系统工程理论与实践
繫統工程理論與實踐
계통공정이론여실천
Systems Engineering—Theory & Practice
2013年
4期
996~1005
,共null页
离散时间Geo;G;1排队 延迟D-策略 全概率分解技术 队长分布 随机分解 系统容量的优化设计
離散時間Geo;G;1排隊 延遲D-策略 全概率分解技術 隊長分佈 隨機分解 繫統容量的優化設計
리산시간Geo;G;1배대 연지D-책략 전개솔분해기술 대장분포 수궤분해 계통용량적우화설계
discrete-time Geo/G/1 queue; delayed D-policy; total probability decomposition technique;queue length distribution; stochastic decomposition; system capacity optimum design
考虑延迟D-策略离散时间Geo／C／1排队系统，使用全概率分解技术，从任意初始状态出发，研究了队长的瞬态和稳态性质，推导出了在任意时刻n＋瞬态队长分布的z＋变换的递推表达式和稳态队长分布的递推表达式，并获得稳态队长的随机分解结果，同时得到了系统在三种任意时刻（n-，n，n＋）处稳态队长分布的重要关系．最后，通过数值实例，讨论了稳态队长分布对系统参数的敏感性，并阐述了获得便于计算的稳态队长分布的表达式在系统容量优化设计中的重要应用价值．
攷慮延遲D-策略離散時間Geo／C／1排隊繫統，使用全概率分解技術，從任意初始狀態齣髮，研究瞭隊長的瞬態和穩態性質，推導齣瞭在任意時刻n＋瞬態隊長分佈的z＋變換的遞推錶達式和穩態隊長分佈的遞推錶達式，併穫得穩態隊長的隨機分解結果，同時得到瞭繫統在三種任意時刻（n-，n，n＋）處穩態隊長分佈的重要關繫．最後，通過數值實例，討論瞭穩態隊長分佈對繫統參數的敏感性，併闡述瞭穫得便于計算的穩態隊長分佈的錶達式在繫統容量優化設計中的重要應用價值．
고필연지D-책략리산시간Geo／C／1배대계통，사용전개솔분해기술，종임의초시상태출발，연구료대장적순태화은태성질，추도출료재임의시각n＋순태대장분포적z＋변환적체추표체식화은태대장분포적체추표체식，병획득은태대장적수궤분해결과，동시득도료계통재삼충임의시각（n-，n，n＋）처은태대장분포적중요관계．최후，통과수치실례，토론료은태대장분포대계통삼수적민감성，병천술료획득편우계산적은태대장분포적표체식재계통용량우화설계중적중요응용개치．
This paper considers the discrete-time Geo/G/1 queueing system with delayed D-policy. By using the total probability decomposition technique, we study the transient and equilibrium properties of the queue length from the beginning of the any initial state, obtain both the recursion expressions of the z-transformation of the transient queue length distribution at any time n＋ and the recursion expressions of the steady state queue length distribution, and then we give the stochastic decomposition of the queue length in equilibrium. The important relations between the steady state queue length distributions at different epochs （n , n, n＋） are discovered. Finally, by numerical examples we discuss the sensitivity of the steady state queue length distribution towards system parameters and illustrate the important value of the expressions of the steady state queue length distribution for calculating conveniently in the system capacity design.
