動態號誌時制控制之研究

本研究利用雙層規劃問題之觀念，構建動態號誌時制控制系統，上層為系統總旅行成本最小化，下層為變分不等式的用路人均衡模型。在求解過程中，若直接採用目標函數對號誌變數偏微作為尋優方向，則依據連鎖率，路段流入率必須對號誌變數偏微，但由於此函數不具封閉型式，因此無法直接求出其導函數。此一問題可藉由敏感度分析加以克服。變分不等式敏感度分析理論，必須滿足均衡解為局部唯一解之假設，但用路人均衡問題無法滿足此假設，因此本研究利用廣義反矩陣，針對Tobin and Friesz所提出之演算法進行修正，以連鎖律獲得路段流入率函數對號誌變數偏微資訊，並以動態號誌時制統數值例證實敏感度分析的正確性。

關鍵字

雙層規劃模型；敏感度分析；動態號誌時制最佳化；動態用路人均衡

並列摘要

A bilevel model is formulated to represent a dynamic signal control problem. In the upper level, total network travel time is to be minimized, while in the lower level a variational inequality formulation is constructed to characterize dynamic user equilibrium. Since the function of link inflow with respect to green time at the corresponding intersection is not in closed form, the derivative, which is normally used to search for an. optimum, cannot be obtained. As a result, an alternative approach, usually named sensitivity analysis, is adopted for solution. In the context of sensitivity analysis, the technique of computing general inverse matrix is exploited. By means of chain rule, the sensitivity information can be further used for searching dynamic user equilibrium. A numerical example is then used for testing. Few remarks are also given in the end to conclude the paper.

並列關鍵字

Bilevel model ； Sensitivity analysis ； Dynamic signal control problem ； Dynamic user equilibrium

參考文獻

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