應用偏差控制變異技術估計網路等候之平均等候時間

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林妤璟(Yu-Ching Lin) 查詢紙本館藏

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工業管理研究所

論文名稱

應用偏差控制變異技術估計網路等候之平均等候時間
(The Mean Waiting Time Estimation of Queueing Network via Biased Control Variates)

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摘要(中)

在等候模型中，估計等候時間及延遲機率是一般研究之主要方向。由M/M/s模型開始推廣，目前已有許多學者在對M/G/s等候線提出相關研究，即放寬服務時間服從指數分配的條件的擁塞測量進行估計模型研究。而對於GI/G/s等候線，將到達過程分配條件放寬，使得等候線模型更符合現實狀態，因此在估計擁塞測量上較為困難，也尚未有一個確切的估計模型。故此，至今持續有許多學者在GI/G/s等候線之各項數值及參數估計進行更深入的研究。本研究將探討，目前GI/G/s等候線之平均等候時間估計模型的估計變異，並以Kimura (1986)之系統插值(System Interpolating) 近似模型為主要觀察對象。在其研究中，以QNA (Queueing Network Analyzer)為基礎，轉換參數設定提出各項擴展模型，並以模型期望等候時間與實際平均等候時間之差作為準確率的判斷，但未提及其估計模型之估計變異，且估計量是否為穩定狀態。在模擬實驗中，已有研究證明變異數縮減技術能幫助模擬估計值更加準確且使實驗更有效率，本研究使用其中一個方法：偏差控制變異技術(Biased Control Variates)，在此方法中加入相關性高的近似法對原模型估計作調整，能使得預估計參數的變異改善，並且使估計量能比原估計模型更穩定。因此，本研究預將QNA之平均等候時間近似模型結合控制變異技術，並與QNA後的擴展模型進行精準度比較。

摘要(英)

For the queueing system, generally pay close attention on two issues: the waiting time and the queueing length, because these can show the important information for manager that is where is the delay problem. The M/M/s model has been extended for many years. For GI/G/s queue, the distribution conditions for arrival process are relaxed, making the queueing model more realistic, so it is difficult to estimate the congestion measurement, and there is not yet an exact estimation model. As a result, many researcher have continued to conduct more in-depth studies on the numerical and parameter estimates of the GI/G/s queue.
In Kimura’s research, based on the QNA (Queue Network Analyzer), the conversion parameters were set to propose various expansion models, and the difference between the expected waiting time of the model and the actual average waiting time was used as the judgment of the accuracy rate, but he didn’t mention about the variance and the estimated statement is stable or not.
In simulation experiments, studies have shown that variate reduction techniques can help to make simulation estimates more accurate and make experiments more efficient. This study uses one of the methods: Biased Control Variates, and it be used highly approximated pairs of approximations. The adjustment of the original model estimate can improve the variation of the pre-estimation parameter and make the estimator more stable than the original estimation model. Therefore, in this study, the approximation model of the average waiting time of QNA is combined with the control mutation technique, and the accuracy of the extended model after QNA is compared.

關鍵字(中)

★ 網路等候
★ 等候時間
★ QNA
★ 變異縮減

關鍵字(英)

★ queueing network
★ waiting time
★ QNA
★ variate reduction

論文目次

目錄頁
摘要 iii
Abstract iv
表目錄 vii
圖目錄 viii
第一章、緒論 1
1.1 研究背景與動機 1
1.2 研究目的 3
1.3 研究架構 4
第二章、文獻探討 5
2.1 GI/G/s平均等候時間估計方法 5
2.1.1. 等候網路分析模型(The Queueing Network Analyzer, QNA) 5
2.1.2. 擴展近似模型 7
2.2 控制變異技術 11
2.2.1 經典的控制變異技術(Classical Control Variates, CVs) 11
2.2.2. 偏差控制變異技術(Biased Control Variates, BCVs) 13
2.2.3. 近似模型協助點估計量 14
2.3.估計量之偏差與變異數 16
第三章、研究方法 19
3.1實驗方法及參數定義 19
3.2 實驗步驟 20
第四章、實驗結果 23
4.1 模型及參數設定 23
4.2 實驗結果 24
第五章結論與未來方向 35
5.1 結論 35
5.2 未來方向 36
參考文獻 37

參考文獻

參考文獻
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指導教授

葉英傑(Ying-chieh Yeh)

審核日期

2018-7-23

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