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Density Oscillations Between Lanes of a Multilane Highway

Author

Listed:
  • Denos C. Gazis

    (IBM Research Center, Yorktown Heights, New York)

  • Robert Herman

    (General Motors Research Laboratories, Warren, Michigan)

  • George H. Weiss

    (Institute for Fluid Dynamics and Applied Mathematics, University of Maryland)

Abstract

The interchange of traffic density between lanes moving in the same direction is investigated on the basis of a simple mathematical model. Emphasis is placed on the question of stability, i.e., attenuation of disturbances from an “equilibrium density distribution.” A solution is obtained for a system of differential difference equations with a time lag corresponding to the interaction of two lanes. This solution is directly applicable to other problems described by similar equations, such as the follow-the-leader problem. The solution is generalized to n lanes, and it is found that the inherent instability is twice as great for n approaching infinity as it is for two lanes.

Suggested Citation

  • Denos C. Gazis & Robert Herman & George H. Weiss, 1962. "Density Oscillations Between Lanes of a Multilane Highway," Operations Research, INFORMS, vol. 10(5), pages 658-667, October.
    • Handle: RePEc:inm:oropre:v:10:y:1962:i:5:p:658-667
    DOI: 10.1287/opre.10.5.658
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. Coifman, Benjamin, 2006. "Extracting More Information from the Existing Freeway Traffic Monitoring Infrastructure," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt34n479gz, Institute of Transportation Studies, UC Berkeley.
    4. Gomes, Gabriel C., 2004. "Optimization and Microsimulation of On-ramp Metering for Congested Freeways," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt95k1q411, Institute of Transportation Studies, UC Berkeley.
    5. 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.
    6. 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.
    7. Nie, Yu (Marco), 2010. "Equilibrium analysis of macroscopic traffic oscillations," Transportation Research Part B: Methodological, Elsevier, vol. 44(1), pages 62-72, January.
    8. Malachy Carey & Chandra Balijepalli & David Watling, 2015. "Extending the Cell Transmission Model to Multiple Lanes and Lane-Changing," Networks and Spatial Economics, Springer, vol. 15(3), pages 507-535, September.
    9. Ponnu, Balaji & Coifman, Benjamin, 2017. "When adjacent lane dependencies dominate the uncongested regime of the fundamental relationship," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 602-615.
    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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