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

Author

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  • W.-L. Jin

    (Department of Mathematics, University of California, Davis, California 95616)

  • H. M. Zhang

    (Department of Civil and Environmental Engineering, University of California, Davis, California 95616)

Abstract

The kinematic wave traffic flow model for an inhomogeneous road is studied as a resonant nonlinear system, where an additional conservation law is introduced to model time-invariant road inhomogeneities such as changes in grades or number of lanes. This resonant system has two families of waves, one of which is a standing wave originated at the inhomogeneity. The nature of these waves are examined and their time-space structures are studied under Riemann initial conditions and proper entropy conditions. Moreover, the system is solved numerically with Godunov's method, and the solutions are found to be consistent with those of Daganzo (1995) and Lebacque (1996) for the same initial conditions. Finally, the numerical approximation is applied to model traffic flow on a ring road with a bottleneck and the results conform to expectations.

Suggested Citation

  • W.-L. Jin & H. M. Zhang, 2003. "The Inhomogeneous Kinematic Wave Traffic Flow Model as a Resonant Nonlinear System," Transportation Science, INFORMS, vol. 37(3), pages 294-311, August.
    • Handle: RePEc:inm:ortrsc:v:37:y:2003:i:3:p:294-311
    DOI: 10.1287/trsc.37.3.294.16046
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    References listed on IDEAS

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    1. Zhang, H. M., 2000. "Structural properties of solutions arising from a nonequilibrium traffic flow theory," Transportation Research Part B: Methodological, Elsevier, vol. 34(7), pages 583-603, September.
    2. Daganzo, Carlos F., 1995. "The cell transmission model, part II: Network traffic," Transportation Research Part B: Methodological, Elsevier, vol. 29(2), pages 79-93, April.
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    5. Paul I. Richards, 1956. "Shock Waves on the Highway," Operations Research, INFORMS, vol. 4(1), pages 42-51, February.
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    7. Zhang, H. M., 2001. "A finite difference approximation of a non-equilibrium traffic flow model," Transportation Research Part B: Methodological, Elsevier, vol. 35(4), pages 337-365, May.
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    Citations

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    Cited by:

    1. Jin, Wen-Long & Zhang, H. Michael, 2013. "An instantaneous kinematic wave theory of diverging traffic," Transportation Research Part B: Methodological, Elsevier, vol. 48(C), pages 1-16.
    2. Jin, Wen-Long, 2007. "A dynamical system model of the traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 41(1), pages 32-48, January.
    3. Jin, Wen-Long, 2010. "A kinematic wave theory of lane-changing traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 44(8-9), pages 1001-1021, September.
    4. Li, Jia & Zhang, H.M., 2013. "Modeling space–time inhomogeneities with the kinematic wave theory," Transportation Research Part B: Methodological, Elsevier, vol. 54(C), pages 113-125.
    5. Jin, Wen-Long, 2012. "A kinematic wave theory of multi-commodity network traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 46(8), pages 1000-1022.
    6. Jin, Wen-Long & Gan, Qi-Jian & Lebacque, Jean-Patrick, 2015. "A kinematic wave theory of capacity drop," Transportation Research Part B: Methodological, Elsevier, vol. 81(P1), pages 316-329.
    7. Jin, Wen-Long & Laval, Jorge, 2018. "Bounded acceleration traffic flow models: A unified approach," Transportation Research Part B: Methodological, Elsevier, vol. 111(C), pages 1-18.
    8. Leclercq, Ludovic, 2007. "Bounded acceleration close to fixed and moving bottlenecks," Transportation Research Part B: Methodological, Elsevier, vol. 41(3), pages 309-319, March.
    9. Wu, Chun-Xiu & Zhang, Peng & Wong, S.C. & Choi, Keechoo, 2014. "Steady-state traffic flow on a ring road with up- and down-slopes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 403(C), pages 85-93.
    10. Chen, Yi-Ting & Sun, Edward W. & Chang, Ming-Feng & Lin, Yi-Bing, 2021. "Pragmatic real-time logistics management with traffic IoT infrastructure: Big data predictive analytics of freight travel time for Logistics 4.0," International Journal of Production Economics, Elsevier, vol. 238(C).
    11. Jin, Wen-Long, 2017. "Kinematic wave models of lane-drop bottlenecks," Transportation Research Part B: Methodological, Elsevier, vol. 105(C), pages 507-522.
    12. Jin, Wen-Long, 2017. "A Riemann solver for a system of hyperbolic conservation laws at a general road junction," Transportation Research Part B: Methodological, Elsevier, vol. 98(C), pages 21-41.
    13. Jin, Wen-Long, 2009. "Asymptotic traffic dynamics arising in diverge-merge networks with two intermediate links," Transportation Research Part B: Methodological, Elsevier, vol. 43(5), pages 575-595, June.

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