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Propagation of On-Ramp Density Waves on Uniform Unidirectional Multilane Freeways

Author

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  • P. K. Munjal

    (System Development Corporation, Santa Monica, California)

  • L. A. Pipes

    (System Development Corporation, Santa Monica, California)

Abstract

This paper presents a generalized analysis of the effects of on-ramp time varying flow on unidirectional n-lane freeways. The analysis incorporates the speed-density relations for every lane, which are then used to set up separate continuity equations for every lane and are coupled by some reasonable lane-changing hypotheses. The paper assumes the same wave velocities (uniform freeway) for the perturbed flow in each lane of a freeway. Using the generalized n-lane analysis, the paper then predicts the relative propagation of density perturbations in time and space in different lanes of a two-lane, three-lane, and four-lane freeway. The corresponding relaxation distances from the on-ramp, where the initial perturbation had started, have been defined and compared for the two-lane, three-lane, and four-lane freeway. The above studies have then incorporated the effects of controlled ramp flow by suitable mathematical expressions that simulate controlled ramp flow.

Suggested Citation

  • P. K. Munjal & L. A. Pipes, 1971. "Propagation of On-Ramp Density Waves on Uniform Unidirectional Multilane Freeways," Transportation Science, INFORMS, vol. 5(4), pages 390-402, November.
    • Handle: RePEc:inm:ortrsc:v:5:y:1971:i:4:p:390-402
    DOI: 10.1287/trsc.5.4.390
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    Citations

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    Cited by:

    1. Helbing, Dirk, 1995. "Theoretical foundation of macroscopic traffic models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 219(3), pages 375-390.
    2. Nie, Yu (Marco), 2010. "Equilibrium analysis of macroscopic traffic oscillations," Transportation Research Part B: Methodological, Elsevier, vol. 44(1), pages 62-72, January.
    3. Wagner, C., 1997. "A Navier-Stokes-like traffic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 245(1), pages 124-138.
    4. Rickert, M. & Nagel, K. & Schreckenberg, M. & Latour, A., 1996. "Two lane traffic simulations using cellular automata," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 231(4), pages 534-550.
    5. Holland, Edward N. & Woods, Andrew W., 1997. "A continuum model for the dispersion of traffic on two-lane roads," Transportation Research Part B: Methodological, Elsevier, vol. 31(6), pages 473-485, November.
    6. Yu (Marco) Nie & H. Michael Zhang, 2008. "Oscillatory Traffic Flow Patterns Induced by Queue Spillback in a Simple Road Network," Transportation Science, INFORMS, vol. 42(2), pages 236-248, May.
    7. Helbing, Dirk, 1997. "Modeling multi-lane traffic flow with queuing effects," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 242(1), pages 175-194.
    8. Yanhong Wang & Rui Jiang & Yu (Marco) Nie & Ziyou Gao, 2021. "Impact of Information on Topology-Induced Traffic Oscillations," Transportation Science, INFORMS, vol. 55(2), pages 475-490, March.
    9. 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.
    10. Zhao, Tingting & Nie, Yu (Marco) & Zhang, Yi, 2014. "Extended spectral envelope method for detecting and analyzing traffic oscillations," Transportation Research Part B: Methodological, Elsevier, vol. 61(C), pages 1-16.

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