系统工程理论与实践
繫統工程理論與實踐
계통공정이론여실천
Systems Engineering—Theory & Practice
2015年
3期
799~810
,共null页
离散时间排队 min（N,V）一策略 多重休假 队长分布 系统容量设计
離散時間排隊 min（N,V）一策略 多重休假 隊長分佈 繫統容量設計
리산시간배대 min（N,V）일책략 다중휴가 대장분포 계통용량설계
discrete-time queue; min（N, V）-policy; multiple server vacations; queue-length distribution; system capacity design
摘要考虑服务员具有多重休假和系统采用min（N，V）-策略控制的离散时间Ceo／C／1排队系统，使用全概率分解技术和更新过程理论，研究了系统在任意时刻n^＋的瞬态队长分布和稳态队长分布，得到了瞬态队长分布的z-变换表达式和稳态队长分布的递推表达式．进一步，得到了系统在时刻点n，n^-和外部观察时刻点的稳态队长分布．特别地，本文直接获得了一些特殊离散时间排队系统相应的结果．最后，通过数值实例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设计中的重要价值．
摘要攷慮服務員具有多重休假和繫統採用min（N，V）-策略控製的離散時間Ceo／C／1排隊繫統，使用全概率分解技術和更新過程理論，研究瞭繫統在任意時刻n^＋的瞬態隊長分佈和穩態隊長分佈，得到瞭瞬態隊長分佈的z-變換錶達式和穩態隊長分佈的遞推錶達式．進一步，得到瞭繫統在時刻點n，n^-和外部觀察時刻點的穩態隊長分佈．特彆地，本文直接穫得瞭一些特殊離散時間排隊繫統相應的結果．最後，通過數值實例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設計中的重要價值．
적요고필복무원구유다중휴가화계통채용min（N，V）-책략공제적리산시간Ceo／C／1배대계통，사용전개솔분해기술화경신과정이론，연구료계통재임의시각n^＋적순태대장분포화은태대장분포，득도료순태대장분포적z-변환표체식화은태대장분포적체추표체식．진일보，득도료계통재시각점n，n^-화외부관찰시각점적은태대장분포．특별지，본문직접획득료일사특수리산시간배대계통상응적결과．최후，통과수치실례천술료획득편우계산적은태대장분포적표체식재계통용량설계중적중요개치．
In this paper, we consider a discrete-time Geo/G/1 queueing system in which the server takes multiple vacations and the system adopts rain（N, V）-policy. By using the total probability decomposition technique and renewal process theory, we study the transient and steady distributions of the queue length and obtain both the expression of the z-transformation of the transient distribution and the recursion expression of the steady distribution at arbitrary time epoch n＋. Furthermore, we obtain the steady distribution of the queue length at time epoch n, n-, and outside observer＇s time epoch, respectively. Especially, some corresponding results under special cases are directly given by our results obtained in this paper. Finally, by numerical examples we illustrate the important application value of the expression of the steady state queue-length distribution for calculating conveniently in the system capacity design.
