普羅比機率型動態用路人均衡模型演算法求解效率之比較

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施政廷(Zheng-Ting Sh ) 查詢紙本館藏

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土木工程研究所

論文名稱

普羅比機率型動態用路人均衡模型演算法求解效率之比較

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摘要(中)

明確型動態用路人均衡模型係假設用路人具有完整資訊，然而實際上用路人並不一定具有完整資訊，而機率型動態用路人均衡模型以機率分配的形式來處理用路人路徑選擇問題，使得模型更趨向一般化。
機率型動態用路人均衡模型依據機率分配的不同而分為羅吉特模型及普羅比模型。羅吉特模型因為假設方案之間具有獨立且不相關(IIA)的特性，而具有效求解的優點，但卻無法考慮用路人選擇方案間的相關性，而普羅比機率型動態用路人均衡模型，雖然缺乏求解效率，但可以有效解決羅吉特模型的爭議
由於普羅機率型動態用路人均衡模型中，必須考慮時空間的相關性，本研究接續馮君惠(1998)的研究，更加深入探討普羅比機率型動態用路人均衡模型，並試圖將不同的求解演算法應用至動態路徑選擇中，並以不同的測試例比較各演算法的求解效率，提供日後相關應用的參考建議。

摘要(英)

The basic assumption with Wardrop’s principles is that the traffic information is perfect. However, this assumption is generally not correct because the traffic information is likely to be imperfect. It is realistic that stochastic dynamic user equilibrium model hypothesizes that the error term of an actual route travel time is randomly distributed.
We assume the distribution is the Gumbel distribution which yield the logit model or Normal distribution which yield the probit model. The logit model hypothesizes the independent and irrelative between alternative and can solve the problem effectively. The probit model is realistic but it solve the problem ineffectively.
We must consider the relation between time and space in stochastic dynamic user equilibrium model with probit model and develop different algorithms to solve the probit model. Finally, we suggest several indices to evaluste these algorithms and make conclusions to provide a reference for further improvement.

關鍵字(中)

★ 普羅比
★ 機率型
★ 機率型動態用路人均衡模型
★ 變分不等式

關鍵字(英)

★ Dynamic User-Equilibrium
★ probit
★ Stochastic

論文目次

中文摘要……………………………………………………………I
英文摘要...II
目錄………………………………………………………………..III
圖目錄……………………………………………………………..VI
表目錄…..VIII
第一章緒論1
1.1 研究背景與動機1
1.2 研究目的2
1.3 研究假設3
1.4 研究範圍與內容3
1.5 研究流程5
第二章文獻回顧6
2.1 動態旅運選擇模型6
2.2 機率型動態用路人均衡模型9
2.3 小結10
第三章常態機率分配的動態用路人均衡模型11
3.1　路段觀點機率型動態用路人均衡模型11
3.2 巢化對角法13
3.3 時空相關性16
3.4 路段基礎式蒙地卡羅模擬法19
3.4.1 抽樣方法19
3.4.1.1 數值分析19
3.4.1.2 抽樣檢定20
3.4.2寇列斯基法22
3.4.3路段基礎式蒙地卡羅模擬法24
3.4.4數值分析26
3.4.4.1 輸入資料26
3.4.4.2 測試結果27
3.4.4.4 正確性說明28
3.4.5 小結31
3.5　路徑觀點機率型動態用路人均衡模型33
3.6 路徑基礎式蒙地卡羅模擬法33
3.6.1 路徑觀點之共變異矩陣33
3.6.2 路徑基礎式蒙地卡羅模擬法35
3.6.3 數值分析39
3.6.4 正確性說明40
第四章路徑基礎式與路段基礎式蒙地卡羅模擬法之比較46
4.1路段基礎式-蒙地卡羅模擬法分析46
4.1.1時間分析48
4.1.2 迴圈二精度與執行時間分析50
4.2路徑基礎式-蒙地卡羅模擬法分析52
4.2.1時間分析53
4.2.2 迴圈二精度與執行時間分析55
4.3路徑基礎式與路段基礎式模擬法比較57
4.3.1感知旅行時間分析57
4.3.2正確性分析比較62
4.3.3 績效分析64
4.3.4 精度與執行時間比較分析65
4.4小結67
第五章結論與建議68
5.1 結論68
5.2 建議70
參考文獻 72
附錄A 主要符號對照表75
附錄B 寇列斯基法77
附錄C 實例分析………………………………………………..79

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指導教授

陳惠國(Huey-Kuo Chen)

審核日期

2001-7-9

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