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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. Daganzo, Carlos F. & Knoop, Victor L., 2016. "Traffic flow on pedestrianized streets," Transportation Research Part B: Methodological, Elsevier, vol. 86(C), pages 211-222.
    2. 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.
    3. 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.
    4. 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.
    5. Daganzo, Carlos F., 2006. "On the Variational Theory of Traffic Flow: Well-Posedness, Duality and Applications," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt61v1r1qq, Institute of Transportation Studies, UC Berkeley.
    6. 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.
    7. 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.
    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.
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    Cited by:

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    3. Lehe, Lewis J., 2017. "Downtown tolls and the distribution of trip lengths," Economics of Transportation, Elsevier, vol. 11, pages 23-32.
    4. 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.
    5. Xu, Guanhao & Gayah, Vikash V., 2023. "Non-unimodal and non-concave relationships in the network Macroscopic Fundamental Diagram caused by hierarchical streets," Transportation Research Part B: Methodological, Elsevier, vol. 173(C), pages 203-227.
    6. 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.
    7. 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.
    8. 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).
    9. 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.
    10. 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.
    11. Lehe, Lewis J. & Pandey, Ayush, 2024. "A bathtub model of transit congestion," Transportation Research Part B: Methodological, Elsevier, vol. 181(C).
    12. 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.
    13. Varga, Balázs & Tettamanti, Tamás & Kulcsár, Balázs & Qu, Xiaobo, 2020. "Public transport trajectory planning with probabilistic guarantees," Transportation Research Part B: Methodological, Elsevier, vol. 139(C), pages 81-101.
    14. 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).
    15. Lapardhaja, Servet & Doig Godier, Jean & Cassidy, Michael J & Kan, Xingan David, 2024. "ACC, queue storage, and worrisome news for cities," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt5w46m77f, Institute of Transportation Studies, UC Berkeley.

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