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研究生:林守信
研究生(外文):Shou-Hsin Lin
論文名稱:具有優先權之M/M/1排隊模型的最佳門檻策略
論文名稱(外文):On the Optimal Threshold Policy of the M/M/1 Priority Queue
指導教授:王家禮
指導教授(外文):Chia-Li Wang
學位類別:碩士
校院名稱:國立東華大學
系所名稱:應用數學系
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2001
畢業學年度:90
語文別:英文
論文頁數:40
中文關鍵詞:M/M/1門檻最佳化優先權preemptive-resumepreemptive-LIFO
外文關鍵詞:M/M/1thresholdoptimizationprioritypreemptive-resumepreemptive-LIFO
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對於一個單一服務者的排隊模型,Naor [1969] 證明了在群體最佳化的條件下獲得的排隊模型的門檻,會小於或等於在顧客自身最佳化的條件下獲得的排隊模型的門檻。本研究延伸自Naor [1969] 研究的範圍,由一個單一等級的服務系統推廣至具有優先權等級的服務系統。
我們首先考慮在自身最佳化的條件下兩個不同等級的顧客的門檻限制。我們發現具有高優先權的等級的門檻和Naor [1969] 的單一等級的排隊模型的門檻是相同的。此外,我們發現具有低優先權的等級的門檻是和在系統內具有高優先權的等級的顧客人數相依。
接著我們考慮在群體最佳化的條件下兩個不同等級的顧客的門檻限制。我們介紹三種控制策略,系統管理者可以經由選擇其中一種策略,使系統可以獲得最大期望總淨收益,也因此,系統藉由限制進入系統的顧客人數以達到群體最佳化。此外,我們引導出幾個數值對照,比較三個策略何者會產生每單位時間最大期望總淨收益。
最後,我們指出藉由徵收服務費,系統管理者可以控制進入系統的顧客流量到一個最適合系統的情況,也就是所謂的群體最佳化。

For the single-server queue, Naor [1969] showed that the threshold of queue length under social optimization is less than or equal to that under self optimization. In this study, we extend the scope of Naor's research to the system with priority class of service.
We first consider the thresholds of queue length of each class under self optimization. We find that the threshold of the class with higher priority is identical to that of the single-class model considered by Naor [1969]. Besides, we find that the threshold of the low-priority class depends on the number of customers of higher priority class in system.
We next consider the thresholds of queue length of each class under social optimization. We introduce three control policies that the system administrator can select one of these policies to derive maximum expected total net gain and therefore, the system reaches the social optimization by restricting the number of the entering customers. Furthermore, we conduct several numerical comparisons between these policies to see which one yields the maximum expected total net gain per unit time.
Finally we show that by levying tolls, the system administrator can control the flow of the entering customers in the most suitable situation for the system, that is the so-called social
optimization.

Abstract ....................................................1
Chapter 1 Introduction .....................................2
Chapter 2 Preliminary ......................................4
Chapter 3 Self Optimization ................................6
Chapter 4 Social Optimization .............................11
4.1 Administrative Control Policies .......................11
4.2 Comparisons Among Policies ............................17
Chapter 5 Self Optimization v.s. Social Optimization ......31
Chapter 6 Entrance Fee Imposition .........................34
Chapter 7 Conclusions .....................................37
References .................................................39

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