智能交通系統(Intelligent Transportation Systems, ITS)使用即時交通資訊監視交通狀況，以提升交通運輸系統的效能。取得即時交通資訊方法有二：在道路設置車輛偵測器(Vehicle detector, VD)或收集探測車(Probe vehicle, PV)的行車軌跡。PV的成本較低且能達到更高的覆蓋率，但其無法如VD一樣能直接量測交通流量，故許多研究方法使用探測車軌跡中的速度資訊以基本圖(Fundamental diagram, FD)探討速度、密度和流量之間的關係，再加上更多的道路特徵來改進FD於城市道路流量的估算，然而他們並沒有考慮到紅綠燈對於行車行為及城市交通的影響。因為行車速度為會隨著燈號的轉換而改變，在這種情況下僅以速度推測密度會產生蠻大的變化及誤差，故本論文提出一稱之為Flow Estimation with Traffic Signal (FETS)的方法，以PV軌跡並考慮紅綠燈燈號來估測城市道路的流量。其將在綠燈的燈號下測量速度，並於PV在紅燈時的停車位置推測排隊長度進而取得密度，分別於不同的燈號狀態下估量速度與密度以減少誤差。由實驗可得知FETS的速度與流量分布關係合乎城市道路的實際情況。在流量估計方面，FETS在模擬器中的估計結果其平均相關誤差優於最佳的FD模型15.9%，而在現實資料中則優於86.3%。此結果顯示FETS的準確度明顯優於FD模型，證明FETS更符合城市道路的車流模式。

Intelligent Transportation Systems (ITS) can monitor the traffic condition and improve the transport efficiency by the real-time traffic information. For collecting traffic information, there are two general ways: installing the fixed-point vehicle detectors (VDs) by the roadside or collecting the trajectories reported from the probe vehicles (PVs). In general, using PVs has a lower cost and a larger coverage but cannot get the traffic flow directly like VDs. Some studies used the speed information in PVs trajectories to discuss the relationship between speed, density, and flow by the Fundamental diagram (FD) to estimate the traffic flow in the urban roads and further improved the result via considering more traffic features. However, they didn't concern about the impact of the traffic signal on the driving behavior and the urban traffic. Since the vehicle speed varies with the states of the traffic signal, the density only derived from the speed will cause significant deviations and errors. Accordingly, we propose an approach, Flow Estimation with Traffic Signal (FETS), to estimate the traffic flow in urban roads, by the trajectories of PVs. FETS considers the traffic signal to get the speed and density, i.e., the speed is measured at the green light state and the density is calibrated by the queue length that is obtained at red light state. The experiment results show that the mean relative error of FETS is better than the best one of the FD models 15.9% in the simulator and 86.3% in real-world. These results indicate the accuracy of FETS is better than FD models and prove that FETS is more suitable to estimate traffic flows in urban roads.

[1] 　B. Greenshields, W. Channing, and H. Miller, “A study of traffic capacity,” in Highway research board proceedings, 1935, vol. 1935.
[2] 　M. Van Aerde, “Single regime speed-flow-density relationship for congested and uncongested highways,” in Annual Conference on Transportation Research Board, 1995.
[3] 　M. Van Aerde and H. Rakha, “Multivariate calibration of single regime speed-flow-density relationships,” in IEEE 6th International Conference on Vehicle Navigation and Information Systems, 1995, pp. 334-341.
[4] 　K. Anuar, F. Habtemichael, and M. Cetin, “Estimating Traffic Flow Rate on Freeways from Probe Vehicle Data and Fundamental Diagram,” in IEEE 18th International Conference on Intelligent Transportation Systems (ITSC), 2015, pp. 2921-2926.
[5] 　H. Rakha and B. Crowther,” Comparison of Greenshields, Pipes, and Van Aerde car-following and traffic stream models,” Transportation Research Record: Journal of the Transportation Research Board, 2002, pp. 248-262.
