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Continuum Approximation for Congestion Dynamics Along Freeway Corridors

Author

Listed:
  • Jorge A. Laval

    (School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332)

  • Ludovic Leclercq

    (Université de Lyon, ENTPE/INRETS, Laboratoire Ingénierie Circulation Transport, 69518 Lyon, France)

Abstract

In this paper, congestion dynamics along crowded freeway corridors are modeled as a conservation law with a source term that is continuous in space. The source term represents the net inflow from ramps, postulated here as a location-dependent function of the demand for entering and exiting the corridor. Demands are assumed to be time-independent, which is appropriate for understanding the onset of congestion. Numerical and analytical results reveal the existence of four well-defined regions in time-space, two of which are transient. The conditions for the existence of congestion both in the freeway and in the on-ramps are identified, as well as the set of on-ramps that are most likely to become active bottlenecks. The results in this paper help explain the stochastic nature of bottleneck activation, and can be applied to devise effective system-wide ramp metering strategies that would prevent excessively long on-ramp queues.

Suggested Citation

  • Jorge A. Laval & Ludovic Leclercq, 2010. "Continuum Approximation for Congestion Dynamics Along Freeway Corridors," Transportation Science, INFORMS, vol. 44(1), pages 87-97, February.
    • Handle: RePEc:inm:ortrsc:v:44:y:2010:i:1:p:87-97
    DOI: 10.1287/trsc.1090.0294
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    References listed on IDEAS

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    1. 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.
    2. Jin, W. L. & Zhang, H. M., 2003. "On the distribution schemes for determining flows through a merge," Transportation Research Part B: Methodological, Elsevier, vol. 37(6), pages 521-540, July.
    3. Paul I. Richards, 1956. "Shock Waves on the Highway," Operations Research, INFORMS, vol. 4(1), pages 42-51, February.
    4. M. Gugat & M. Herty & A. Klar & G. Leugering, 2005. "Optimal Control for Traffic Flow Networks," Journal of Optimization Theory and Applications, Springer, vol. 126(3), pages 589-616, September.
    5. Laval, Jorge A. & Leclercq, Ludovic, 2008. "Microscopic modeling of the relaxation phenomenon using a macroscopic lane-changing model," Transportation Research Part B: Methodological, Elsevier, vol. 42(6), pages 511-522, July.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Sun, Lu & Jafaripournimchahi, Ammar & Hu, Wusheng, 2020. "A forward-looking anticipative viscous high-order continuum model considering two leading vehicles for traffic flow through wireless V2X communication in autonomous and connected vehicle environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 556(C).
    2. Laval, Jorge A. & Costeseque, Guillaume & Chilukuri, Bargavarama, 2016. "The impact of source terms in the variational representation of traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 94(C), pages 204-216.
    3. Aliyu Nuhu Shuaibu, 2015. "Simulation of Crowd Movement in Spiral Pattern during Tawaf, in Makkah, Saudi Arabia," Modern Applied Science, Canadian Center of Science and Education, vol. 9(11), pages 192-192, October.
    4. Coifman, Benjamin & Kim, Seoungbum, 2011. "Extended bottlenecks, the fundamental relationship, and capacity drop on freeways," Transportation Research Part A: Policy and Practice, Elsevier, vol. 45(9), pages 980-991, November.
    5. Laval, Jorge A. & Chilukuri, Bhargava R., 2016. "Symmetries in the kinematic wave model and a parameter-free representation of traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 89(C), pages 168-177.

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