This study proposes a real-time monitoring method for two-dimensional (2D) networks via the fusion of probe data and a traffic flow model. In the Great East Japan Earthquake occurring on March 11, 2011, there was major traffic congestion as evacuees concentrated in cities on the Sanriku Coast. A tragedy occurred when a tsunami overtook the stuck vehicles. To evacuate safely and efficiently, the state of traffic must be monitored in real time on a 2D network, where all networks are linked. Generally, the traffic state is monitored only at observation points. However, observation data presents the risk of errors. Additionally, in the estimated traffic state of the 2D network, unlike non-intersecting road sections (i.e., one-dimensional), it is necessary to model user route choice behavior and origin/destination (OD) demand to input in the model. Therefore, in this study, we develop a state-space model that assimilates vehicle density and divergence ratio data obtained from probe vehicles in a traffic flow model that considers route choice. Our state-space model considers observational errors in the probe data and can simultaneously estimate traffic state and destination component ratio of OD demand. The result of simulated traffic model verification shows that the proposed model has good congestion estimation precision in a small-scale test network.

1. [1] Y. Hara and M. Kuwahara, “Traffic Monitoring immediately after a major natural disaster as revealed by probe data – A case in Ishinomaki after the Great East Japan Earthquake,” Transportation Research Part A: Policy and Practice, Vol.75, pp. 1-15, 2015.
2. [2] T. Higuch, G. Ueno, S. Nakano, K. Nakamura, and R. Yoshida, “Introduction to Data Assimilation – Next Generation Simulation Technology –,” Asakura book,2011.
3. [3] Y. Kawasaki, Y. Hara, and M. Kuwahara, “Construction of Traffic State Estimation Method of the Two-Dimensional Network by State-Space Model Considering Route Choice,” Journal of JSCE (D3), Vol.73, No.5, 2017 (in Japanese).
4. [4] C. F. Daganzo, “The cell transmission model, part II: network traffic,” Transportation Research Part B : Methodological, Vol.29, No.2, pp. 79-93, 1995.
5. [5] L. Bengtsson, X. Lu, A. Thorson, R. Garfield, and J. von Schreeb, “Improved response to disasters and outbreaks by tracking population movements with mobile phone network data: a post-earthquake geospatial study in Haiti,” PLoS Med., Vol.8, No.8, pp. e1001083, 2011.
6. [6] X. Lu, L. Bengtsson, and P. Holme, “Predictability of population displacement after the 2010 Haiti earthquake,” Proc. Natl. Acad. Sci. USA, Vol.109, No.29, pp. 11576-11581, 2012.
7. [7] Y. Kawasaki, M. Kuwahara, Y. Hara, T. Mitani, A. Takenouchi, T. Iryo, and J. Urata, “Investigation of Traffic and Evacuation Aspects at Kumamoto Earthquake and the Future Issues,” Journal of Disaster Research, Vol.12, No.2, 2017.
8. [8] C. G. Claudel and A. M. Bayen, “Convex Formulations of Data Assimilation Problems for a Class of Hamilton-Jacobi Equations,” SIAM Journal on Control and Optimization, Vol.49, No.2, pp. 383-402, 2011.
9. [9] W. Deng, H. Lei, and X. Zhou, “Traffic state estimation and uncertainty quantification based on heterogeneous data sources: A three detector approach,” Transportation Research Part B: Methodological, Vol.57, pp. 132-157, 2013.
10. [10] D. Work, S. Blandin, O. P. Tossavainen, B. Piccoli, and A. Bayen, “A traffic model for velocity data assimilation,” Appl. Math. Res. Exp., Vol.2010, No.1, pp. 1-35, 2010.
11. [11] N. Nartuoka, T. Seo, T. Kusakabe, and Y. Asakura, “Simultaneous estimation of traffic flow conditions and model parameters based on speed data,” Journal of JSCE, Vol.51, 2015 (in Japanese).
12. [12] T. Seo, T. Kusakabe, and Y. Asakura, “Traffic state estimation with the advanced probe vehicles using data assimilation,” IEEE 18^th Int. Conf. on Intelligent Transportation Systems, pp. 824-830, 2015.
13. [13] M. Takashima and Y. Shiomi, “Monitoring Traffic Flow Dynamics at Sags: Data Assimilation Approach,” Journal of JSCE (D3), Vol.73, No.5. 2017 (in Japanese).
14. [14] T. Seo, T. Tchrakian, S. Zhuk, and A. Bayen, “Filter comparison for estimation on discretized PDEs modeling traffic: Ensemble Kalman filter and Minimax filter,” 2016 IEEE 55^th Conf. on Decision and Control (CDC), pp. 3979-3984, 2016.
15. [15] A. Nantes, D. Ngoduy, A. Bhaskar, M. Miska, and E. Chung, “Real-time traffic state estimation in urban corridors from heterogeneous data,” Transportation Research Part C: Emerging Technologies, 2015.
16. [16] A. Takenouchi and M. Kuwahara, “Study on traffic state estimation method using only mobile data,” Journal of JSCE, Vol.53, 2016 (in Japanese).
17. [17] Y. Kawasaki, Y. Hara, T. Mitani, and M. Kuwahara, “Real-time Simulation of Dynamic Traffic Flow with Traffic Data Assimilation Approach,” Journal of Disaster Research, Vol.11, No.2, 2016.
18. [18] R. P. Otsuka, D. B. Work, and J. Song, “Estimating post disaster traffic conditions using real-time data streams,” Structure and Infrastructure Engineering, Vol.12, 2016.
19. [19] Civil Engineering Studies Committee, “Equilibrium analysis of traffic network – latest theory and solution,” Maruzen, 1998 (in Japanese).
20. [20] T. Awaji, M. Kabachi, M. Ikeda, and Y. Ishikawa, “Data assimilation Observation - Innovation combining experiment with model,” Kyoto University, 2009 (in Japanese).
21. [21] G. Kitagawa, “Monte Carlo Filter and Smoother for Non-Gaussian Nonlinear State Space Models,” Journal of Computational and Graphical Statistics, Vol.5, No.1, pp. 1-25, 1996.