路網容量信賴度之研究

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曾瓊玉(Chung-Yu Tseng) 查詢紙本館藏

畢業系所

土木工程學系

論文名稱

路網容量信賴度之研究
(Network Capacity reliability)

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摘要(中)

本研究以Chen and Hsueh(1996)發展之動態用路人均衡模型為基礎，分別構建動態多重用路人均衡模型與路段等候長度動態用路人均衡模型。動態多重用路人均衡模型主要探討當用路人為多種類(multiclass)多準則(multicriteria)之模型，以各用路人主觀決定旅行時間與旅行成本之權重，組成該用路人之旅行負效用，在該基礎下進行動態用路人均衡模型求解，以數值範例進行測試與分析。
就時間向度而言，路段流入率、流出率與車輛數是同一實體三種表象之轉換，過去研究已探討路段流入率與路段流出率容量之模型，因此本研究嘗試將容量限制於路段車輛數上，構建路段等候長度動態用路人均衡模型，利用擴張拉式對偶法及懲罰法兩種演算法求解，以測試範例驗證模型與演算法之正確性，分別比較兩種演算法之績效，及三種限制下構建之模型的結果與績效差異。
本研究參照Chen et al.(2002)提出之信賴度分析程序，結合蒙地卡羅模擬、動態用路人均衡模型、敏感度分析、不確定分析等以獲得各項信賴度資訊，探討路網容量信賴度。分析架構主要以蒙地卡羅模擬產生路段容量變數，獲得路網退化資料後，進行動態用路人均衡模型求解，並利用卓訓榮(1991)提出之廣義反矩陣法(Generalized Inverse Approach)求算敏感度分析資訊，其後結合各項信賴度分析方法，進一步獲得路網各項信賴度分析資訊進行評估。

摘要(英)

Dynamic user equilibrium problem explored travelers’ choice behavior involving temporal dimension consideration, which has been tackled for years. Contrast to link flow as the decision variable in static traffic assignment, three variables are identified in the dynamic user equilibrium problem, i.e., link inflow, number of vehicles and exit flow. However, by concept of flow propagation, these three flow variables can be transformed each other. For example, the number of vehicles and exit flows can be deemed as subsequent states of link inflows. With only one decision variable adopted, the structure of dynamic user equilibrium model can be significantly simplified.
Based on the results that have been developed so far, this study attempts to strengthen the applicability of the dynamic user equilibrium model by taking three more issues into study. The first issue is to relax the assumption of single class of travelers, thus yielding a multiclass or multicriteria dynamic user equilibrium model.
The second issue is to retrospect the link capacity requirement from the practical point of view. In the past, either link inflow or exit flow was taken for link capacity constraint in the dynamic user equilibrium problem. Here, we take the number of vehicle (or equivalently link queue length) as the link capacity constraint instead, and solve it accordingly by the penalty and augmented Lagrangian methods. The results show that under the assumption that time dependent network constructed by the actual link travel times, the outputs obtained from the link capacity constraints formed by link inflow, exit flow or the number of vehicles are basically comparable.
The last issue is to deal with link capacity reliability analysis. The framework is mainly borrowed from Chen et al. (2002), which involves sensitivity analysis embedding a generalized inverse approach, uncertainly/risk analysis within a Monte Carlo simulation. This systematic procedure is general in that the reliability on connectivity and travel times is constructed as special cases. The findings associated with the three issues are summarized and few remarks are given in the end to conclude the research.

關鍵字(中)

★ 蒙地卡羅模擬
★ 信賴度分析
★ 動態用路人均衡模型
★ 多重用路人
★ 額外限制式

關鍵字(英)

★ reliability analysis
★ Monte Carlo simulation
★ dynamic user equilibrium model
★ the multiclass and multucriteria user

論文目次

摘要 i
Abstract ii
圖目錄 vi
表目錄 vii
第一章緒論 1
1.1研究動機 1
1.2研究目的 1
1.3研究範圍與內容 1
1.3.1研究假設 2
1.3.2研究範圍與內容 2
1.4研究流程 3
第二章文獻回顧 4
2.1動態用路人均衡模型 4
2.2多重用路人均衡模型 5
2.3路段流入率與流出率容量限制 5
2.4變分不等式敏感度分析 7
2.5信賴度分析 8
第三章動態多重用路人均衡模型 9
3.1模型構建 9
3.1.1均衡條件 9
3.1.2變分不等式模型 10
3.1.3最佳化條件 11
3.1.4對等性證明 12
3.2求解演算法 15
3.3路網測試 16
3.3.1輸入資料 16
3.3.2測試結果 19
3.3.3績效比較 21
3.4小結 22
第四章路段等候長度限制動態用路人均衡模型 23
4.1模型構建 23
4.1.1均衡條件 23
4.1.2變分不等式模型 24
4.1.3最佳化條件 25
4.1.4對等性證明 29
4.2求解演算法 32
4.2.1擴張拉式法 33
4.2.2懲罰法 36
4.2.3梯度投影法 38
4.3路網測試 43
4.3.1輸入資料 44
4.3.2測試結果 44
4.3.3拉式參數更新 48
4.3.4互補鬆弛條件維持之探討 50
4.3.5績效比較 51
4.4小結 53
第五章信賴度分析 54
5.1網路容量問題 55
5.1.1剩餘容量 55
5.1.2不確定來源 57
5.1.3隨機變量之分配與相依性 58
5.2變分不等式敏感度分析 58
5.2.1變分不等式敏感度分析原理 58
5.2.2變分不等式敏感度在網路均衡問題之應用 61
5.2.3以路徑流量進行敏感度分析 62
5.3.4利用廣義反矩陣進行敏感度分析 66
5.3不確定分析 69
5.4信賴度評估程序 70
5.4.1蒙地卡羅模擬(Monte Carlo simulation) 71
5.4.2隨機變量產生 72
5.4.3以敏感度分析為基礎計算偏微值 73
5.4.4各項資料分析 75
5.5測試例 76
5.5.1輸入資料 76
5.5.2 蒙地卡羅模擬 77
5.5.3動態用路人均衡模型 80
5.5.3容量信賴度分析 82
5.5.4旅行時間信賴度分析 82
5.5.5敏感度分析 84
5.6小結 86
第六章結論與建議 88
6.1結論 88
6.2建議 89
符號說明 91
參考文獻 95
附錄A I

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指導教授

陳惠國(Huey-Kuo Chen)

審核日期

2002-7-17

推文