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研究生:王安台
研究生(外文):AnTai Wang
論文名稱:以蒙地卡羅法模擬通訊網路中重撥現象之分析研究
論文名稱(外文):Analytical study of retrial / redial phenomena on communication networks with Monte Carlo Simulation
指導教授:劉宗平劉宗平引用關係
學位類別:博士
校院名稱:元智大學
系所名稱:電機工程學系
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2011
畢業學年度:99
語文別:中文
論文頁數:90
中文關鍵詞:模型模擬性能評估阻塞率無線網路
外文關鍵詞:Modelingsimulationperformance evaluationblocking probabilitywireless networks
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實際的顧客撥打電話的行為,包括了一次就撥打成功的電話,一次撥打不成功便放棄的電話,及一次撥打不成功,但未放棄再撥打的電話。通常,在分析型的模型中,多採用電話公司所收集和建立的網路交換器裏的資料庫,來探討這些行為。
在他們的模型中,到達率和服務率的分佈是固定的和受限制的,在我們以蒙第卡羅法所建立的模型中,係以亂數的方式來產生一個起始的輸入值。為了模擬真實世界中的情況,我們採用不同的到達率和服務率來進行各種情況的模擬,以檢視阻塞率、排隊長度和等候時間。在我們的模擬過程中,還採用了排隊論中的生死過程和馬可夫程序。經由模擬後,我們發現排隊長度和等待時間的數值會受到到達率很大的影響。
在馬可夫過程中,雖然可變化時間,如到達時間,服務時間和重撥時間等,但還必需考慮變數的隨機性,才能遵守具有固定平均值的負指數分佈。然而,在現實的世界中,大部份的分佈函數都不是負指數的形式。因此,馬可夫過程所推出的某些結論,尚需利用其他的方式來證明。實際上,在整個模擬過程中,所用到的方法,如 M/M/1、指數分配、馬可夫程序等,尚須強調無記憶性。為了解決這些問題,蒙地卡羅法將是一個,來建構一個合理的模型,以進行實際狀況的模擬與分析,而不需要使用分析模型中的假設條件。

Practical customer behaviors for dialing a call include a fresh (new) call, a hand-off call, and a retrial (repeated attempt) call. In analytical models, these behaviors generally were studied by use of a data warehouse of network switches collected and established by the telephone company.
The distribution of the arrival and service rates in their models are fixed and limited. In our model based on Monte Carlo method, the random generator was used to produce a value as an initial input data. To mimic real world, the blocking probability, the queueing length, and the waiting time were examined for several cases with different arrival and service rates. In our simulations, the birth-death process and Markov process in queue theory were utilized. Through simulations, we found that the values of the queueing length and the waiting time would be strongly influenced by the variation of the arrival rate.
Although the times, in Markovian processes, such as arrival time, service time, and retrial time, can be varied, the stochastic of random variables needed to be considered to obey negative exponential distribution functions with constant averages. However, most distribution functions in problems are not negative exponential in the real world. Therefore, some conclusions deduced from Markovian processes were needed to be justified by some other means. Actually, all methods, such as M/M/1, exponential distribution, Markovian property, used in the whole simulation model, still emphasis the memoryless property. To solve these problems, Monte Carlo method can be the candidate to construct a reasonable model to simulate and analyze the real problem without the assumptions made in the analytical model.

中文摘要 iv
英文摘要 vi
誌謝 viii
目錄 x
圖錄 xiii
第一章、緒 論 1
1.1 研究背景與動機 1
1.2 研究目的與方法 3
第二章、模擬 8
2.1 模擬的定義與方法 8
2.2 蒙地卡羅法(Monte Carlo method) 13
第三章、排隊模型 17
3.1 典型的排隊系統 17
3.2 排隊系統的基本要素 18
3.2.1 顧客來源 19
3.2.2 顧客到達的分配情形 20
3.2.3 佇列服務規則 21
3.2.4 服務機制 23
3.2.5 顧客最大容納量 24
3.2.6 顧客服務及離去之分配情形 24
3.3 排隊狀態與符號說明 25
3.3.1 排隊系統的分類描述 27
3.4 馬可夫過程 29
3.4.1 泊松流與指數分佈 29
3.5 生死過程 32
3.5.1 純生過程 35
3.5.2 純死過程 38
第四章、有線電話網路系統的模擬與分析 42
4.1 阻塞的形成 42
4.2 電話重撥 42
4.2.1 到達率 46
4.2.2 重撥率 46
4.2.3 服務率 47
4.3 系統特性 47
4.4 分析模型 49
4.5 數值結果與討論 50
4.5.1 時間率變化的影響 52
4.5.2 Erlang分佈的服務率 55
第五章、無線電話網路系統的模擬與分析 58
5.1 顧客行為模式 58
5.2 分析模式:二維生死狀態程序 60
5.3 模擬模型:蒙地卡羅法 63
5.4 性能量測 64
5.5 資料分析 65
5.5.1 一天中的時間變化率 66
5.5.2 到達間隔時間,服務間隔時間與重撥間隔時間 68
5.6 數值結果與討論 72
5.6.1 蒙地卡羅法的收斂測試 72
5.6.2 蒙地卡羅法與分析模型的一致性 74
5.6.3 蒙地卡羅法的Erlang分佈 76
5.6.4 一天中每小時的流量負載 82
5.6.5 保留(reserved)通道的影響與重撥上的流量負載 84
第六章、結論 86
參考文獻 89


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[3] Chung Ping Liu, An Tai Wang, “Performance measures on a customer retrial calls in telephone networks by using Monte Carlo simulation,” International Mathematical Forum, Vol. 6, no. 21 – 24, pp. 1181-1196, 2011.
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