带灾难的二维M^(X)/M/1排队模型  

The Two-dimensional M^(X)/M/1 Queueing Model with Catastrophes

作　　者：李俊平[1] Li Junping(School of Mathematics and Statistics,Central South University,Changsha 410083,China)

机构地区：[1]中南大学数学与统计学院,长沙410083

出　　处：《数学理论与应用》2020年第1期66-76,共11页Mathematical Theory and Applications

基　　金：国家自然科学基金项目(No.11771452,No.11971486);湖南省自然科学基金项目(No.2020JJ4674)资助。

摘　　要：本文考虑一类带灾难的二维M^(X)/M/1排队模型,给出其有效灾难首次发生时间的概率密度函数的Laplace变换的精确表达式,以及有效灾难首次发生时间的数学期望和方差及其渐近性质.In this paper we consider the two-dimensional M^(X)/M/1 queueing model with catastrophes.The Laplace transform of the probability density function of the first occurrence time of effective catastrophes is obtained explicitly,and the mathematical expectation and variance of the first occurrence time of effective catastrophes as well as their asymptotic properties are derived.

关 键 词：二维M^(X)/M/1排队模型 有效灾难 渐近性质 

分 类 号：O226[理学—运筹学与控制论]