摘要
在研究只允许部分服务台进入休假状态的多服务台M/M/c排队系统时,发现了条件Erlang分布的双参数加法性质,进一步研究发现相对应离散随机状态的负二项分布也具有类似的性质。本文证明了当X服从参数(m,p)的负二项分布,Y和Z服从参数为p和θ的几何分布且相互独立时,在X<Z<X+Y条件下,Z的条件分布是参数(m+1,p+θ-pθ)的负二项分布,可称之为条件负二项分布的双参数加法定理;并给出了在X<Z的条件下,X的条件分布是参数(m,p+θ-pθ)的负二项分布。它们对导出复杂排队系统中离散状态下顾客等待时间分布及保险公司中破产概率上界的计算起着重要作用。
We had finded a Erlang distribution biparametri additive theorem under the condition when we study the multi-server vacation M/M/c queue with partial servers vacations.It is similar for Negative binomial distribution under discrete state too.Let X be Negative binomial distribution with parameter,(m,p),Y and Z be geometric distribution with parameter p and θ,X and Y and Z are mutually independent.In this paper,we demonstrate that the conditional distribution of Z is a Negative binomial distribution with parameter(m+1,p+θ-pθ) under the condition X<Z<X+Y.We call this result as biparametric additive theorem of conditional Negative binomial distribution.We also give the conditional distribution of X is Negative binomial distribution with parameter(m,p+θ-pθ) under the condition X<Z.It plays an important role in deriving waiting time distribution in multi-sever queuing systems under discrete state and in calculation Ruin probability.
出处
《河南科技大学学报（自然科学版）》
CAS
2005年第5期77-79,共3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)
关键词
多重休假排队
负二项分布
条件分布
加法定理
Multiple vacations queue
Negative binomial distribution
Conditional distribution
Additive theorem.
作者简介
王增富（1965-）,男,河北邯郸人,高级讲师,硕士生;
田乃硕（1941-）,男,黑龙江巴彦人,教授,博士生导师,研究方向为多重休假排队.
