Quality Properties of Connected Flow Model and Application for Traffic

Alexander Pavlovich Buslaev; M.g. Gorodnichev; A.v. Provorov; M.v. Yashina

Quality Properties of Connected Flow Model and Application for Traffic

Yıl 2016, Cilt: 4 Sayı: 4, - , 30.12.2016

Alexander Pavlovich Buslaev M.g. Gorodnichev A.v. Provorov M.v. Yashina

Öz

Sequential moving of particles in one direction is considered. Model of totally-connected flow is introduced in [1] -[4] and concerned to the type of follow-the-leader in traffic flow theory.Properties of traffic flow are significantly determinate by state-function. For describing of non connected flow we introduce new model when acceleration of particles takes into consideration the dynamics of neighborhoods particles.For a chain of particles the model is describing by differential equations of second degree. The function of communication for this model is defined. Inpartial case the sufficient conditions for convergence of solution the model to totally-connected state are obtained.In the case of leader-follower pair of particles with linear state and communication functionsthe statements of belonging of solutions to some Sobolev classes of function are proved.

Kaynakça

V.V. Kozlov, A.P. Buslaev. On a system of
nonlinear differential equations for the model of
totally connected traffic. Journal of Concrete and
Applicable Mathematics. Eudoxus Press, LLC. Vol. 12
Num’s 1-2, 2014, 86 – 93.
Rothery R.W. Car Following Models in Traffic Flow
Theory, Transportation research board, ed. Gartner
N, Special report, 165, 1992, p. 4.1 - 4.42
Pipes L.A. An Operational Analysis of Traffic
Dynamics, Journal of Applied Physics, 1953, v. 24, p.
-281.
Buslaev A.P. et al. Selected Mathematical Problems
of Traffic Flow Theory International Journal of
Computer Mathematics Vol. 89, 3, 2012, p.409-432
A.N. Kolmogorov, Selected works. In 6
volumes.Volume 1: Mathematics and mechanics. Nauka
Moscow, 1985, pp. 1469 (in Russian) (V.M.
Tikhomirov and G.G. Magaril – Ilyaev, Inequalities for
derivatives, pp. 387389).
Bugaev A.S., Buslaev A.P., Kozlov V.V., Yashina M.V.
Distributed Problems of Monitoring and Modern
Approaches to Traffic Modeling, p. 6, 14th International
IEEE Conference on Intelligent Transportation Systems
(ITSC 2011), Washington, USA, 5-7.10.2011
Buslaev A.P., Provorov A.V., Yashina M.V.
Infocommunication Systems of Saturated Traffic
Control in Megalopolises. Proceedings of the 2013
International Conference on Internet Computing and
Big Data (WORLDCOMP13), 2013, Las Vegas, USA.
pp. 622-625.
Yashina M.V., Provorov A.V. Verification of
Infocommunication System Components for Modeling
and Control of Saturated Traffic in Megalopolis.
Proceedings of the 8th International Conference on
Dependability and Complex Systems DepCoSRELCOMEX
Brunow, Poland. Springer, 2013. pp.
-542.
A.P. Buslaev, M.G. Gorodnichev, A.V. Provorov. Onedimensional
Models of Particles Flow and
Infocommunication Methods of Verification.
Proceeding of The 2014 International Conference on
Computational Science and Computational
Intelligence, 10-12 March 2014, Las Vegas, USA
V.V. Kozlov, A.P. Buslaev. On a system of
nonlinear differential equations for the model of
totally connected traffic. Journal of Concrete and
Applicable Mathematics. Eudoxus Press, LLC. Vol. 12
Num’s 1-2, 2014, 86 – 93.
Rothery R.W. Car Following Models in Traffic Flow
Theory, Transportation research board, ed. Gartner
N, Special report, 165, 1992, p. 4.1 - 4.42
Pipes L.A. An Operational Analysis of Traffic
Dynamics, Journal of Applied Physics, 1953, v. 24, p.
-281.
Buslaev A.P. et al. Selected Mathematical Problems
of Traffic Flow Theory International Journal of
Computer Mathematics Vol. 89, 3, 2012, p.409-432
A.N. Kolmogorov, Selected works. In 6
volumes.Volume 1: Mathematics and mechanics. Nauka
Moscow, 1985, pp. 1469 (in Russian) (V.M.
Tikhomirov and G.G. Magaril – Ilyaev, Inequalities for
derivatives, pp. 387389).
Bugaev A.S., Buslaev A.P., Kozlov V.V., Yashina M.V.
Distributed Problems of Monitoring and Modern
Approaches to Traffic Modeling, p. 6, 14th International
IEEE Conference on Intelligent Transportation Systems
(ITSC 2011), Washington, USA, 5-7.10.2011
Buslaev A.P., Provorov A.V., Yashina M.V.
Infocommunication Systems of Saturated Traffic
Control in Megalopolises. Proceedings of the 2013
International Conference on Internet Computing and
Big Data (WORLDCOMP13), 2013, Las Vegas, USA.
pp. 622-625.
Yashina M.V., Provorov A.V. Verification of
Infocommunication System Components for Modeling
and Control of Saturated Traffic in Megalopolis.
Proceedings of the 8th International Conference on
Dependability and Complex Systems DepCoSRELCOMEX
Brunow, Poland. Springer, 2013. pp.
-542.
A.P. Buslaev, M.G. Gorodnichev, A.V. Provorov. Onedimensional
Models of Particles Flow and
Infocommunication Methods of Verification.
Proceeding of The 2014 International Conference on
Computational Science and Computational
Intelligence, 10-12 March 2014, Las Vegas, USA