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A simple physical principle for the simulation of freeways with special lanes and priority vehicles

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  • Daganzo, Carlos F.
  • Lin, Wei-Hua
  • Del Castillo, Jose M.

Abstract

This paper presents a simple physical principle that can be used to solve the kinematic wave problem for freeways with special lanes and priority vehicles. The principle is shown to yield the flows for all possible 'Riemann problems' arising in a homogeneous highway, so that its application in a simulation is equivalent to the Godunov 'classic' finite difference approximation method. The principle is appealing because its physical basis, unlike purely mathematical formulae, suggests a natural way in which boundary conditions for practical problems may be treated. Perhaps the IT principle will prove useful for solving general problems, e.g. involving multicommodity networks. This issue deserves more study. As an illustration of this potential the paper shows that an IT simulation of the finite highway problem solved in the companion paper (Daganzo, Transportation Research B, 31, 83-102, 1997) matches rather well the exact solution. Additional tests using other boundary conditions for the same problem also revealed a good match.

Suggested Citation

  • Daganzo, Carlos F. & Lin, Wei-Hua & Del Castillo, Jose M., 1997. "A simple physical principle for the simulation of freeways with special lanes and priority vehicles," Transportation Research Part B: Methodological, Elsevier, vol. 31(2), pages 103-125, April.
    • Handle: RePEc:eee:transb:v:31:y:1997:i:2:p:103-125
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    1. Daganzo, Carlos F., 1997. "A continuum theory of traffic dynamics for freeways with special lanes," Transportation Research Part B: Methodological, Elsevier, vol. 31(2), pages 83-102, April.
    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.
    3. Daganzo, Carlos F., 1995. "A finite difference approximation of the kinematic wave model of traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 29(4), pages 261-276, August.
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    Cited by:

    1. Nair, Rahul & Mahmassani, Hani S. & Miller-Hooks, Elise, 2011. "A porous flow approach to modeling heterogeneous traffic in disordered systems," Transportation Research Part B: Methodological, Elsevier, vol. 45(9), pages 1331-1345.
    2. Daganzo, Carlos F., 1999. "A Behavioral Theory of Multi-Lane Traffic Flow Part I: Long Homogeneous Freeway Sections," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt8n96n91w, Institute of Transportation Studies, UC Berkeley.
    3. Flötteröd, Gunnar & Rohde, Jannis, 2011. "Operational macroscopic modeling of complex urban road intersections," Transportation Research Part B: Methodological, Elsevier, vol. 45(6), pages 903-922, July.
    4. Logghe, S. & Immers, L.H., 2008. "Multi-class kinematic wave theory of traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 42(6), pages 523-541, July.
    5. Laval, Jorge A. & Daganzo, Carlos F., 2004. "Multi-Lane Hybrid Traffic Flow Model: Quantifying the Impacts of Lane-Changing Maneuvers on Traffic Flow," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt8w70q261, Institute of Transportation Studies, UC Berkeley.
    6. Jin, Wen-Long, 2013. "A multi-commodity Lighthill–Whitham–Richards model of lane-changing traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 361-377.
    7. Zheng, Zuduo, 2014. "Recent developments and research needs in modeling lane changing," Transportation Research Part B: Methodological, Elsevier, vol. 60(C), pages 16-32.
    8. Robert, Tim & Lin, Wei-Hua & Cassidy, Michael, 1999. "Validation of the Incremental Transfer Model," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt48s3v44r, Institute of Transportation Studies, UC Berkeley.
    9. Laval, Jorge A. & Daganzo, Carlos F., 2006. "Lane-changing in traffic streams," Transportation Research Part B: Methodological, Elsevier, vol. 40(3), pages 251-264, March.
    10. Newell, G. F., 1999. "Delays caused by a queue at a freeway exit ramp," Transportation Research Part B: Methodological, Elsevier, vol. 33(5), pages 337-350, June.
    11. Wen-Long Jin, 2015. "Analysis of Kinematic Waves Arising in Diverging Traffic Flow Models," Transportation Science, INFORMS, vol. 49(1), pages 28-45, February.
    12. Aghamohammadi, Rafegh & Laval, Jorge A., 2020. "A continuum model for cities based on the macroscopic fundamental diagram: A semi-Lagrangian solution method," Transportation Research Part B: Methodological, Elsevier, vol. 132(C), pages 101-116.
    13. Laval, Jorge A., 2003. "Some Properties of a Multi-Lane Extension of the Kinematic Wave Model," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt6hg2g0nq, Institute of Transportation Studies, UC Berkeley.
    14. Horowitz, Roberto & May, Adolf & Skabardonis, Alex & Varaiya, Pravin & Zhang, Michael & Gomes, Gabriel & Munoz, Laura & Sun, Xiaotian & Sun, Dengfeng, 2005. "Design, Field Implementation and Evaluation of Adaptive Ramp Metering Algorithms," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt5p06q6k5, Institute of Transportation Studies, UC Berkeley.
    15. Muñoz, Juan Carlos & Daganzo, Carlos F., 2002. "The bottleneck mechanism of a freeway diverge," Transportation Research Part A: Policy and Practice, Elsevier, vol. 36(6), pages 483-505, July.
    16. Munoz, Juan Carlos & Daganzo, Carlos, 2000. "Experimental Characterization of Multi-Lane Freeway Traffic Upstream of an Off-Ramp Bottleneck," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt8635j1df, Institute of Transportation Studies, UC Berkeley.
    17. Juan Carlos Muñoz & Carlos F. Daganzo, 2003. "Structure of the Transition Zone Behind Freeway Queues," Transportation Science, INFORMS, vol. 37(3), pages 312-329, August.
    18. Daganzo, C. F. & Cassidy, M. J. & Bertini, R. L., 1999. "Possible explanations of phase transitions in highway traffic," Transportation Research Part A: Policy and Practice, Elsevier, vol. 33(5), pages 365-379, June.
    19. Daganzo, Carlos F., 2002. "A behavioral theory of multi-lane traffic flow. Part I: Long homogeneous freeway sections," Transportation Research Part B: Methodological, Elsevier, vol. 36(2), pages 131-158, February.
    20. Helbing, Dirk & Hennecke, Ansgar & Shvetsov, Vladimir & Treiber, Martin, 2001. "MASTER: macroscopic traffic simulation based on a gas-kinetic, non-local traffic model," Transportation Research Part B: Methodological, Elsevier, vol. 35(2), pages 183-211, February.
    21. Zhou, Hao & Toth, Christopher & Guensler, Randall & Laval, Jorge, 2022. "Hybrid modeling of lane changes near freeway diverges," Transportation Research Part B: Methodological, Elsevier, vol. 165(C), pages 1-14.

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