条件Γ-分布的单参数加法定理的推广  

Extension of Parametric Additive Theorem of Conditional Γ-distribution

作　　者：王增富[1] 田乃硕[2] 

机构地区：[1]燕山大学继续教育学院,河北秦皇岛066004 [2]燕山大学理学院,河北秦皇岛066004

出　　处：《河南科技大学学报（自然科学版）》2005年第2期76-78,i006,共4页Journal of Henan University of Science And Technology:Natural Science

基　　金：国家自然科学基金资助项目(10271102)

摘　　要：在研究只允许部分服务台进入休假状态的多服务台MMc排队系统时,发现了条件Erlang分布的双参数加法性质,进一步研究发现它对Γ分布也成立。设X(α)和Y(β)服从参数(α,λ)和(β,μ)的Γ分布,且相互独立,证明了在X(α)<Y(β)<X(α+1)条件下,Y(β)的条件分布是(α+β,λ+μ)参数的Γ分布,并称这一结果是条件Γ分布的双参数加法定理。它对导出复杂排队系统中顾客等待时间分布起着重要作用。An Erlang distribution biparametric additive theorem under the condition is found when the multi-server vacation M/M/c queue with partial servers vacations is studied.It is also the case with Γ-distribution.Let and be ~Γ-distribution with parameter and,and are mutually independent.It is proved that the conditional distribution of is a Γ-distribution with parameter under the condition,which is called biparametric additive theorem of conditional ~Γ-distribution .It plays an important role in deriving waiting time distribution in multi-sever queuing systems.

关 键 词：Г-分布 加法定理 单参数 ERLANG分布 等待时间分布 排队系统 多服务台 相互独立 条件分布 双参数 休假 

分 类 号：O211.3[理学—概率论与数理统计] TN011[理学—数学]