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.
出处
《河南科技大学学报（自然科学版）》
CAS
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)
