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On the Stability of Freeway Traffic

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  • Daganzo, Carlos F.

Abstract

Traffic flow theory is used to analyze the spatio-temporal distribution of flow and density on closed loop homogeneous freeways with many ramps, which produce inflows and allow outflows. It is shown that if the on-ramp demand is space-independent then this distribution tends toward uniformity in space if the freeway is either: (i) uncongested; or (ii) congested with queues on its on-ramps and enough inflow to cause the average freeway density to increase with time. In all other cases, including any recovery phase of a rush hour where the freeway's average density declines, the distribution of flow and density quickly becomes uneven. The flow-density deviations from the average are shown to grow exponentially in time and propagate backwards in space with a fixed wave speed. A consequence of this type of instability is that, during recovery, gaps of uncongested traffic will quickly appear in the unevenly congested stream, reducing average flow. This extends the duration of recovery and invariably creates clockwise hysteresis loops on scatter-plots of average system flow vs. density. All these effects are quantified with formulas and verified with simulations.

Suggested Citation

  • Daganzo, Carlos F., 2010. "On the Stability of Freeway Traffic," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt4vf597r5, Institute of Transportation Studies, UC Berkeley.
    • Handle: RePEc:cdl:itsrrp:qt4vf597r5
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    References listed on IDEAS

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    1. Daganzo, Carlos F. & Gayah, Vikash V. & Gonzales, Eric J., 2010. "Macroscopic Relations of Urban Traffic Variables: An Analysis of Instability," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt7qd590bv, Institute of Transportation Studies, UC Berkeley.
    2. Paul I. Richards, 1956. "Shock Waves on the Highway," Operations Research, INFORMS, vol. 4(1), pages 42-51, February.
    3. Geroliminis, Nikolas & Daganzo, Carlos F., 2008. "Existence of urban-scale macroscopic fundamental diagrams: Some experimental findings," Transportation Research Part B: Methodological, Elsevier, vol. 42(9), pages 759-770, November.
    4. Newell, G. F., 1993. "A simplified theory of kinematic waves in highway traffic, part II: Queueing at freeway bottlenecks," Transportation Research Part B: Methodological, Elsevier, vol. 27(4), pages 289-303, August.
    5. 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.
    6. Siamak Ardekani & Robert Herman, 1987. "Urban Network-Wide Traffic Variables and Their Relations," Transportation Science, INFORMS, vol. 21(1), pages 1-16, February.
    7. Newell, G. F., 1993. "A simplified theory of kinematic waves in highway traffic, part I: General theory," Transportation Research Part B: Methodological, Elsevier, vol. 27(4), pages 281-287, August.
    8. Robert Herman & Siamak Ardekani, 1984. "Characterizing Traffic Conditions in Urban Areas," Transportation Science, INFORMS, vol. 18(2), pages 101-140, May.
    9. Olszewski, Piotr & Fan, Henry S. L. & Tan, Yan-Weng, 1995. "Area-wide traffic speed-flow model for the Singapore CBD," Transportation Research Part A: Policy and Practice, Elsevier, vol. 29(4), pages 273-281, July.
    10. Daganzo, Carlos F., 2007. "Urban gridlock: Macroscopic modeling and mitigation approaches," Transportation Research Part B: Methodological, Elsevier, vol. 41(1), pages 49-62, January.
    11. Newell, G. F., 1993. "A simplified theory of kinematic waves in highway traffic, part III: Multi-destination flows," Transportation Research Part B: Methodological, Elsevier, vol. 27(4), pages 305-313, August.
    12. Gayah, Vikash V. & Daganzo, Carlos F., 2010. "Exploring the Effect of Turning Maneuvers and Route Choice ona Simple Network," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt6kg0d8ds, Institute of Transportation Studies, UC Berkeley.
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