[6] 　R. Zhang, Y. Shu, Z. Yang, P. Cheng, and J. Chen, “Hybrid traffic speed modeling and prediction using real-world data,” IEEE International Congress on Big Data (BigData Congress), 2015, pp. 230-237.
[7] 　X. Zhan, Y. Zheng, X. Yi, and S. V. Ukkusuri, "Citywide Traffic Volume Estimation Using Trajectory Data," IEEE Transactions on Knowledge and Data Engineering, 2017, vol. 29, no. 2, pp. 272-285.
[8] 　T. Neumann, P. L. Bohnke, and L. C. T. Tcheumadjeu, "Dynamic representation of the fundamental diagram via Bayesian networks for estimating traffic flows from probe vehicle data," in IEEE 16th International Conference on Intelligent Transportation Systems-(ITSC), 2013, pp. 1870-1875.
[9]　 B. Donovan and D. B. Work, "Using coarse GPS data to quantify city-scale transportation system resilience to extreme events," in Annual Conference on Transportation Research Board, 2015, pp. 15-5465.
[10]　X. Xu, X. Gao, X. Zhao, Z. Xu, and H. Chang, "A novel algorithm for urban traffic congestion detection based on GPS data compression," in IEEE International Conference on Service Operations and Logistics, and Informatics (SOLI), 2016, pp. 107-112.
[11]　J. García-Nieto, E. Alba, and A. C. Olivera, "Swarm intelligence for traffic light scheduling: Application to real urban areas," Engineering Applications of Artificial Intelligence, 2012, vol. 25, no. 2, pp. 274-283.
[12]　Rong Du, Cailian Chen, Bo Yang, Xinping Guan, “VANET Based Traffic Estimation: A Matrix Completion Approach,” in IEEE 32th International Conference on Global Communications (GLOBECOM), December 2013.
[13]　T. Seo, T. Kusakabe, and Y. Asakura, "Estimation of flow and density using probe vehicles with spacing measurement equipment," Transportation Research Part C: Emerging Technologies, 2015, vol. 53, pp. 134-150.
[14]　T. Seo, T. Kusakabe, and Y. Asakura, "Traffic state estimation with the advanced probe vehicles using data assimilation," in IEEE 18th International Conference on Intelligent Transportation Systems (ITSC), 2015, pp. 824-830.
[15]　Y. Jagadeesh, G. M. Suba, S. Karthik, and K. Yokesh, "Smart autonomous traffic light switching by traffic density measurement through sensors," in International Conference on Computers, Communications, and Systems (ICCCS), 2015, pp. 123-126.
[16]　S. A. Fayazi, A. Vahidi, G. Mahler, and A. Winckler, "Traffic signal phase and timing estimation from low-frequency transit bus data," IEEE Transactions on Intelligent Transportation Systems, 2015, vol. 16, no. 1, pp. 19-28.
[17]　Z. He, D. Zhang, J. Cao, X. Liu, X. Fan, and C. Xu, "Exploiting Real-time Traffic Light Scheduling with Taxi Traces," in 45th International Conference on Parallel Processing (ICPP), 2016, pp. 314-323.
[18]　N. Srisakda, A. Fukuda, and T. Ishizaka, "Queue Length Estimation for Adaptive Traffic Signal Control Based on Traffic Information Collected from GPS Probe Data ", http://www.atransociety.com/2017/pdf/8thSymposiumDownloadable/8thSymposium/Session2C/AYRF15-056.pdf.
[19]　T. Tange, A. Hiromori, H. Yamaguchi, T. Higashino, and T. Umedu, "An analysis model of queue length fluctuation at signals using vehicle trajectories," in International Conference on Connected Vehicles and Expo (ICCVE), 2014, pp. 577-583.
[20]　"OpenStreetMap," https://www.openstreetmap.org.
[21]　"Open data of Taipei city government", http://data.taipei/.