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Analytical Deriving of Second Order Model of Payne from First Order Lighthil-Whitham-Richards Model Cover

Analytical Deriving of Second Order Model of Payne from First Order Lighthil-Whitham-Richards Model

Cybernetics and Information Technologies
Volume 13 (2013): Issue 4 (December 2013)
By: Vasilka Stoilova,  Emil Nikolov and  Nina Nikolova  
Open Access
|Dec 2013

References

  1. 1. Bellemans, T. Traffic Control on Motorways. Dissertation Thesis, Katholieke Universiteit Leuven, D/2003/7515/25, ISBN 90-5682-413-9, 2003.
    Search in Google Scholar
  2. 2. Buisson, C. Analyse bibliographique et première classification des algorithmes de simulation de lécoulement du trafic routier. - Recherches transports et sécurité, 1996, No 53, 35-48.
    Search in Google Scholar
  3. 3. Cassidy, M. J. Bivariate Relations in Nearly Stationary Highway Traffic Flow. - Transportation Research, Vol. 32B, 1998, No 1, 49-59.10.1016/S0191-2615(97)00012-X
    Search in Google Scholar
  4. 4. Daganzo, C. F. The Cell Transmission Model: A Dynamic Representation of Highway Traffic Consistent with the Hydrodynamic Theory. − Transportation Research, Part B, Vol. 28B, 1994, No 4, 269-287.10.1016/0191-2615(94)90002-7
    Search in Google Scholar
  5. 5. Daganzo, C. F. A Finite Difference Approximation of the Kinematic Wave Model of Traffic Flow. - Transportation Research, Part B, Vol. 29B,1995, No 4, 261-276.10.1016/0191-2615(95)00004-W
    Search in Google Scholar
  6. 6. Daganzo, C. F. Requiem for Second-Order Fluid Approximations of Traffic Flow. - Transportation Research, Part B, Vol. 29B, 1995, No 4, 277-286.10.1016/0191-2615(95)00007-Z
    Search in Google Scholar
  7. 7. Drake, J. A Statistical Analyses of Speed Density Hypotheses. Drake, J. S., J. L. Schofer, and A. D. May (1967). - Highway Research Record, Vol. 154, 1967, 53-87.
    Search in Google Scholar
  8. 8. Gartner, N. H. Development of Demand-Responsive Strategies for Urban Traffic Control. - In: Proceedings of the llthl FIP Conf. Syst. Modelling and Optimiz. P. Thoft-Christensen, Ed., New York, Springer-Verlag, 1984, 166-174.10.1007/BFb0008888
    Search in Google Scholar
  9. 9. Gartner, N. H., C. J. Messer, A. Rath i. Traffic Flow Theory: A State of the Art Report. US Project of: Department of Transportation Federal Highway Administration, Transportation Research Board, Oak Ridge National Laboratory, 1998. www.tfhrc.gov/its/tft/tft.htm trafficbook
    Search in Google Scholar
  10. 10. Greenber g, H. An Analysis of Traffic Flow. - Operations Research, Vol. 7, January-February 1959, No 1, 79-85.10.1287/opre.7.1.79
    Search in Google Scholar
  11. 11. Greenshields, B. D. A Study of Traffic Capacity. - In: Highway Research Board Proceedings, Vol. 14, 1935, 448-477.
    Search in Google Scholar
  12. 12. Helbing, D. Gas-Kinetic Derivation of Navier-Stokes-Like Traffic Equations. - Physical Review E, Vol. 53, 1996, No 3, 2266-2381.10.1103/PhysRevE.53.2366
    Search in Google Scholar
  13. 13. Helbing, D. Derivation, Properties, and Simulation ofa Gas-Kinetic-Based, Nonlocal Traffic Model. - Physical Review E, Vol. 59, 1999, No 1, 239-253.10.1103/PhysRevE.59.239
    Search in Google Scholar
  14. 14. Helbing, D., A. Hennecke, M. Treibe r. Phase Diagram of Traffic States in the Presence of Inhomogeneities. - Physical Review Letters, Vol. 82, May 1999, No 21, 4360-4363.10.1103/PhysRevLett.82.4360
    Search in Google Scholar
  15. 15. Helbing, D., M. Schreckenber g. Cellular Automata Simulating Experimental Properties of Traffic Flow. ar Xiv:cond-mat9812300v2, 21 Marth 1999.
    Search in Google Scholar
  16. 16. Hoogendoorn, S. P., P. H. L. Bovy. Modelling Multiple User-Class Traffic Flow. - Transportation Research B, Vol. 34, 2000, No 2, 123-146.10.1016/S0191-2615(99)00017-X
