系统工程理论与实践
繫統工程理論與實踐
계통공정이론여실천
Systems Engineering—Theory & Practice
2012年
7期
1494~1500
,共null页
离散时间排队 负顾客 反馈 拟生灭链 随机分解
離散時間排隊 負顧客 反饋 擬生滅鏈 隨機分解
리산시간배대 부고객 반궤 의생멸련 수궤분해
discrete-time queue; negative customer; feedback; quasi birth-death chain; stochastic decomposition
综合利用离散补充变量法、矩阵几何解及拟生灭链的方法研究了带有负顾客及伯努利反馈的Geo／Geo／1多重工作休假排队系统．首先运用离散补充变量方法得到了此复杂系统的转移概率矩阵．其次，再利用矩阵几何解及拟生灭链的技术通过解方程组获得了队长的稳态分布、平均队长及稳态队长的随机分解结果．最后，通过引入数值例子，作出了系统的二维图形，进而可以更直观地分析一些参数对系统性能的影响．
綜閤利用離散補充變量法、矩陣幾何解及擬生滅鏈的方法研究瞭帶有負顧客及伯努利反饋的Geo／Geo／1多重工作休假排隊繫統．首先運用離散補充變量方法得到瞭此複雜繫統的轉移概率矩陣．其次，再利用矩陣幾何解及擬生滅鏈的技術通過解方程組穫得瞭隊長的穩態分佈、平均隊長及穩態隊長的隨機分解結果．最後，通過引入數值例子，作齣瞭繫統的二維圖形，進而可以更直觀地分析一些參數對繫統性能的影響．
종합이용리산보충변량법、구진궤하해급의생멸련적방법연구료대유부고객급백노리반궤적Geo／Geo／1다중공작휴가배대계통．수선운용리산보충변량방법득도료차복잡계통적전이개솔구진．기차，재이용구진궤하해급의생멸련적기술통과해방정조획득료대장적은태분포、평균대장급은태대장적수궤분해결과．최후，통과인입수치례자，작출료계통적이유도형，진이가이경직관지분석일사삼수대계통성능적영향．
Applying the discrete supplementary variables method, matrix-geomertic solution and quasibirth-death technique, we investigate a discrete time Geo/Geo/1 queue system with negative customer, Bernoulli feedback and multiple working vacations. Firstly, by applying the discrete supplementary variable technique, we give the transition probability matrix of this complex system. Secondly, using the matrix-geometric solution and quasi birth-death technique and solving equation sets, we get the equilibrium distributions for the number of customers, the average number of customers and the stochastic decomposition of the steady-state queue length. Finally, by presenting the numerical examples, we make some two-dimensinal graphs, which help us to intuitively analyze the influence of parameters on the system performance.
