開發有效之列車運轉與調度等基本作業管理方法與程序，將有助於現在與未來各 鐵路系統營運績效之提昇；其中，列車站間運轉時分之推估是列車調度與排點等作業規劃之 第一步工作。列車運行之時空變化為一動態系統，本研究將列車運行表示為時空軌跡線，在 路線軌道與列車運轉特性之限制下， 利用最佳化控制理論， 冀望達成不同的運行目標 - - 運行時間最短或最省能源，建立列車運行之最佳時空變化過程。本研究發展之模式利用臺灣 鐵路管理局實際資料進行測試，顯示良好結果。

　　　　　Estimation of standard running is critical for the planning process of train operations. Among several types of standard running, the following two are considered in the study: the movement with minimum running time, and the movement under minimum energy consumption. The estimation of standard running is to construct a time-space trajectory for a train movement between two adjacent stations. The study attempts to build and solve models based on the optimal control theory for the estimation of standard running. The models are tested with real data from Taiwan Railway Administration to demonstrate applicability to practical train operations.