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Continuum signalized junction model for dynamic traffic networks: Offset, spillback, and multiple signal phases

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  • Han, Ke
  • Gayah, Vikash V.

Abstract

This paper extends the continuum signalized intersection model exhaustively studied in Han et al. (2014) to more accurately account for three realistic complications: signal offsets, queue spillbacks, and complex signal phasing schemes. The model extensions are derived theoretically based on signal cycle, green split, and offset, and are shown to approximate well traffic operations at signalized intersections treated using the traditional (and more realistic) on-and-off model. We propose a generalized continuum signal model, which explicitly handles complex vehicle spillback patterns on signalized networks with provable error estimates. Under mild conditions, the errors are small and bounded by fixed values that do not grow with time. Overall, this represents a significant improvement over the original continuum model, which had errors that grew quickly with time in the presence of any queue spillbacks and for which errors were not explicitly derived for different offset cases. Thus, the new model is able to more accurately approximate traffic dynamics in large networks with multiple signals under more realistic conditions. We also qualitatively describe how this new model can be applied to several realistic intersection configurations that might be encountered in typical urban networks. These include intersections with multiple entry and exit links, complex signal phasing, all-red times, and the presence of dedicated turning lanes. Numerical tests of the models show remarkable consistency with the on-and-off model, as expected from the theory, with the added benefit of significant computational savings and higher signal control resolution when using the continuum model.

Suggested Citation

  • Han, Ke & Gayah, Vikash V., 2015. "Continuum signalized junction model for dynamic traffic networks: Offset, spillback, and multiple signal phases," Transportation Research Part B: Methodological, Elsevier, vol. 77(C), pages 213-239.
  • Handle: RePEc:eee:transb:v:77:y:2015:i:c:p:213-239
    DOI: 10.1016/j.trb.2015.03.005
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    1. Han, Ke & Friesz, Terry L. & Yao, Tao, 2013. "A partial differential equation formulation of Vickrey’s bottleneck model, part I: Methodology and theoretical analysis," Transportation Research Part B: Methodological, Elsevier, vol. 49(C), pages 55-74.
    2. Cassidy, Michael J., 1998. "Bivariate relations in nearly stationary highway traffic," Transportation Research Part B: Methodological, Elsevier, vol. 32(1), pages 49-59, January.
    3. Friesz, Terry L. & Han, Ke & Neto, Pedro A. & Meimand, Amir & Yao, Tao, 2013. "Dynamic user equilibrium based on a hydrodynamic model," Transportation Research Part B: Methodological, Elsevier, vol. 47(C), pages 102-126.
    4. Han, Ke & Gayah, Vikash V. & Piccoli, Benedetto & Friesz, Terry L. & Yao, Tao, 2014. "On the continuum approximation of the on-and-off signal control on dynamic traffic networks," Transportation Research Part B: Methodological, Elsevier, vol. 61(C), pages 73-97.
    5. Newell, G. F., 1993. "A simplified theory of kinematic waves in highway traffic, part II: Queueing at freeway bottlenecks," Transportation Research Part B: Methodological, Elsevier, vol. 27(4), pages 289-303, August.
    6. 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.
    7. Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-260, May.
    8. Lo, Hong K., 1999. "A novel traffic signal control formulation," Transportation Research Part A: Policy and Practice, Elsevier, vol. 33(6), pages 433-448, August.
    9. Newell, G. F., 1993. "A simplified theory of kinematic waves in highway traffic, part I: General theory," Transportation Research Part B: Methodological, Elsevier, vol. 27(4), pages 281-287, August.
    10. Guler, S. Ilgin & Cassidy, Michael J., 2012. "Strategies for sharing bottleneck capacity among buses and cars," Transportation Research Part B: Methodological, Elsevier, vol. 46(10), pages 1334-1345.
    11. Ceylan, Halim & Bell, Michael G. H., 2004. "Traffic signal timing optimisation based on genetic algorithm approach, including drivers' routing," Transportation Research Part B: Methodological, Elsevier, vol. 38(4), pages 329-342, May.
    12. Terry L. Friesz & David Bernstein & Tony E. Smith & Roger L. Tobin & B. W. Wie, 1993. "A Variational Inequality Formulation of the Dynamic Network User Equilibrium Problem," Operations Research, INFORMS, vol. 41(1), pages 179-191, February.
    13. Han, Ke & Friesz, Terry L. & Yao, Tao, 2013. "A partial differential equation formulation of Vickrey’s bottleneck model, part II: Numerical analysis and computation," Transportation Research Part B: Methodological, Elsevier, vol. 49(C), pages 75-93.
    14. Gu, Weihua & Gayah, Vikash V. & Cassidy, Michael J. & Saade, Nathalie, 2014. "On the impacts of bus stops near signalized intersections: Models of car and bus delays," Transportation Research Part B: Methodological, Elsevier, vol. 68(C), pages 123-140.
    15. Newell, G. F., 1993. "A simplified theory of kinematic waves in highway traffic, part III: Multi-destination flows," Transportation Research Part B: Methodological, Elsevier, vol. 27(4), pages 305-313, August.
    16. Mike J. Smith, 2010. "Intelligent Network Control: Using an Assignment–Control Model to Design Fixed Time Signal Timings," Chapters, in: Chris M.J. Tampere & Francesco Viti & Lambertus H. (Ben) Immers (ed.), New Developments in Transport Planning, chapter 3, Edward Elgar Publishing.
    17. Improta, G. & Cantarella, G. E., 1984. "Control system design for an individual signalized junction," Transportation Research Part B: Methodological, Elsevier, vol. 18(2), pages 147-167, April.
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