高速公路依時性道路收費雙層規劃模型

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嚴國基(Kuo-Chi Yen) 查詢紙本館藏

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土木工程學系

論文名稱

高速公路依時性道路收費雙層規劃模型
(A Time-Dependent Bi-Level Model for Road Pricing on Freeways)

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摘要(中)

近年來私人運具快速成長且缺乏有效的道路費率定價政策，導致目前國道高速公路在尖峰時間道路容量與服務水準嚴重不足。因此衍生「國道差別費率」的需求管理措施，期望透過差別費率舒緩尖峰車流，然而，策略目標並不如預期顯著。主管機關應細緻的規劃推動國道定價策略，以系統化的角度進行思考如何確實反映尖峰時間使用國道所應付出的價格。費率定價的制定必須能夠達到「替代效果」，此替代效果包含時間替代、道路替代以及運輸工具的替代。鑒此本研究建立以依時性用路人路徑選擇最佳化模型為基礎的費率規劃方式導入時間向度、路徑選擇以及運具選擇等因素，藉由落實使用者付費，使得用路人因有效的道路定價產生道路替代、運具替代以及出發時間替代的效果。進而規劃出切實有效的最佳化費率作為公務部門政策推行的依據。
本研究將以四個階段進行討論，首先以B演算法應用求解依時性用路人路徑選擇最佳化模型以說明該演算法的特性與運算績效；第二階段，則是探討含流出率容量限制與先進先出限制之依時性用路人最佳化模型以說明依時性模型所遭遇的問題並提出解決方式，以更一般化的模型詮釋依時性用路人路徑選擇行為。由於收費政策的推行期望達成時間替代、道路替代以及運輸工具替代等效果，因此第三階段討論依時性用路人最佳化運具選擇/路徑選擇/出發時間選擇問題，並且加入第二階段的限制條件以構建含額外限制之依時性用路人最佳化運具選擇/路徑選擇/出發時間選擇模型。最後於第四階段討論道路收費定價問題，建構國道收費定價最佳化設計雙層規劃模型。由於本研究屬網路設計問題之範疇，因此建立雙層規劃模型，上層為系統最佳化，追求路網總成本最小為目標；下層問題則利用含額外限制之依時性用路人最佳化運具選擇/路徑選擇/出發時間選擇模型的特性，分析最佳化費率下依時性用路人旅運行為。藉此提供政府相關權責單位有效的決策支援。

摘要(英)

Rapid growth in private vehicle ownership and the lack of an effective pricing policy for road tolls has led to congestion and inadequate service on freeways, especially during peak hours. Differential toll rates have been introduced in an attempt to stem traffic flows during peak hours; however, results have failed to meet expectations. To overcome this, the authorities should promote the road pricing strategy that accurately reflects the cost of using the freeway during peak hours is required. The pricing strategy must achieve the “alternative effect” which includes departure time replacement, path substitute and modes alternative. This study try to formulate the dynamic user-optimal route choice model integrates time dimension, route choice and mode choice factors. The users will be affecting by efficiency road pricing and changing the behavior. This model can be used as reference in establishing public policies that facilitate effective toll rates.
This research was conducted in four stages. We first demonstrated the features and performance of Algorithm B by applying it to solve the dynamic user-optimal route choice model. Second, we discussed the problems of exit-capacity and first-in-first-out constraints, and proposed countermeasures in order to explain the dynamic user behavior more exactly. Since the roed pricing policy must achieve the above three substitution efficacy. In the third stage the dynamic user-optimal mode choice/departure time/route choice model with side-constraints will be discussed. In Stage 4, the dynamic bi-level optimal toll design model for superhighway has been formulated. Our study is in the field of network design, which is formulated network design field as a Bi-level programming model. The upper level objective of the model is to minimize the total network costs. The objective of the lower level is to apply the dynamic user-optimal mode choice/departure time/route choice model with side-constraints to analyze the behavior of the travelers under optimal toll rates. By solving the problem, the variational inequality sensitivity analysis method, generalized inverse matrix method, and Lagrangian-B algorithm are adopted to provide the algorithms for the bi-level method. The results of this study serve as reference for policy-making authorities.

