Second order traffic flow modelIing: supply-demand analysis of the inhomogeneous Riemann problem and of boundary conditions

• Autorzy: Lebacque J.-P. J.-P. , Mammar S. , Salem H. H.

Warianty tytułu

PL

Modelowanie przeplywu ruchu drugiego rzędu: podażowo-popytowa analiza niejednorodnego problemu Riemanna i warunków brzegowych

• Języki publikacji: EN

Abstrakty

EN

Recently Aw, Rascle, and Zhang introduced a second order model (ARZ) that does not exhibit the usual drawbacks of this family of models, i.e. negative velocities and/or densities. In this paper, we analyse the inhomogeneous Riemann problem for this model, which is shown to be equivalent to the inhomogeneous Riemann problem for a related first order model with modified equilibrium flow density relationship. The boundary conditions for the ARZ model are deduced. They can be expressed in terms of an upstream demand and downstream supply.

PL

Ostatnio Aw, Rascle i Zhang zdefiniowali model drugiego rzędu (ARZ), który nie wykazuje wad dotychczasowych modeli tego typu, jak ujemne prędkości i/lub gęstości. W artykule zanalizowano niejednorodny problem Riemanna dla tego modelu, który okazal się równoważny niejednorodnemu problemowi Riemanna dla odpowiedniego modelu pierwszego rzędu ze zmodyfikowaną zależnością natężenia ruchu od jego gęstości. Wyprowadzono warunki brzegowe dla modelu ARZ, które mogą być wyrażone jako popyt dopływu i podaż odpływu.

Słowa kluczowe

EN

Riemann problem; traffic flow modelling; analytical solutions; boundary conditions

PL

problem Riemanna; natężenie ruchu; modelowanie przepływu ruchu; struktura ruchu

• Wydawca: Warsaw University of Technology, Faculty of Transport
• Czasopismo: Archives of Transport
• Rocznik: 2008
• Tom: Vol. 20, iss. 1-2
• Strony: 47--67
• Opis fizyczny: Bibliogr. 16 poz., rys., wykr.

Twórcy

autor

Lebacque J.-P. J.-P.

autor

Mammar S.

autor

Salem H. H.

• National Institute for Transport and Safety Research, France

Bibliografia

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• 7. Lebacque J.P., Khoshyaran M.M.: Macroscopic flow models. [In:] Patriksson M., Labbe M. ed.: Transportation planning: the state of the art, 119-139, Kluwer Academic Press, 2002.
• 8. Lebacque J.P., Khoshyaran M.M.: First order macroscopic traffic flow models: intersection modeling, network modeling. Published in Transportation and Traffic Theory, Proceedings of the 16th ISTTT (International Symposium on Transportation and Traffic Theory), H. Mahmassani ed., 365-386, 2005.
• 9. Lebacque J.P., Mammar S., Haj-Salem H.: The AW-Rascle and Zhang's model: vacuum problems, existence and regularity of solutions of the Riemann problem. Accepted for publication in Transportation Research Part B, 2006.
• 10. Lebacque J.P., Mammar S., Haj-Salem H.: Generic second order traffic flow modeling. Published in the Proceedings of the 17th ISTTT, 2007.
• 11. Lighthill M.H., Whitham G.B.: On kinematic waves II: a theory of traffic flow on long crowded roads. Proc. Royal Soc., A, 229: 317-345, London, 1955.
• 12. Mammar S., Lebacque J.P., Haj-Salem H.: Second order traffic flow modeling: the Riemann problem resolution in homogeneous case without relaxation term. Proceedings of the Euro Working Group on Transportation, Poznań, 2005.
• 13. Mammar S., Lebacque J.P., Haj-Salem H.: Resolution of the Aw Rascle & Zhang macroscopic traffic flow model. Proceedings of the IMA Conference, London, 2005.
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