不同決策變數下動態用路人均衡路徑選擇模型之研究

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黃士沛(Shih-Pei Huang) 查詢紙本館藏

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土木工程學系

論文名稱

不同決策變數下動態用路人均衡路徑選擇模型之研究

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摘要(中)

本研究依據Chen and Hsueh (1996)以路段流入率為決策變數所構建之動態用路人均衡路徑選擇模型為基礎，考慮不同問題特性，應用不同決策變數進行動態用路人均衡路徑選擇問題之構建，在此分別就路段流出率與路徑流量兩種不同決策變數進行探討。在以路徑流量為決策變數之動態用路人均衡路徑選擇模型下，本研究除了證明此模型對等於動態用路人均衡條件外，並利用不動點理論(Fixed Point Theorem)進行變分不等式的轉換，以提出此一變分不等式解的存在性證明。
因應不同決策變數模型，本研究提出相對應演算法以進行問題求解，並透過數值例，驗證此模型及演算法的正確性。另外，在以路徑流量為決策變數之動態用路人均衡路徑選擇模型上，分別考慮路段流入率容量限制與路段流出率容量限制的影響，以證實路徑流量模型在動態用路人均衡路徑選擇問題上的適用性。

摘要(英)

As follow-up study of Chen and Hsueh (1996) base on link inflow being decision variable to create Dynamic User-Optimal Route Choice Model, this thesis takes into account of figures and applies different decision variables to create dynamic user-optimal route choice problem, discussing by link inflow and route flows. Based on route flows be decision variable, this thesis not only verifies the model be equal to equilibrium conditions but also offers the proof of existence by transferring from Fixed Point Theorem to variational inequality.
To match up different decision variables, this thesis supplies several algorithms and proves its correction with numerical examples. Besides, based on dynamic user-optimal route choice model with route flows being decision variables, it considers individually link inflow capacity and exit flow capacity, to verify the suitability of dynamic user-optimal route choice problem with route flows.

關鍵字(中)

★ 動態用路人均衡路徑選擇
★ 不動點理論

關鍵字(英)

★ dynamic user-optimal route choice
★ Fixed Point Theorem

論文目次

第一章、緒論1
1.1 研究動機1
1.2 研究目的2
1.3 研究範圍與假設2
1.3.1 研究範圍2
1.3.2 研究假設3
1.4 研究流程4
第二章、文獻回顧5
2.1 動態用路人均衡路徑選擇模型5
2.2 路段容量限制12
第三章、以路段流出率為決策變數之動態用路人均衡路徑
選擇模型18
3.1 模型構建19
3.1.1 均衡條件19
3.1.2 模型建立19
3.1.3 對等性證明21
3.2 求解演算法24
3.3 範例測試26
3.3.1 輸入資料26
3.3.2 測試結果27
3.3.3 模型比較與結果分析28
3.4 小結35
第四章、以路徑流量為決策變數之動態用路人均衡路徑選
擇模型36
4.1 模型構建36
4.1.1 均衡條件36
4.1.2 模型建立37
4.1.3 對等性證明38
4.2 動態路徑旅行成本41
4.3 均衡解之存在性44
4.4 求解演算法48
4.4.1 巢化梯度投影法(Nested Gradient Projection Method)51
4.4.2 流線投影法(Streamlined Projection Method)54
4.5 範例測試60
4.5.1 輸入資料60
4.5.2 結果分析62
4.5.3 運算績效之比較66
4.6 小結69
第五章、路段容量限制動態用路人均衡路徑選擇模型70
5.1 模型構建71
5.1.1 均衡條件71
5.1.2 模型建立72
5.1.3 對等性證明74
5.2 一般化路徑旅行成本77
5.3 均衡解之存在性79
5.4 求解演算法79
5.5 範例測試85
5.5.1 輸入資料85
5.5.2 結果分析86
5.6 循環不收斂現象88
5.7 修正演算法及其效率93
5.7.1 修正拉氏-梯度投影法93
5.7.2 範例測試96
5.8 路段流出率容量限制101
5.8.1 均衡條件101
5.8.2 模型構建I102
5.8.3 模型構建II105
5.8.4 範例測試105
5.8.5 運算績效之比較112
5.9 小結113
第六章、結論與建議115
6.1 結論115
6.2 建議117
參考文獻119
符號說明123

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指導教授

陳惠國(Huey-Kuo Chen)

審核日期

2000-7-13

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