Abstract
We consider acceleration oriented vehicular traffic flow (VTF) model and study evolution of the N-particle systems, which are governed by a homogeneous Boltzmann-like equation. For this model we obtain a linear integral equation of the second kind and suggest to solve it by the weight Monte Carlo algorithms. The numerical results show that the approach to simulation suggested by the authors is reasonable to apply to the vehicular traffic problems. Moreover, this modification enabled us to study parametric dependencies of our functionals of interest.
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References
Chowdhury, D., Santen, L., Schadschneider, A.: Statistical physics of vehicular traffic and some related systems. Phys. Rep. 329 (4–6) 199–329 (2000)
Ivanov, M.S., Korotchenko, M.A., Mikhailov, G.A., Rogasinsky, S.V.: New Monte Carlo global weight method for the approximate solution of the nonlinear Boltzmann equation. Russ. J. Numer. Anal. Math. Modelling, 19 (3), 223–238 (2004)
Ivanov, M.S., Rogasinsky, S.V.: The Direct Statistical Simulation Method in Dilute Gas Dynamics. Publ. Comput. Center, Sib. Branch, USSR Acad. Sci., Novosibirsk (1988) [in Russian]
Kac, M.: Probability and Related Topics in Physical Sciences. Interscience, New York (1959)
Korotchenko, M.A., Mikhailov, G.A., Rogasinsky, S.V.: Value modifications of weighted statistical modeling for solving nonlinear kinetic equations. Russ. J. Numer. Anal. Math. Modelling, 22 (5), 471–486 (2007)
Mahnke, R., Kaupužs, J., Lubashevsky, I.: Probabilistic description of traffic flow. Phys. Rep. 408 (1–2), 1–130 (2005)
Mikhailov, G.A.: Parametric Estimates by the Monte Carlo Method. VSP, Utrecht (1999)
Mikhailov, G.A., Rogasinsky, S.V.: Weighted Monte Carlo methods for approximate solution of the nonlinear Boltzmann equation. Sib. Math. J. 43 (3), 496–503 (2002)
Waldeer, K.T.: The direct simulation Monte Carlo method applied to a Boltzmann-like vehicular traffic flow model. Comput. Phys. Commun. 156 (1), 1–12 (2003)
Waldeer, K.T.: A vehicular traffic flow model based on a stochastic acceleration process. Transp. Theory Stat. Phys. 33 (1), 7–30 (2004)
Acknowledgements
The authors acknowledge the kind hospitality of the Warsaw University and the MCQMC’2010 conference organizers. This work was partly supported by Russian Foundation for Basic Research (grants 09–01–00035, 09–01–00639, 11–01–00252) and SB RAS (Integration Grant No. 22). The authors would also like to thank Dr. S. V. Rogasinsky, Professor M. S. Ivanov and Corresponding member of RAS G. A. Mikhailov for valuable discussions.
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Burmistrov, A., Korotchenko, M. (2012). Weight Monte Carlo Method Applied to Acceleration Oriented Traffic Flow Model. In: Plaskota, L., Woźniakowski, H. (eds) Monte Carlo and Quasi-Monte Carlo Methods 2010. Springer Proceedings in Mathematics & Statistics, vol 23. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27440-4_14
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DOI: https://doi.org/10.1007/978-3-642-27440-4_14
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