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Oscillatory Traffic Flow Patterns Induced by Queue Spillback in a Simple Road Network

Author

Listed:
  • Yu (Marco) Nie

    (Department of Civil and Environmental Engineering, Northwestern University, Evanston, Illinois 60208)

  • H. Michael Zhang

    (Department of Civil and Environmental Engineering, University of California, Davis, Davis, California 95616)

Abstract

We study in this paper some consequences of queue spillback in a simple road network with a steady demand and provide exact formulas for traffic flow patterns. This one origin-destination pair, two-route network contains a diverge and a merge, and the interaction of queues formed at the merge produces several interesting traffic flow patterns, of which two types of oscillatory solutions are of particular interest. One of the oscillatory solutions is decaying, and the other is perfectly periodic. The latter resembles the stop-and-go pattern found in real-world traffic. Because a general road network usually contains many components like the simple network studied here, interaction of queues at junctions provides an alternative explanation to the formation of stop-and-go traffic.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ortrsc:v:42:y:2008:i:2:p:236-248
    DOI: 10.1287/trsc.1070.0229
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    References listed on IDEAS

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    1. Carlos F. Daganzo, 1998. "Queue Spillovers in Transportation Networks with a Route Choice," Transportation Science, INFORMS, vol. 32(1), pages 3-11, February.
    2. 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.
    3. Robert E. Chandler & Robert Herman & Elliott W. Montroll, 1958. "Traffic Dynamics: Studies in Car Following," Operations Research, INFORMS, vol. 6(2), pages 165-184, April.
    4. Daganzo, Carlos F., 2005. "A variational formulation of kinematic waves: basic theory and complex boundary conditions," Transportation Research Part B: Methodological, Elsevier, vol. 39(2), pages 187-196, February.
    5. Jin, W. L. & Zhang, H. M., 2003. "The formation and structure of vehicle clusters in the Payne-Whitham traffic flow model," Transportation Research Part B: Methodological, Elsevier, vol. 37(3), pages 207-223, March.
    6. 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.
    7. 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.
    8. Robert Herman & Elliott W. Montroll & Renfrey B. Potts & Richard W. Rothery, 1959. "Traffic Dynamics: Analysis of Stability in Car Following," Operations Research, INFORMS, vol. 7(1), pages 86-106, February.
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    Cited by:

    1. Nie, Yu (Marco), 2010. "Equilibrium analysis of macroscopic traffic oscillations," Transportation Research Part B: Methodological, Elsevier, vol. 44(1), pages 62-72, January.
    2. Bao, Yue & Verhoef, Erik T. & Koster, Paul, 2021. "Leaving the tub: The nature and dynamics of hypercongestion in a bathtub model with a restricted downstream exit," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 152(C).
    3. 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.
    4. Friesz, Terry L. & Kim, Taeil & Kwon, Changhyun & Rigdon, Matthew A., 2011. "Approximate network loading and dual-time-scale dynamic user equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 45(1), pages 176-207, January.
    5. 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.
    6. Jin, Wen-Long, 2010. "Continuous kinematic wave models of merging traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 44(8-9), pages 1084-1103, September.
    7. Jin, Wen-Long, 2009. "Asymptotic traffic dynamics arising in diverge-merge networks with two intermediate links," Transportation Research Part B: Methodological, Elsevier, vol. 43(5), pages 575-595, June.

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