Numerical study of traffic flows by the hydrodynamic models

Morozov I.I., Gasnikov A.V., Tarasov V.N., Kholodov Y.A., Kholodov A.S.
 pdf (1733K)  / Annotation

List of references:

  1. M. J. Lighthill, G. B. Whitham. On kinematic waves: II. Theory of traffic flow on long crowded roads // Proc. R. Soc. London, Ser. A. — 1955. — V. 229. — P. 281–345. — DOI: 10.1098/rspa.1955.0088. — MathSciNet: MR0072606. — ads: 1955RSPSA.229..281L.
  2. P. I. Richards. Shock Waves on the Highway // Oper. Res. — 1956. — V. 4. — P. 42–51. — DOI: 10.1287/opre.4.1.42. — MathSciNet: MR0075522.
  3. H. J. Payne. Models of freeway traffic and control / Simulation Council Proc. 28, Mathematical Models of Public Systems. — 1971. — V. 1. — P. 51–61. — Edited by G. A. Bekey. — MathSciNet: MR0446564.
  4. Дж. Уизем. Линейные и нелинейные волны. — М: Мир, 1977.
  5. B. S. Kerner, H. Rehborn. Experimental features and characteristics of traffic jams // Phys. Rev. E. — 1996. — V. 53, no. 2. — DOI: 10.1103/PhysRevE.53.R1297.
  6. B. S. Kerner, H. Rehborn. Experimental properties of complexity in traffic flow // Phys. Rev. E. — 1996. — V. 53, no. 5. — DOI: 10.1103/PhysRevE.53.R4275.
  7. B. S. Kerner, H. Rehborn. Experimental Properties of Phase Transitions in Traffic Flow // Phys. Rev. Let. — 1997. — V. 79. — P. 4030–4033. — DOI: 10.1103/PhysRevLett.79.4030. — ads: 1997PhRvL..79.4030K.
  8. B. S. Kerner. Experimental Features of Self-Organization in Traffic Flow // Phys. Rev. Let. — 1998. — V. 81. — DOI: 10.1103/PhysRevLett.81.3797.
  9. B. S. Kerner. Introduction to modern traffic flow theory and control. The long road to three — phase traffic theory. — Springer, 2009.
  10. A. Aw, M. Rascle. Resurrection of “second order” models of traffic flow // SIAM Journal of Applied Mathematics. — 2000. — V. 60. — P. 916–938. — DOI: 10.1137/S0036139997332099. — MathSciNet: MR1750085.
  11. H. M. Zhang. A non-equilibrium traffic model devoid of gas-like behavior // Transp. Res. B. — 2002. — V. 36. — P. 275–290. — DOI: 10.1016/S0191-2615(00)00050-3.
  12. H. M. Zhang. Anisotropic property revisited–does it hold in multi-lane traffic? // Transportation Research Part B: Methodological. — 2003. — V. 37, no. 6. — P. 561–577. — DOI: 10.1016/S0191-2615(02)00030-9.
  13. F. Siebel, W. Mauser. On the Fundamental Diagram of Traffic Flow // SIAM J. Appl. Math. — 2006. — V. 66. — P. 1150–1162. — DOI: 10.1137/050627113. — MathSciNet: MR2246050.
  14. F. Siebel, W. Mauser. Synchronized flow and wide moving jams from balanced vehicular traffic // Physical Review E. — 2006. — V. 73, no. 6. — 066108. — DOI: 10.1103/PhysRevE.73.066108. — MathSciNet: MR2276289. — ads: 2006PhRvE..73f6108S.
  15. A. S. Kholodov, Y. A. Kholodov. Computational models on graphs for the nonlinear hyperbolic system of equations / Proceedings of ASME 2004 PVP Conference. — 2004. — V. 476. — P. 161–167. — DOI: doi:10.1115/PVP2004-2580.
  16. С. К. Годунов, Е. И. Роменский. Элементы механики сплошных сред и законы сохранения. — М: Наука, 1998. — 280 с.
  17. А. С. Холодов, Я. А. Холодов. О критериях монотонности разностных схем для уравнений гиперболического типа // Журнал выч. математики и мат. физики. — 2006. — Т. 46, № 9. — С. 1560–1588.
  18. Л. И. Седов. Методы подобия и размерности в механике. — М: Наука, Гл. ред. Физ.-Мат. Лит, 1987. — 432 с.

Indexed in Scopus

Full-text version of the journal is also available on the web site of the scientific electronic library eLIBRARY.RU

The journal is included in the Russian Science Citation Index

The journal is included in the RSCI

International Interdisciplinary Conference "Mathematics. Computing. Education"

Copyright © 2009–2024 Institute of Computer Science