應用條件逆矩陣進行路段流量推估起迄對運輸需求之研究

Applying a Conditional Inverse Matrix Approach to Origin-destination Demand Estimation by Link Traffic Flows

本研究旨在建立一套求解程序，利用路段、路徑流量與起迄對運輸需求間的流量守恆關係，以變數產生法結合梯度投影法求解起迄對間可行的路徑，建立線性方程式系統，再利用條件逆矩陣求出路段／路徑鄰接矩陣的條件逆矩陣，以進行路段流量反推起迄對運輸需求的運算。經由路網測試發現，本研究所發展之求解程序，在不同路網的測試中均可獲得相當精確之起迄對運輸需求推估結果。另在敏感度分析的測試結果發現，可利用Hermite form矩陣的性質，判斷是否能反推出準確之起迄對運輸需求。此外，本研究所研提之求解程序，可同時針對符合使用者均衡，以及不符合使用者均衡之兩種路網流量形態，正確地推估其所對應的起迄對運輸需求，相較傳統上的反推起迄對運輸需求模型，本研究之成果則更具一般性。

In this research, we built a procedure to solve the O-D demand estimation problem. The procedure first applied the flow conservation relationship between link flows, path flows and O-D trips to build a linear equation system. Then we used Column Generation Method combined with Gradient Projection Method to calculate the possible paths between O-D pairs in the linear equation system. We then applied the Conditional Inverse Matrix approach to derive the O-D trip matrix. We tested this procedure in different networks; the results showed that the estimates are highly accurate. From the sensitivity analysis, we found that estimation accuracy is highly related to the mathematical properties of a Hermite form matrix. Compared to the traditional O-D demand inference models, the model developed in this research can handle all the link flow situations, whether the link flow is restricted by the UE condition or not. The present study is a more general O-D demand estimation method than most traditional estimation models.