關鍵字(中)

★ 道路定價問題
★ 雙層規劃問題
★ 依時性用路人路徑選擇最佳化問題

關鍵字(英)

★ road pricing problem
★ bi-level planning problem
★ the dynamic user-optimal route choice model problem

論文目次

中文摘要 II
英文摘要 III
致謝 V
目錄 VI
表目錄 IX
圖目錄 XI
符號說明 XII
一、緒論 1
1-1 研究動機 1
1-2 研究目的 3
1-3 研究方法 5
1-4 研究範圍與假設 8
1-5 研究流程 11
1-6 研究貢獻 12
二、文獻回顧 14
2-1 依時性路網均衡問題 14
2-2 依時性用路人最佳化路徑選擇模型 17
2-3 額外限制式問題 19
2-3-1 路段流出率容量限制 19
2-3-2 依時性車流先進先出原則 20
2-4 依時性用路人最佳化運具/出發時間選擇問題 22
2-5 快速精準演算法應用於依時性用路人最佳化路徑選擇問題 24
2-6 雙層規劃問題與路網敏感度分析 25
2-6-1 雙層規劃問題 25
2-6-2 路網敏感度分析 29
2-7 道路收費定價問題 33
2-8 綜合評析 39
三、 B演算法應用於求解依時性用路人最佳化模型 44
3-1 依時性用路人最佳化模型與求解演算法 45
3-1-1 巢化對角法 (Nested Diagonalization Method, NDM) 45
3-1-2 B演算法 47
3-2 數值範例測試與運算績效 50
3-3 小結 53
四、含額外限制依時性用路人最佳化模型 55
4-1 路段流出率容量限制 55
4-2 時間變動下之車流先進先出限制 58
4-3 含先進先出與流出率容量限制之依時性旅運選擇均衡模型 60
4-3-1 均衡條件 60
4-3-2 模型建立 61
4-3-3 最佳化條件 63
4-3-4 對等性證明 66
4-4 求解演算法 69
4-4-1 拉氏法 70
4-4-2 求解演算法 72
4-5 數值範例測試 75
五、含額外限制之依時性用路人最佳化運具選擇/路徑選擇/出發時間選擇模型 81
5-1 依時性用路人最佳化運具選擇/路徑選擇/出發時間選擇問題 81
5-2 模型建立與對等性證明 83
5-2-1 模型建立 83
5-2-2 對等性證明 86
5-3 求解演算法 88
5-4 數值例測試 92
六、國道收費定價最佳化設計雙層規劃模型 97
6-1 模型建立 98
6-2 模型求解 100
6-2-1 變分不等式敏感度分析適用時機 101
6-2-2 變分不等式敏感度分析 105
6-2-3 變分不等式敏感度分析於網路均衡問題之應用 108
6-2-4 敏感度分析與廣義反矩陣 110
6-2-5 應用廣義反矩陣於網路均衡問題敏感度分析 113
6-2-6 廣義反矩陣與敏感度分析例證說明 116
6-3 國道收費定價設計最佳化模型求解演算法 126
6-4 台北至宜蘭路網與起迄需求資訊 129
6-5 數值測試與分析 132
6-5-1 國道基本收費政策分析 133
6-5-2 國道收費最佳化訂價分析 135
6-5-3 固定最佳化費率下路網流量狀態 140
6-5-4 政策定價費率求解下層模型 143
6-6 小結 148
七、結論與建議 150
7-1 結論 150
7-2 建議 152
參考文獻 156
附錄1：3-2節測試路網1路段流量表 163
附錄2：國道五號日交通量參考值 168
附錄3：國道五號系統交流道至宜蘭交流道分時交通量 169

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指導教授

陳惠國(Huey-Kuo Chen)

審核日期

2016-1-28

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