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Intersection Modeling, Application to Macroscopic Network Traffic Flow Models and Traffic Management

  • Conference paper
Traffic and Granular Flow ’03

Summary

The object of the paper is to analyze intersection modeling in the context of macroscopic traffic flow models. The paper begins with a brief review of classical boundary conditions of the Dubois-LeFloch and the Bardos-Nédélec-LeRoux type, and their relation to the concepts of local traffic supply and demand. It will be shown that the local traffic supply and demand concept extends and simplifies these classical approaches. The resulting constraints on phenomenological intersection models will be discussed. Several examples of intersection models are deduced. Some of these recapture earlier models; others are specifically designed for congested traffic conditions and take into account the bounds on car acceleration. The last part of the paper is devoted to network modeling and to applications to network traffic management.

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References

  1. Buisson, C., Lebacque, J.P., Lesort, J.B. 1. Macroscopic modelling of traffic flow and assignment in mixed networks. Proc. of the Berlin ICCCBE Conf. 1367–1374. (ed. Pahl, P.J., Werner, H.). 1995. 2. STRADA, a discretized macroscopic model of vehicular flow in complex networks based on the Godunov scheme. Proc. of the CESA'96 IEEE Conference. 1996. 3. The STRADA model for dynamic assignment. Proceedings of the 1996 ITS Conference. 1996.

    Google Scholar 

  2. Bardos, C., LeRoux, A., Nédélec, J.C. First order quasilinear equations with boundary conditions. Comm. partial Differ. Equations 4, 1017–1034, 1979.

    Article  MATH  Google Scholar 

  3. Coclite, G.M., Piccoli, B. Traffic flow on a road network. Technical Report, SISSA, 2002.

    Google Scholar 

  4. Daganzo, C.F. The cell transmission model 2: network traffic simulation. Transportation Research 29B. 2: 79–93. 1995.

    Article  Google Scholar 

  5. Dubois, F., LeFloch, P. Boundary conditions for nonlinear hyperbolic systems of conservation laws. J. Differential Equations 71, 93–122, 1988.

    Article  MATH  MathSciNet  Google Scholar 

  6. Elloumi, E., Haj-Salem, H., Papageorgiou, M. METACOR, a macroscopic modelling tool for urban corridors. TRISTAN II Int. Conf., Capri, 1994.

    Google Scholar 

  7. Holden, H., Risebro, N. A mathematical model of traffic flow on a network of unidirectional roads. SIAM J. Math. Anal. 4, 999–1017, 1995.

    Article  MathSciNet  Google Scholar 

  8. Klar, A., Herty, M. Modeling of traffic flow networks. Proceedings of the Autumn school: “Modélisation mathématique du trafic automobile” (Editors: J.P. Lebacque, J.P. Quadrat, M. Rascle). In press, 2003.

    Google Scholar 

  9. Kröner, D. Numerical schemes for conservation laws. Wiley-Teubner. 1997.

    Google Scholar 

  10. Jin, W.L., Zhang, H.M. On the distribution schemes for determining flows through a merge. In press, Transportation Research B, 2002.

    Google Scholar 

  11. Lebacque, J.P. Semimacroscopic simulation of urban traffic. Int. 84 Minneapolis Summer Conference. AMSE. 1984.

    Google Scholar 

  12. Lebacque, J.P. The Godunov scheme and what it means for first order traffic flow models. Transportation and traffic flow theory, Proceedings of the 13th ISTTT (J.B. Lesort Editor). Pergamon, 1996.

    Google Scholar 

  13. Lebacque, J.P. A two-phase extension of the LWR model based on the boundedness of traffic acceleration. Transportation and traffic flow theory in the 21st century, Proceedings of the 15th ISTTT (M.A.P. Taylor Editor). Pergamon, 2002.

    Google Scholar 

  14. Lebacque, J.P. Two-phase extension of the LWR model: analytical solutins and applications. TRB 2002 and TRR (in press). 2003.

    Google Scholar 

  15. Lebacque, J.P. Problèmes de modélisation des réseaux par les modèles du premier ordre: conditions aux limites, intersections, affectation. Proceedings of the Autumn school: “Modélisation mathématique du trafic automobile” (Editors: J.P. Lebacque, J.P. Quadrat, M. Rascle). In press, 2003.

    Google Scholar 

  16. Lebacque, J.P., Haj-Salem, H. Speed limit control: a problem formulation and theoretical discussions. Preprints of the Tristan IV Symposium, tome 2, 421–426, 2001.

    Google Scholar 

  17. Lebacque, J.P., Khoshyaran, M.M. Macroscopic flow models. Presented at the 6th Meeting of the EURO Working Group on Transportation. Published in “Transportation planning: the state of the art” (Editors: M. Patriksson, M. Labbé), 119–139. Kluwer Academic Press, 2002.

    Google Scholar 

  18. Lo, H.K. A dynamic traffic assignment formulation that encapsulates the Celltransmission model. Transportation and traffic flow theory, Proceedings of the 14th ISTTT (A. Ceder Editor). Pergamon, 1999.

    Google Scholar 

  19. Lighthill, M.H., Whitham, G.B. On kinematic waves II: A theory of traffic flow on long crowded roads. Proc. Royal Soc. (Lond.) A 229: 317–345. 1955.

    MATH  MathSciNet  Google Scholar 

  20. Messner, A., Papageorgiou, M. METANET: a macroscopic modelling simulation for motorway networks. Technische Universität München, 1990.

    Google Scholar 

  21. Osher, S. Riemann solvers, the entropy condition, and difference approximations. SIAM J. Num. Analysis 21: 217–235, 1984.

    Article  MATH  MathSciNet  Google Scholar 

  22. Payne, H.J. Models of freeway traffic and control. Simulation Council Proceedings 1: ch 6, 1971.

    Google Scholar 

  23. Richards, P.I. Shock-waves on the highway. Opns. Res. 4: 42–51, 1956.

    Article  MathSciNet  Google Scholar 

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© 2005 Springer-Verlag Berlin Heidelberg

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Lebacque, J. (2005). Intersection Modeling, Application to Macroscopic Network Traffic Flow Models and Traffic Management. In: Hoogendoorn, S.P., Luding, S., Bovy, P.H.L., Schreckenberg, M., Wolf, D.E. (eds) Traffic and Granular Flow ’03. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-28091-X_26

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