance $\Theta$. In order to obtain a distribution function in terms of the spatial derivatives of the macroscopic variables we consider a relaxation behavior of the distribution function. With the distribution function obtained we compute the third moment of the distribution which provides us the clousure of the macroscopic model. Once the model is closed we solve numericaly and analyse the solution finding some interesting caracteristics present in real traffic. References:\\ 1) S. L. Paveri-Fontana,Transp. Res 9, 1975,(225-235)\\ 2) R. M. Velasco and Marques, Jr, Willson,Phys. Rev. E 72, 2005, (046102)\\ 3) H. Grad,CPAM 2, 1949,(331-407)}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Rodriguez, A.R. Mendez and Belmont, R.M. Velasco}, biburl = {https://www.bibsonomy.org/bibtex/2ff9161ca0f91b7ea88f48ccbc9aee596/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {9db67f3b12357219d77e09f254d7db49}, intrahash = {ff9161ca0f91b7ea88f48ccbc9aee596}, keywords = {flow hydrodynamic model statphys23 topic-11 traffic}, month = {9-13 July}, timestamp = {2007-06-20T10:16:13.000+0200}, title = {Alternative model for traffic flow}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=159}, year = 2007 }