應用格位傳送模式建構高速公路動態起迄矩陣推估演算法

Abstract

正確的動態起迄資訊需要有即時的交通控制調查結果，如即時路徑導引以及號誌控制。過去許多文獻企圖藉由所獲得的主線與匝道流量，來發展動態OD矩陣推估演算法，然而，此課題中都存在著相同的問題，即為推估參數的數量仍遠多於所獲得的可用資訊，導致動態OD矩陣推估為一相當大的挑戰。因此，必須增加額外的假設或是外生的資訊，如路徑選擇行為、歷史OD矩陣，或是已知的依時性交通流量資料等。 其中，在動態OD矩陣推估的課題中，最具挑戰性的問題為依時OD矩陣中旅行時間變異之影響，相關的研究皆假設於某時間點進入高速公路路段中車輛的到達型態，均會分佈在固定的小範圍內或是服從某種分配，然而，當某OD pair之運行係經過距離較長的路廊或是壅塞路段時，旅行時間之變異就會相當大，該結果將對交通產生消散的影響，進一步影響推估結果。因此，嚴謹的動態起迄矩陣推估模式，需要具備於不同交通條件下，正確的預測車輛的到達型態。基此，為了能在不同的交通情況下有效率且準確的獲取車輛到達型態之交通行為，本研究藉由結合進階卡門濾波(extended Kalman filtering, EKF)與格位傳送模式(cell transmission model, CTM)來建構遞迴的動態OD矩陣推估演算法，藉由該方法模擬車輛運行的行為，並預測各依時OD pair之到達型態，以便推估動態OD矩陣。 為驗證此演算法之績效，本文以每6秒為1時階，同時藉由6個OD pair之小路網推估90分鐘的OD矩陣為一驗證範例。首先給定一組動態OD矩陣，並藉由DynaTAIWAN (Dynamic Traffic Assignment and Information in Wide Area Network) 模式模擬路段流量以獲得計算EKF之相關資訊。同時為比較本模式於旅行時間預測之績效，以Greenshields巨觀模式預測車輛旅行時間並假設進入路網之車輛會於兩時階範圍內到達迄點。結果顯示本模式推估結果之RMSE為0.073遠較Greenshields之0.145為低。此外本研究亦針對不同交通流量及高速公路路網設計作敏感度分析，結果顯示本模式推估之正確率會隨著交通流量增加而有些微的減低；然而，不同交流道路網的設計並未對演算法之績效有顯著的影響。另外為分析此演算法之應用範疇，本文以國道1號路網進行兩組實驗分別為:楊梅至泰山收費站之小規模路網及台中至台北間所有交流道之大規模路網，上述實驗結果之RMSE仍在可接受範圍內，分別為0.133與0.125。透過上述，足以證明本研究所提出之演算法的績效與適用範圍。

Accurate dynamic origin-destination (O-D) information is required for the implementation of real-time traffic control measures, such as real-time route guidance and signal control. Numerous studies have devoted to developing estimation algorithms for the dynamic O-D matrix based mainly on observable mainline and ramp flow rates. However, this issue remains challenging in that the number of parameters to be estimated is always far greater than the available information, thus additional assumption or exogenous information, such as route choice behaviors, priori O-D matrix information, sequence of observational periods of traffic counts data should be further considered.

One of the most challenging issues remained to be tackled in the context of dynamic O-D matrices estimation is the impact of travel time variability on the time-varying O-D matrices. Related studies commonly assumed that the vehicles entering the freeway in a time interval will arrive at their destination in a small time range or in a certain distribution. However, if O-D pair traffic traverses a sufficiently long distance or experiences moderate to heavy congestions, then the travel time variability may be rather large, which can result in a serious traffic dispersion phenomenon. Thus, an accurate prediction model for the arrival distribution of entering O-D pair traffic under various traffic conditions is undoubtedly imperial for dynamic O-D matrices estimation. To efficiently and accurately capture the traffic behaviors along with their arrival distributions under various traffic conditions, this study proposes iterative dynamic O-D matrices estimation algorithm by combining extended Kalman filtering (EKF) and cell transmission model (CTM) to simulate the traffic movement behaviors, to predict the arrival distributions of all O-D pair traffic in various time intervals, and then to estimate the dynamic OD matrices.

To validate the performance of the proposed estimation algorithm, an exemplified example of a small freeway corridor with a total of six O-D pairs and a set of 90 minutes O-D matrices, varying at every six seconds. With the given dynamic O-D traffics, DynaTAIWAN (Dynamic Traffic Assignment and Information in Wide Area Network) is then used to simulate the link flows to facilitate the tuning process of EKF. For comparison, the performance of a model which uses the Greenshields macroscopic model to predict travel time and assumes entering traffics will arrive at their destination within two time intervals is also computed. The results show that the proposed model can obtain a relatively accurate estimation result with RMSE=0.073, which is much lower than the compared model with RMSE=0.145. Sensitive analysis on various traffic demands and freeway network layouts show that the accuracy of the proposed model would be slightly lowered down once the traffic demand increases. However, the various network layouts do not remarkably affect the algorithm performance. To further investigate the applicability of the proposed algorithm, two case studies of Taiwan Freeway No.1 corridors: small-scaled network (Yangmei toll station to Taishan toll station) and large-scaled network (Taichung interchange to Taipei interchange) are conducted. The results show that the proposed algorithm can still obtain acceptable RMSE values of 0.133 and 0.125 respectively. The performance and applicability of the proposed algorithm have been proved.