The Inhomogeneous Kinematic Wave Traffic Flow Model as a Resonant Nonlinear System

References

• Courant R., Friedrichs K., Lewy H. Ber die partiellen Differenzengleichungen der mathematischen Physik. Mathematische Annalen (1928) 100:32–74Translated as: On the partial difference equations of mathematical physics. 1967. IBM J. Res. Development 11 215–234Crossref, Google Scholar
• Daganzo C. F. The cell transmission model, Part II: Network traffic. Transportation Res. B (1995) 29(2):79–93Crossref, Google Scholar
• Godunov S. K. A difference method for numerical calculations of discontinuous solutions of the equations of hydrodynamics. Matematicheskii Sbornik (1959) 47(3):271–306Google Scholar
• Herrmann M., Kerner B. S. Local cluster effect in different traffic flow models. Physica A (1998) 255:163–198Crossref, Google Scholar
• Isaacson E., Temple J. B. Nonlinear resonance in systems of conservation laws. SIAM J. Appl. Math. (1992) 52(5):1260–1278Crossref, Google Scholar
• Kerner B. S., Konhäuser P. Structure and parameters of clusters in traffic flow. Physical Rev. E (1994) 50(1):54–83Crossref, Google Scholar
• Lax P. D.Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves (1972) (SIAM, Philadelphia PA) Google Scholar
• Lebacque J. P. The Godunov scheme and what it means for first order traffic flow models. Transportation and Traffic Theory (1996) . ISTTTGoogle Scholar
• Lighthill M. J., Whitham G. B. On kinematic waves: II. A theory of traffic flow on long crowded roads. Proc. Roy. Soc. London A (1955) 229:317–345Crossref, Google Scholar
• Lin L., Temple J. B., Wang J. A comparison of convergence rates for Godunov's method and Glimm's method in resonant nonlinear systems of conservation laws. SIAM J. Numer. Anal. (1995) 32(3):824–840Crossref, Google Scholar
• Payne H. J. Models of freeway traffic and control. Mathematical Models of Public Systems (1971) 1:51–60La Jolla CAGoogle Scholar
• Richards P. I. Shock waves on the highway. Oper. Res. (1956) 4:42–51Link, Google Scholar
• Whitham G. B.Linear and Nonlinear Waves (1974) (John Wiley and Sons, New York) Google Scholar
• Zhang H. M. A theory of nonequilibrium traffic flow. Transportation Res. B (1998) 32(7):485–498Crossref, Google Scholar
• Zhang H. M. An analysis of the stability and wave properties of a new continuum theory. Transportation Res. B (1999) 33(6):387–398Crossref, Google Scholar
• Zhang H. M. Structural properties of solutions arising from a non-equilibrium traffic flow theory. Transportation Res. B (2000) 34(7):583–603Crossref, Google Scholar
• Zhang H. M. A finite difference approximation of a non-equilibrium traffic flow model. Transportation Res. B (2001) 35(4):337–365Crossref, Google Scholar