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Quality Properties of Connected Flow Model and Application for Traffic

Year 2016, Volume: 4 Issue: 4, - , 30.12.2016

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.

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
  • 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

Quality Properties of Connected Flow Model and Application for Traffic

Year 2016, Volume: 4 Issue: 4, - , 30.12.2016

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.

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
  • 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
There are 86 citations in total.

Details

Journal Section RV
Authors

Alexander Pavlovich Buslaev

M.g. Gorodnichev This is me

A.v. Provorov This is me

M.v. Yashina This is me

Publication Date December 30, 2016
Published in Issue Year 2016 Volume: 4 Issue: 4

Cite

APA Buslaev, A. P., Gorodnichev, M., Provorov, A., Yashina, M. (2016). Quality Properties of Connected Flow Model and Application for Traffic. International Journal of Applied Mathematics Electronics and Computers, 4(4).
AMA Buslaev AP, Gorodnichev M, Provorov A, Yashina M. Quality Properties of Connected Flow Model and Application for Traffic. International Journal of Applied Mathematics Electronics and Computers. March 2016;4(4).
Chicago Buslaev, Alexander Pavlovich, M.g. Gorodnichev, A.v. Provorov, and M.v. Yashina. “Quality Properties of Connected Flow Model and Application for Traffic”. International Journal of Applied Mathematics Electronics and Computers 4, no. 4 (March 2016).
EndNote Buslaev AP, Gorodnichev M, Provorov A, Yashina M (March 1, 2016) Quality Properties of Connected Flow Model and Application for Traffic. International Journal of Applied Mathematics Electronics and Computers 4 4
IEEE A. P. Buslaev, M. Gorodnichev, A. Provorov, and M. Yashina, “Quality Properties of Connected Flow Model and Application for Traffic”, International Journal of Applied Mathematics Electronics and Computers, vol. 4, no. 4, 2016.
ISNAD Buslaev, Alexander Pavlovich et al. “Quality Properties of Connected Flow Model and Application for Traffic”. International Journal of Applied Mathematics Electronics and Computers 4/4 (March 2016).
JAMA Buslaev AP, Gorodnichev M, Provorov A, Yashina M. Quality Properties of Connected Flow Model and Application for Traffic. International Journal of Applied Mathematics Electronics and Computers. 2016;4.
MLA Buslaev, Alexander Pavlovich et al. “Quality Properties of Connected Flow Model and Application for Traffic”. International Journal of Applied Mathematics Electronics and Computers, vol. 4, no. 4, 2016.
Vancouver Buslaev AP, Gorodnichev M, Provorov A, Yashina M. Quality Properties of Connected Flow Model and Application for Traffic. International Journal of Applied Mathematics Electronics and Computers. 2016;4(4).