    Search in Google Scholar
  17. 17. Klar, A., Wegener. A Hierarchy of Models for Multilane Vehicular Traffic I & II: Modelling. - SIAM Journal of Applied Mathematics, 1998.10.1137/S0036139997326958
    Search in Google Scholar
  18. 18. Kotsialos, A., M. Papageorgiou, C. Diakak i, Y. Pavlis, F. Middelha m. Traffic Flow Modelling of Large-Scale Motorway Networks Using the Macroscopic Modelling Tool METANET. - In: Recent Advances in Traffic Flow Modelling and Control, Proceedings of the Expert Seminar on Recent Advances in Traffic Flow. 1999.
    Search in Google Scholar
  19. 19. Lesort, J. B., J. P. Lebacque. The Godunov Scheme and What is Means for First Order Traffic Flwo Models. - In: Proceedings of the 13th International Symposium on Transportation and Traffic Theory, Lyon, France, July 1996, 647-677.
    Search in Google Scholar
  20. 20. Lighthill, M. J., G. B. Whitham. On Kinematic Waves: I: Flow Movement in Long Rivers, II: A Theory of Traffic Flow on Long Crowded Roads. - In: Proceedings of the Royal Society: A229, London, 1955.
    Search in Google Scholar
  21. 21. Liu, G., A. S. Lyrintzi s, P. G. Michalopoulo s. Improved High-Order Model for Freeway Traffic Flow. - Transportation Research Record, Vol. 1644, 1998, 37- 46.
    Search in Google Scholar
  22. 22. Papageorgiou, M. Application of Automatic Control Concept to Traffic Flow Modeling and Control. - In: A. V. Balakrishan, M. Thoma, Eds. Lecture Notes in Control and Information Sciences. Berlin, Springer, 1983, 4-41.10.1007/BFb0044049
    Search in Google Scholar
  23. 23. Papageorgiou, M. Dynamic Modeling, Assignment, and Route Guidance in Traffic Networks. - Transportation Research, Part B, Vol. 24B, 1990, No 6, 471-495.10.1016/0191-2615(90)90041-V
    Search in Google Scholar
  24. 24. Papageorgiou, M. Some Remarks on Macroscopic Traffic Flow Modelling. - Transportation Research, Part A, Vol. 32, 1998, No 5, 323-329.10.1016/S0965-8564(97)00048-7
    Search in Google Scholar
  25. 25. Payne, H. J. Models of Freeway Traffic and Control. - In: Simulation Council Proceedings, 1971, No 1, 51-61.
    Search in Google Scholar
  26. 26. Richards, P. I. Shock Waves on the Highway. - Operations Research, Vol. 4, 1956, 42-57.10.1287/opre.4.1.42
    Search in Google Scholar
  27. 27. Stoilova, V. Methods for Modelling Transport Traffic in Highways - Part I. - In: Proc. of International Conf. Automatics and Informatics, Sofia, 2013.
    Search in Google Scholar
  28. 28. Treiber, M., A. Hennecke, D. Helbing. Congested Traffic States in Empirical Observations and Microscopic Simulations. - Physical Review E, Vol. 62, August 2000, No 2, 1805-1824.10.1103/PhysRevE.62.1805
    Search in Google Scholar
  29. 29. Zhang, H. M. Structural Properties of Solutions Arising froma Nonequilibrium Traffic Flow Theory. - Transportation Research, Part B, Vol. 34, 2000, 583-603. 10.1016/S0191-2615(99)00041-7
    Search in Google Scholar
DOI: https://doi.org/10.2478/cait-2013-0053 | Journal eISSN: 1314-4081 | Journal ISSN: 1311-9702
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Language: English
Page range: 54 - 62
Published on: Dec 31, 2013
Published by: Bulgarian Academy of Sciences, Institute of Information and Communication Technologies
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year
Keywords:
First order model,
second order model,
traffic flow
Related subjects:
Computer sciences,
Information technology

© 2013 Vasilka Stoilova, Emil Nikolov, Nina Nikolova, published by Bulgarian Academy of Sciences, Institute of Information and Communication Technologies
This work is licensed under the Creative Commons License.

Volume 13 (2013): Issue 4 (December 2013)