Skip to main content
Log in

Well Posedness for Multilane Traffic Models

  • Published:
ANNALI DELL'UNIVERSITA' DI FERRARA Aims and scope Submit manuscript

Abstract

We give rigorous results on the analytical properties of multilane traffic flow models based on hyperbolic balance laws.

Keywords: Traffic flows, Hyperbolic conservatin laws, Operator splitting method

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

References

  • 1. Aw, A., Rascle, M.: Resurrection of “second order” models of traffic flow. SIAM J. Appl. Math. 60, no. 3, 916–938 (2000)

    Google Scholar 

  • 2. Bagnerini, P., Colombo, R.M., Corli, A.: On the role of source terms in continuum traffic flow models. Mathematical and Computer Modeling, to appear (2006)

  • 3. Bressan, A.: Hyperbolic systems of conservation laws. Oxford University Press, Oxford (2000)

  • 4. Chanut, S., Buisson, C.: A macroscopic model and its numerical solution for a two-flow mixed traffic with different speeds and lengths. Transportation Res. Rec. 1852, 209–219 (2003)

    Google Scholar 

  • 5. Colombo, R.M.: A 2× 2 hyperbolic traffic flow model. Math. Comput. Modelling 35, no. 5-6, 683–688 (2002)

  • 6. Colombo, R.M.: Hyperbolic phase transitions in traffic flow. SIAM J. Appl. Math. 63, no. 2, 708–721 (2002)

    Google Scholar 

  • 7. Colombo, R.M., Corli, A.: Dynamic parameters identification in traffic flow modeling. In Proceedings of the Fifth International Conference on Dynamical Systems and Differential Equations (2004)

  • 8. Colombo, R.M., Corli, A.: On a class of hyperbolic balance laws. J. Hyperbolic Differ. Equ. 1, no. 4, 725–745 (2004)

    Google Scholar 

  • 9. Colombo, R.M., Goatin, P., Priuli, F.S.: Global Well posedness of a traffic flow model with phase transitions. Nonlinear Analysis Ser. A: Theory, Methods & Applications, to appear (2006)

  • 10. Dafermos, C.M.: Hyperbolic conservation laws in continuum physics. Springer-Verlag, Berlin-Heidelberg (2000)

  • 11. Filippov, A.F.: Differential equations with discontinuous righthand sides. Kluwer Academic Publishers Group, Dordrecht (1988)

  • 12. Greenberg, J.M., Klar, A., Rascle, M.: Congestion on multilane highways. SIAM J. Appl. Math. 63, no. 3, 818–833 (2003)

    Google Scholar 

  • 13. Helbing, D., Greiner, A.: Modeling and simulation of multi-lane traffic flow. Phys. Rev. E 55, no. 3, 5498 (1997)

    Google Scholar 

  • 14. Herty, M., Klar, A.: Modeling, simulation, and optimization of traffic flow networks. SIAM J. Sci. Comput. 25, no. 3, 1066–1087 (2003)

    Google Scholar 

  • 15. Hoff, D.: Invariant regions for systems of conservation laws. Trans. Amer. Math. Soc. 289, no. 2, 591–610 (1985)

    Google Scholar 

  • 16. Hoogendoorn, S.: Multiclass continuum modelling of multilane traffic flow. Delft University Press, Delft (1999)

  • 17. Klar, A., Kühne, R.D., Wegener, R.: Mathematical models for vehicular traffic. Surveys Math. Indust. 6, no. 3, 215–239 (1996)

    Google Scholar 

  • 18. Klar, A., Wegener, R.: A hierarchy of models for multilane vehicular traffic. I. Modeling. SIAM J. Appl. Math. 59, no. 3, 983–1001 (1999)

    Google Scholar 

  • 19. Klar, A., Wegener, R.: A hierarchy of models for multilane vehicular traffic. II. Numerical investigations. SIAM J. Appl. Math. 59, no. 3, 1002–1011 (1999)

    Google Scholar 

  • 20. Nagumo, M.: Über die Lage der Integralkurven gewöhnlicher Differentialgleichungen. Proc. Phys. Math. Soc. Japan 24, no. 3, 551–559 (1942)

  • 21. Temple, B.: Systems of conservation laws with invariant submanifolds. Trans. Amer. Math. Soc. 280, no. 2, 781–795 (1983)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Colombo, R.M., Corli, A. Well Posedness for Multilane Traffic Models. Ann. Univ. Ferrara 52, 291–301 (2006). https://doi.org/10.1007/s11565-006-0022-5

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11565-006-0022-5

Navigation