Quality Properties of Connected Flow Model and Application for Traffic

Alexander Pavlovich Buslaev, M.G. Gorodnichev, A.V. Provorov, M.V. Yashina
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Abstract


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.

Keywords


follow-the-leader model, totally-connected flow, dynamical dimension|, communication function, Sobolev classes of function

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References


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,






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