高校应用数学学报A辑
高校應用數學學報A輯
고교응용수학학보A집
APPLIED MATHEMATICS A JOURNAL OF CHINESE UNIVERSITIES
2010年
1期
27-37
,共11页
离散时间排队%多级适应性休假%Bernoulli反馈%队长分布%随机分解
離散時間排隊%多級適應性休假%Bernoulli反饋%隊長分佈%隨機分解
리산시간배대%다급괄응성휴가%Bernoulli반궤%대장분포%수궤분해
discrete-time queue%multiple adaptive vacation%Bernoulli feedback%queue-length distribution%stochastic decomposition
考虑带有Bernoulli反馈的多级适应性休假的Geo/G/1离散时间排队系统,通过引入服务员忙期和使用一种简洁的分解方法,讨论了队长的瞬时分布,得到了在任意时刻n队长为j的概率关于时刻n的z-变换的递推式,及队长平稳分布的递推式,且证明了稳态队长的随机分解性质.最后,给出了在特殊情形下相应的一些结果和数值计算实例.
攷慮帶有Bernoulli反饋的多級適應性休假的Geo/G/1離散時間排隊繫統,通過引入服務員忙期和使用一種簡潔的分解方法,討論瞭隊長的瞬時分佈,得到瞭在任意時刻n隊長為j的概率關于時刻n的z-變換的遞推式,及隊長平穩分佈的遞推式,且證明瞭穩態隊長的隨機分解性質.最後,給齣瞭在特殊情形下相應的一些結果和數值計算實例.
고필대유Bernoulli반궤적다급괄응성휴가적Geo/G/1리산시간배대계통,통과인입복무원망기화사용일충간길적분해방법,토론료대장적순시분포,득도료재임의시각n대장위j적개솔관우시각n적z-변환적체추식,급대장평은분포적체추식,차증명료은태대장적수궤분해성질.최후,급출료재특수정형하상응적일사결과화수치계산실례.
This paper considers a discrete-time Geo/G/1 queue with multiple adaptive vacations and Bernoulli feedback. By introducing the server busy period and using a concise decomposition method, the transient distribution of the queue length is studied. Both the recursion expression of the z-transform about epoch n of the probability that the queueing length equals to j at any epoch n and the recursion formulae of the stationary distribution for the queue length are obtained. The stochastic decomposition property of steady-state queue length has been proved. Finally, some corresponding results and numerical examples under special cases are also given.
