本研究以Chen and Hsueh(1998a,b)所提出之動態用路人均衡路徑選擇模型及求解演算法為基礎，延續蕭淑芸(1999)、周鄭義(1999)之研究，應用變分不等式理論繼續探討動態起迄旅次矩陣推估雙層規劃模型問題。本研究利用雙層規劃方法(Bi-level Programming Approach)構建動態起迄旅次矩陣推估模型，上層模型為以最小平方法的觀念，以使得推估起迄旅次量及路段流量，與先驗旅次量及觀測路段流量間之差距最小；下層模型為用路人均衡路徑選擇問題，即相同起迄對相同出發時區之用路人均利用最短路徑到達目的地。並透過變分不等式敏感度分析理論，以卓訓榮(1991)提出之廣義反矩陣方法(Generalized Inverse Approach)獲得敏感度分析資訊，發展動態起迄旅次矩陣推估問題之求解演算法，最後以測試範例證實模型及演算法之正確性。
由於受道路幾何設計及路口號誌時制影響，道路有一容量限制，為使模型更符合實際，加入額外限制式(路段容量限制式)，構建含路段容量限制之動態起迄旅次矩陣推估模型。在求解演算法方面，以拉氏法結合梯度投影法求解含額外限制式的問題，並以測試範例進行測試與分析。

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