Double randomization method for estimating the moments of solution to vehicular traffic problems with random parameters

References

[1] A. V. Burmistrov and M. A. Korotchenko, Algorithms of Monte Carlo method for simulating the vehicular traffic flow with random parameters. In: Marchuk Scientific Readings 2019: Proc. Int. Conf. ‘Advanced Mathematics, Computations and Applications, AMCA-2019’. NSU PPC, Novosibirsk. 2019, pp. 72–79 (in Russian).Suche in Google Scholar

[2] A. V. Burmistrov and M.A. Korotchenko, Application of kinetic models and simulation of multi-particle systems in some fields of science. Mathematical Modeling, Computer and Field Experiment in Natural Sciences1 (2019), 3–12.Suche in Google Scholar

[3] A. V. Burmistrov and M. A. Korotchenko, Application of statistical methods for the study of kinetic model of traffic flow with separated accelerations. Russ. J. Numer. Anal. Math. Modelling26 (2011), No. 3, 275–293.10.1515/rjnamm.2011.015Suche in Google Scholar

[4] A. Burmistrov and M. Korotchenko, Monte Carlo algorithm for simulation of the vehicular traffic flow within the kinetic model with velocity dependent thresholds. Springer Proc. Math. Stat. 114 (2014), 109–117.10.1007/978-1-4939-2104-1_10Suche in Google Scholar

[5] A. Burmistrov and M. Korotchenko, Weight Monte Carlo method applied to acceleration oriented traffic flow model. Springer Proc. Math. Stat. 23 (2012), 297–311.10.1007/978-3-642-27440-4_14Suche in Google Scholar

[6] B. Coifman, Empirical flow-density and speed-spacing relationships: evidence of vehicle length dependency. Transportation Research Part B78 (2015), 54–65.10.1016/j.trb.2015.04.006Suche in Google Scholar

[7] M. S. Ivanov and S. V. Rogasinsky, The Direct Statistical Simulation Method in Dilute Gas Dynamics. CC SB USSR AS, Novosibirsk, 1988 (in Russian).Suche in Google Scholar

[8] M. A. Korotchenko and A. V. Burmistrov, The Monte Carlo algorithms for solving the Smoluchowski equation with random coefficients. In: Mathematical and Computer Modeling of Natural Scientific and Social Problems. 2019, pp. 35–40 (in Russian).Suche in Google Scholar

[9] M. A. Korotchenko, G. A. Mikhailov, and S. V. Rogazinskii, Value modifications of weighted statistical modelling for solving nonlinear kinetic equations. Russ. J. Numer. Anal. Math. Modelling22 (2007), No. 5, 471–486.10.1515/rnam.2007.023Suche in Google Scholar

[10] M. A. Marchenko and G. A. Mikhailov, Distributed computing by the Monte Carlo method. Automation and Remote Control68 (2007), No. 5, 888–900.10.1134/S0005117907050141Suche in Google Scholar

[11] G. A. Mikhailov, Efficient Monte Carlo algorithms for evaluating the correlation characteristics of conditional mathematical expectations. USSR Comp. Math. Math. Phys. 17 (1977) No. 1, 244–247 (in Russian).10.1016/0041-5553(77)90088-XSuche in Google Scholar

[12] G. A. Mikhailov, Randomized Monte Carlo algorithms for problems with random parameters (‘double randomization’ method). Numer. Anal. Appl. 12 (2019), No. 2, 155–165.10.1134/S1995423919020058Suche in Google Scholar

[13] G. A. Mikhailov and S. V. Rogazinskii, Weighted Monte Carlo methods for approximate solution of a nonlinear Boltzmann equation. Sib. Math. J. 43 (2002) No. 3, 496–503.10.1023/A:1015467719806Suche in Google Scholar

[14] G. A. Mikhailov and A. V. Voitishek, Numerical Statistical Modelling. Monte Carlo Methods. Akademia, Moscow, 2006 (in Russian).Suche in Google Scholar

[15] S. V. Rogazinskii, Weighted statistical modelling algorithms with branching and extension of a model ensemble of interacting particles. Russ. J. Numer. Anal. Math. Modelling31 (2016) No. 4, 207–215.10.1515/rnam-2016-0021Suche in Google Scholar

[16] E. Roidl, B. Frehse, and R. Höger, Emotional states of drivers and the impact on speed, acceleration and traffic violations – a simulator study. Accident Analysis and Prevention70 (2014), 282–292.10.1016/j.aap.2014.04.010Suche in Google Scholar

[17] E. I. Vlahogianni, M. G. Karlaftis, and J. C. Golias, Short-term traffic forecasting: where we are and where we are going. Transportation Research Part C43 (2014) No. 1, 3–19.10.1016/j.trc.2014.01.005Suche in Google Scholar

[18] K. T. Waldeer, The direct simulation Monte Carlo method applied to a Boltzmann-like vehicular traffic flow model. Computer Physics Communications156 (2003) No. 1, 1–12.10.1016/S0010-4655(03)00368-0Suche in Google Scholar

[19] K. T. Waldeer, A vehicular traffic flow model based on a stochastic acceleration process. Transport Theory and Statistical Physics33 (2004) No. 1, 7–30.10.1081/TT-120030341Suche in Google Scholar