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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. Paul I. Richards, 1956. "Shock Waves on the Highway," Operations Research, INFORMS, vol. 4(1), pages 42-51, February.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    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. 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.
    3. 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.
    4. 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.
    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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