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Traffic flow on signalized streets

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  • Daganzo, Carlos F.
  • Lehe, Lewis J.

Abstract

This paper considers a signalized street of uniform width and blocks of various lengths. Its signals are pretimed in an arbitrary pattern, and traffic on it behaves as per the kinematic-wave/variational theory with a triangular fundamental diagram. It is shown that the long run average flow on the street when the number of cars on the street (i.e. the street’s density) is held constant is given by the solution of a linear program (LP) with a finite number of variables and constraints. This defines a point on the street’s macroscopic fundamental diagram. For the homogeneous special case where the block lengths and signal timings are identical, all the LP constraints but one are redundant and the result has a closed form. In this case, the LP recipe matches and simplifies the so-called “method of cuts”. This establishes that the method of cuts is exact for homogeneous problems. However, in the more realistic inhomogeneous case the difference between the two methods can be arbitrarily large.

Suggested Citation

  • Daganzo, Carlos F. & Lehe, Lewis J., 2016. "Traffic flow on signalized streets," Transportation Research Part B: Methodological, Elsevier, vol. 90(C), pages 56-69.
    • Handle: RePEc:eee:transb:v:90:y:2016:i:c:p:56-69
    DOI: 10.1016/j.trb.2016.03.010
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    References listed on IDEAS

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    1. Laval, Jorge A. & Castrillón, Felipe, 2015. "Stochastic approximations for the macroscopic fundamental diagram of urban networks," Transportation Research Part B: Methodological, Elsevier, vol. 81(P3), pages 904-916.
    2. 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.
    3. repec:cdl:itsrrp:qt61v1r1qq is not listed on IDEAS
    4. Daganzo, Carlos F., 2005. "A variational formulation of kinematic waves: Solution methods," Transportation Research Part B: Methodological, Elsevier, vol. 39(10), pages 934-950, December.
    5. Daganzo, Carlos F. & Knoop, Victor L., 2016. "Traffic flow on pedestrianized streets," Transportation Research Part B: Methodological, Elsevier, vol. 86(C), pages 211-222.
    6. Daganzo, Carlos F. & Geroliminis, Nikolas, 2008. "An analytical approximation for the macroscopic fundamental diagram of urban traffic," Transportation Research Part B: Methodological, Elsevier, vol. 42(9), pages 771-781, November.
    7. Leclercq, Ludovic & Geroliminis, Nikolas, 2013. "Estimating MFDs in simple networks with route choice," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 468-484.
    8. Newell, G. F., 2002. "A simplified car-following theory: a lower order model," Transportation Research Part B: Methodological, Elsevier, vol. 36(3), pages 195-205, March.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

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    2. Sadek, Bassel & Doig Godier, Jean & Cassidy, Michael J & Daganzo, Carlos F, 2022. "Traffic signal plans to decongest street grids," Transportation Research Part B: Methodological, Elsevier, vol. 162(C), pages 195-208.
    3. Biyao Wang & Yi Han & Siyu Wang & Di Tian & Mengjiao Cai & Ming Liu & Lujia Wang, 2022. "A Review of Intelligent Connected Vehicle Cooperative Driving Development," Mathematics, MDPI, vol. 10(19), pages 1-31, October.
    4. Wada, Kentaro & Usui, Kento & Takigawa, Tsubasa & Kuwahara, Masao, 2018. "An optimization modeling of coordinated traffic signal control based on the variational theory and its stochastic extension," Transportation Research Part B: Methodological, Elsevier, vol. 117(PB), pages 907-925.
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    6. Pandey, Ayush & Lehe, Lewis J. & Gayah, Vikash V., 2024. "Local stability of traffic equilibria in an isotropic network," Transportation Research Part B: Methodological, Elsevier, vol. 179(C).
    7. Lehe, Lewis J., 2017. "Downtown tolls and the distribution of trip lengths," Economics of Transportation, Elsevier, vol. 11, pages 23-32.
    8. Zhang, Lele & Finn, Caley & Garoni, Timothy M. & de Gier, Jan, 2018. "Behaviour of traffic on a link with traffic light boundaries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 116-138.
    9. Lehe, Lewis J. & Pandey, Ayush, 2024. "A bathtub model of transit congestion," Transportation Research Part B: Methodological, Elsevier, vol. 181(C).
    10. Tilg, Gabriel & Ambühl, Lukas & Batista, Sergio & Menendez, Monica & Busch, Fritz, 2021. "On the application of variational theory to urban networks," Transportation Research Part B: Methodological, Elsevier, vol. 150(C), pages 435-456.
    11. Xue, Jiawei & Ka, Eunhan & Feng, Yiheng & Ukkusuri, Satish V., 2024. "Network macroscopic fundamental diagram-informed graph learning for traffic state imputation," Transportation Research Part B: Methodological, Elsevier, vol. 189(C).
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    13. Alonso, Borja & Ibeas, Ángel & Musolino, Giuseppe & Rindone, Corrado & Vitetta, Antonino, 2019. "Effects of traffic control regulation on Network Macroscopic Fundamental Diagram: A statistical analysis of real data," Transportation Research Part A: Policy and Practice, Elsevier, vol. 126(C), pages 136-151.
    14. Daganzo, Carlos F. & Lehe, Lewis J. & Argote-Cabanero, Juan, 2018. "Adaptive offsets for signalized streets," Transportation Research Part B: Methodological, Elsevier, vol. 117(PB), pages 926-934.
    15. Bronicki, Nadav & Doig Godier, Jean & Cassidy, Michael J., 2025. "Deploying bus bypasses in dense, congested cities: Practical findings from simulations and abstractions," Transportation Research Part A: Policy and Practice, Elsevier, vol. 196(C).

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