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Macroscopic Fundamental Diagram Estimation Considering Traffic Flow Condition of Road Network
Xiaoli Deng, Yao Hu


A macroscopic fundamental diagram (MFD) is an important basis for road network research. It describes the functional relationship between the average flow and average density of the road network. We proposed an MFD estimation method based on the traffic flow condition. Firstly, according to statistical theories, the road network data are divided into three traffic flow conditions (free flow, chaotic and congested) bounded by a 95% confidence interval of the maximum traffic capacity of each intersection in the road network. Then, in each condition, we combined principal component analysis and the Jolliffe B4 method to reduce dimension for extracting critical intersections. Finally, the full-scale dataset of the road network was reconstructed to estimate the road network MFD. Through numerical simulation and empirical research, it is found that the root mean square error and absolute percentage error between estimated MFD and true MFD considering the traffic flow condition are smaller than those without considering the traffic flow condition. The MFD estimation and the division of the traffic states of the road network were completed at the same time. The proposed method effectively saves the time cost of road network research and is highly accurate.


[1] Seo T, Kusakabe T, Asakura Y. Traffic flow condition estimation with the advanced probe vehicles using data assimilation. 2015 IEEE 18th International Conference on Intelligent Transportation Systems. IEEE; 2015. p. 824-830. DOI: 10.1109/ITSC.2015.13. [2] Seo T, Kusakabe T. Traffic flow condition estimation using satellite remote sensing and probe vehicles. JSTE Journal of Traffic Engineering. 2019;5(2):1-10. [3] Seo T, Kawasaki Y, Kusakabe T, Asakura Y. Fundamental diagram estimation by using trajectories of probe vehicles. Transportation Research Part B: Methodological. 2019;122:40-56. DOI: 10.1016/j.trb.2019.02.005. [4] Godfrey JW. The mechanism of a road network. Traffic Engineering and Control. 1969;11(7):323-327. [5] Ardekani S, Herman R. Urban network-wide traffic variables and their relations. Transportation Science. 1987;21(1):1-16. DOI: 10.1287/trsc.21.1.1. [6] Mahmassani HS, Williams JC, Herman R. Investigation of network-level traffic flow relationships: Some simulation results. Transportation Research Record. 1984;971:121-130. [7] Geroliminis N, Daganzo CF. Existence of urban-scale macroscopic fundamental diagrams: Some experimental findings. Transportation Research Part B: Methodological. 2008;42(9):759-770. DOI: 10.1016/j.trb.2008.02.002. [8] Courbon T, Leclercq L. Cross-comparison of macroscopic fundamental diagram estimation methods. Procedia - Social and Behavioral Sciences. 2011;20(6):417-426. DOI: 10.1016/j.sbspro.2011.08.048. [9] Saberi M, Mahmassani HS. Hysteresis and capacity drop phenomena in freeway networks: Empirical characterization and interpretation. Transportation Research Record. 2013;2391(1):44-55. DOI: 10.3141/2391-05. [10] Tilg G, Amini S, Busch F. Evaluation of analytical approximation methods for the macroscopic fundamental diagram. Transportation Research Part C: Emerging Technologies. 2020;114:1-19. DOI: 10.1016/j.trc.2020.02.003. [11] Andrew S, Nagle Vikash, V Gayah. Accuracy of networkwide traffic flow conditions estimated from mobile probe data. Transportation Research Record. 2018;2421(1):1-11. [12] Knoop VL, van Erp PB, Leclercq L, Hoogendoorn SP. Empirical MFDs using google traffic data. 2018 21st International Conference on Intelligent Transportation Systems (ITSC). IEEE; 2018. p. 3832-3839. DOI: 10.1109/I TSC.2018.8570005. [13] Lin X, Xu J, Cao C. Simulation and comparison of two fusion methods for macroscopic fundamental diagram estimation. Archives of Transport. 2019;51:35-48. [14] Paipuri M, Xu Y, Gonzalez MC, Leclercq L. Estimating MFDs, trip lengths and path flow distributions in a multi-region setting using mobile phone data. Transportation Research Part C: Emerging Technologies. 2020;118:102709. DOI: 10.1016/j.trc.2020.102709. [15] Saffari E, Yildirimoglu M, Hickman M. A methodology for identifying critical links and estimating macroscopic fundamental diagram in large-scale urban networks. Transportation Research Part C: Emerging Technologies. 2020;119:102743. DOI: 10.1016/j.trc.2020.102743. [16] Kerner BS, Klenov SL, Wolf DE. Cellular automata approach to three-phase traffic theory. 2002. p. 35. DOI: 10.1088/0305-4470/35/47/303. [17] Kerner BS. Three-phase traffic theory and highway capacity. Physica A: Statistical Mechanics and its Applications. 2004;333(1):379-440. DOI: 10.1016/j.phy sa.2003.10.017. [18] Xu F et al. Traffic flow condition evaluation based on macroscopic fundamental diagram of urban road network. Procedia - Social and Behavioral Sciences. 2013;96:480-489. DOI: 10.1016/j.sbspro.2013.08.056. [19] Liu S, Xu J. Urban traffic flow condition analysis based on the macroscopic fundamental diagrams of the variability of vehicle densities. 2016 12th World Congress on Intelligent Control and Automation (WCICA). IEEE; 2016. p. 1010-1015. DOI:10.1109/WCICA.2016.7578243. [20] Lin X. A road network traffic flow condition identification method based on macroscopic fundamental diagram and spectral clustering and support vector machine. Mathematical Problems in Engineering. 2019. DOI: 10.1155/2019/6571237. [21] Jolliffe IT. Discarding variables in a principal component analysis. Journal of the Royal Statistical Society: Series C (Applied Statistics). 1972;21(2):160-173. DOI: 10.2307/2348864. [22] Deng X, Hu Y, Hu Q. Fundamental Diagram Estimation Based on Random Probe Pairs on Sub-Segments. Promet – Traffic&Transportation. 2021;33(5):717-730. DOI: 10.7307/ptt.v33i5.3741. [23] Pearson K. LIII. On lines and planes of closest fit to systems of points in space. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. 1901;2(11):559-572. DOI: 10.1080/14786440109462720. [24] Hotelling H. Analysis of a complex of statistical variables into principal components. Journal of Educational Psychology. 1933;24(6):417. DOI: 10.1037/h00 71325. [25] Greenshields BD, Bibbins JR, Channing WS, Miller HH. A study of traffic capacity. Highway Research Board Proceedings. National Research Council (USA): Highway Research Board; 1935. [26] Greenberg H. An analysis of traffic flow. Operations Research. 1959;7(1):79-85. [27] Van Aerde M, Rakha H. Multivariate calibration of single regime speed-flowdensity relationships [road traffic management]. Pacific Rim TransTech Conference. 1995 Vehicle Navigation and Information Systems Conference Proceedings. 6th International VNIS. A Ride into the Future. IEEE; 1995. p. 334-341. DOI: 10.1109/VNIS.1995.518858.
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