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On the fundamental diagram for freeway traffic: A novel calibration approach for single-regime models

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  • Qu, Xiaobo
  • Wang, Shuaian
  • Zhang, Jin

Abstract

The speed-density or flow-density relationship has been considered as the foundation of traffic flow theory. Existing single-regime models calibrated by the least square method (LSM) could not fit the empirical data consistently well both in light-traffic/free-flow conditions and congested/jam conditions. In this paper, first, we point out that the inaccuracy of single-regime models is not caused solely by their functional forms, but also by the sample selection bias. Second, we apply a weighted least square method (WLSM) that addresses the sample selection bias problem. The calibration results for six well-known single-regime models using the WLSM fit the empirical data reasonably well both in light-traffic/free-flow conditions and congested/jam conditions. Third, we conduct a theoretical investigation that reveals the deficiency associated with the LSM is because the expected value of speed (or a function of it) is nonlinear with regard to the density (or a function of it).

Suggested Citation

  • Qu, Xiaobo & Wang, Shuaian & Zhang, Jin, 2015. "On the fundamental diagram for freeway traffic: A novel calibration approach for single-regime models," Transportation Research Part B: Methodological, Elsevier, vol. 73(C), pages 91-102.
    • Handle: RePEc:eee:transb:v:73:y:2015:i:c:p:91-102
    DOI: 10.1016/j.trb.2015.01.001
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    1. Wu, Xinkai & Liu, Henry X. & Geroliminis, Nikolas, 2011. "An empirical analysis on the arterial fundamental diagram," Transportation Research Part B: Methodological, Elsevier, vol. 45(1), pages 255-266, January.
    2. Castillo, J. M. Del & Benítez, F. G., 1995. "On the functional form of the speed-density relationship--I: General theory," Transportation Research Part B: Methodological, Elsevier, vol. 29(5), pages 373-389, October.
    3. Zhang, Lele & Garoni, Timothy M & de Gier, Jan, 2013. "A comparative study of Macroscopic Fundamental Diagrams of arterial road networks governed by adaptive traffic signal systems," Transportation Research Part B: Methodological, Elsevier, vol. 49(C), pages 1-23.
    4. Geroliminis, Nikolas & Sun, Jie, 2011. "Properties of a well-defined macroscopic fundamental diagram for urban traffic," Transportation Research Part B: Methodological, Elsevier, vol. 45(3), pages 605-617, March.
    5. Harold Greenberg, 1959. "An Analysis of Traffic Flow," Operations Research, INFORMS, vol. 7(1), pages 79-85, February.
    6. Geroliminis, Nikolas & Daganzo, Carlos F., 2008. "Existence of urban-scale macroscopic fundamental diagrams: Some experimental findings," Transportation Research Part B: Methodological, Elsevier, vol. 42(9), pages 759-770, November.
    7. Wang, Haizhong & Li, Jia & Chen, Qian-Yong & Ni, Daiheng, 2011. "Logistic modeling of the equilibrium speed-density relationship," Transportation Research Part A: Policy and Practice, Elsevier, vol. 45(6), pages 554-566, July.
    8. Wang, Shuaian & Meng, Qiang, 2012. "Sailing speed optimization for container ships in a liner shipping network," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 48(3), pages 701-714.
    9. Wu, Xinkai & Liu, Henry X., 2011. "A shockwave profile model for traffic flow on congested urban arterials," Transportation Research Part B: Methodological, Elsevier, vol. 45(10), pages 1768-1786.
    10. Gayah, Vikash V. & Daganzo, Carlos F., 2011. "Clockwise hysteresis loops in the Macroscopic Fundamental Diagram: An effect of network instability," Transportation Research Part B: Methodological, Elsevier, vol. 45(4), pages 643-655, May.
    11. Daganzo, Carlos F., 2007. "Urban gridlock: Macroscopic modeling and mitigation approaches," Transportation Research Part B: Methodological, Elsevier, vol. 41(1), pages 49-62, January.
    12. G. F. Newell, 1961. "Nonlinear Effects in the Dynamics of Car Following," Operations Research, INFORMS, vol. 9(2), pages 209-229, April.
    13. Wu, Ning, 2002. "A new approach for modeling of Fundamental Diagrams," Transportation Research Part A: Policy and Practice, Elsevier, vol. 36(10), pages 867-884, December.
    14. 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.
    15. Castillo, J. M. Del & Benítez, F. G., 1995. "On the functional form of the speed-density relationship--II: Empirical investigation," Transportation Research Part B: Methodological, Elsevier, vol. 29(5), pages 391-406, October.
    16. Daganzo, Carlos F & Geroliminis, Nikolas, 2008. "An analytical approximation for the macropscopic fundamental diagram of urban traffic," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt4cb8h3jm, Institute of Transportation Studies, UC Berkeley.
    17. Geroliminis, Nikolas & Sun, Jie, 2011. "Hysteresis phenomena of a Macroscopic Fundamental Diagram in freeway networks," Transportation Research Part A: Policy and Practice, Elsevier, vol. 45(9), pages 966-979, November.
    18. Keyvan-Ekbatani, Mehdi & Kouvelas, Anastasios & Papamichail, Ioannis & Papageorgiou, Markos, 2012. "Exploiting the fundamental diagram of urban networks for feedback-based gating," Transportation Research Part B: Methodological, Elsevier, vol. 46(10), pages 1393-1403.
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