多層引力模式求解高速公路起迄表：Deming-Stephan-Furness 疊代程序之應用

Abstract

在運輸規劃、交通管理、收費費率制訂等領域中，起迄流量矩陣一直是一種重要的輸入資訊。傳統的起迄流量矩陣資訊取得方式，如訪問、車牌登錄調查等，所耗費的人力、物力龐大，且資料的時空涵蓋率和精確程度均有所缺陷。為了改善上述調查缺陷，許多估計方式及數學模式相應而生，其中以引力模式尤其著名。然，引力模式求解中所使用之單調(monotonic)性質的成本函數，無法有效地描述旅行成本影響空間分布的非單調遞減行為。因此，本研究嘗試結合分層的概念於引力模式上，並透過Deming-Stephan-Furness疊代程序進行求解。以起點、迄點流量做為輸入變數，並符合路段流量差值最小，本研究所提出之估計方法不需要前期資訊，並可用於靜態起迄矩陣估計之上。由於高速公路並沒有已知的真實起迄流量矩陣，因此本研究為了瞭解所建立之起迄流量矩陣推估方式之合理性，透過高速鐵路之起迄流量資訊進行分析。經分析後，再將此模式應用於高速公路之起迄流量矩陣推估之上。於高速鐵路的路網上進行驗證發現，透過本研究所提出之多階層引力模式，可獲得較低的估計誤差平方差和。

Origin-Destination matrix is an important information in transportation planning, traffic management, and many other transportation researches. Traditional origin-destination matrix estimation methods, i.e., interview and license plate survey, require tremendous resources and hard to cover both temporal and spatial domains. Many mathematical models are developed to improve the aforementioned deficiencies’, and the gravity model is likely the most well-known among those. However, the monotonic cost function involved in gravity model failed to describe the non-monotonic behavior on how travel costs affect spatial distribution. Therefore, this study combined the hierarchical concept into gravity model and solve the problem with Deming-Stephan-Furness iterative process. With origin and destination flows as input and targets to minimize the difference between observed and estimated link flows, this method is able to estimate a static origin-destination matrix without prior information about the target matrix. In order to understand the result of the established method, this study compares the estimated and real origin-destination matrix derived from Taiwan High Speed Rail. Afterward, the method is implemented on the estimation of freeway origin-destination matrix. As the numerical example derived from Taiwan High Speed Rail shows, the hierarchical gravity model can achieve a lower estimation error.