論文摘要

對可控制之排隊系統而言，「忙碌週期」是一個很重要的系統特徵數。本文研究主要針對可控制 M/G/1 系統之「忙碌週期」做一些統計推論探討及比較分析研究。所謂「<p,N>方策」是指一排隊系統，其運作方式具下列特性：(1)、當系統中沒有任何顧客在排隊時，其服務站就自動關閉。(2)、當系統中服務站是處於關閉狀態中，並於系統中顧客排隊人數達N人時，其服務站會啟動的機率為 ，而會繼續關閉的機率為 。(3)、其他狀況下，系統中服務站是不會自關閉狀態中啟動的。
本論文研究分為四大部分。
第一部分，我們對「服務站」在閒置期間採<p,N>方策之可控制 M/G/1 系統的「期望忙碌週期」(用 來表示)，提出一個估計式。文中我們證明此一估計式具有強烈一致性的性質，且由擬研究的結果，顯示我們所提出之估計式確實為 的一個一致性估計式，並且很合乎理論上的結論。
第二部分，我們使用此一個估計式，並利用五種bootstrap方法來建立有關 的新式信賴區間。執行另一個數據模擬研究，來描述所提出的五種bootstrap信賴區間之特性。
第三部分，我們利用覆蓋百分比( coverage percentage )及相對覆蓋( relative coverage )二種衡量指標，來研究比較五種bootstrap信賴區間的準確性。
第四部分，我們使用因子設計分析方法來對 做敏感度分析。我們研究四個影響 的重要因子，使用24 因子實驗設計分析方法來對 做敏感度分析。藉由變異數分析的結果，我們找到<p,N>方策之可控制 M/G/1 系統中，影響 的主要作用及交互作用的系統參數。

Abstract

Busy period is an important system characteristic for the controllable queueing systems. This study mainly for the controllable M/G/1 systems with <p,N>-policy (bicriterion policy) performs some statistically inference and comparative analysis of the busy period. An operating policy is called a <p,N>-policy if it prescribes the following conditions: (i) turn the server off when the system becomes empty, (ii) if the server is off and the number of customers in the system reaches the predetermined threshold N, then turn the server on with probability p and leave the server off with probability (1-p), (iii) do not turn the server on at other epochs.
This thesis is divided into four major parts.
Firstly, we propose an estimator for the expected busy period (denoted by ) of a controllable M/G/1 queueing system in which the server applies a bicriterion <p,N> policy during his idle period. We show that this estimator is a strongly consistency estimator. From the simulation results, we show that the proposed estimator is a consistent estimator for , which agrees with the theoretical results.
Secondly, using this estimator, we construct new confidence intervals for , which are based on five bootstrap methods. Another a numerical simulation study is conducted in order to demonstrate performance of the proposed bootstrap confidence intervals for .
Thirdly, we investigate the accuracy of the five bootstrap confidence intervals by calculating the coverage percentage and the relative coverage.
Fourthly, we present a sensitivity investigation of the by means of a factorial design statistical analysis. We studies the effect of four important factors (parameters) on . A 24 factorial experimental design is used to evaluate the sensitivity analysis of parameters on the . Based on the analysis of variance, we find the main effect and interaction effect of the significant factors on the system characteristics.

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