## MODELLING OF URBAN TRAFFIC FLOW

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Last modified: 05.06.2017

#### Abstract

In this paper non-deterministic motion of urban traffic is studied under certain assumptions. Based on those assumptions discrete and continuous mathematical models are developed: continuous model is written as the Cauchy initial-value problem for the integro-differential equation, whence among other things it is obtained the Fokker-Planck equation. Besides, the sufficient condition ensuring the mathematical legitimacy of the developed continuous model is formulated.

#### Keywords

#### References

*Mathematical Theories of Traffic Flow*. New York, USA: Academic Press, 1963, xi+242 pp.

[2] D. Helbing, "Traffic and related self-driven many-particle systems", Reviews of Modern Physics, vol. 73, pp. 1067-1141, 2001.

[3] R. Mahnke, J. Kaupuzs, and I. Lubashevsky, "Probabilistic description of traffic flow", Physics Reports, vol. 408, pp. 1-130, 2005.

[4] N. H. Gartner, "Traffic Flow Theory", Transportation Research Board, Special Report 165, World Scientific Press, 1992, 365 pp.

[5] C. F. Daganzo, *Fundamentals of Transportation and Traffic Operations*. New York, USA: Pergamon Press, 1997, 356 pp.

[6] B. S. Kerner, "Three-Phase Traffic Theory and Highway Capacity", Physica A, vol. 333, pp. 379-440, 2004.

[7] K. Nagel, P. Wagner, and R. Woesler, "Still flowing: Approaches to traffic flow and traffic jam modeling", Journal of Operations Research, vol. 51, No. 5, pp. 681-710, 2003.

[8] C. F. Daganzo, "A Behavioral Theory of Multi-Lane Traffic Flow. Part I: Long Homogeneous Freeway Sections", Transportation Research, Part B: Methodological, vol. 36, No. 2, pp. 131-158, 2002.

[9] C. F. Daganzo, "A Behavioral Theory of Multi-Lane Traffic Flow Part II: Merges and the Onset of Congestion", Transportation Research, Part B: Methodological, vol. 36, No. 2, pp. 159-169, 2002.

[10] A. V. Berezhnoy, "Investigation of the traffic flow models managing parameters influence on the efficiency of the urban traffic control", Doctoral Thesis, Transport and Telecommunication Institute, Riga, Latvia, 2008, 256 pp.

[11] N. N. Smirnov, A. B. Kiselev, V. F. Nikitin, and M. V. Yumashev, Mathematical Theory of Traffic Flow. Moscow, Russian Federation: Lomonosov Moscow State University Press, 1999, 30 p.

[12] V. I. Shvetsov and D. Helbing, "Macroscopic dynamics of multilane traffic", Physical Reviews E., vol. 59, 1999, pp. 6328-6339.

[13] H. Risken and T. Frank, The Fokker-Planck Equation: Methods of Solution and Applications. Berlin, Germany: Springer-Verlag, 1989, xiv+472 p.