M/M/1算子的复谱  

Complex Spectra of the M/M/1

作　　者：宋世颖 黄婧雪 艾尼·吾甫尔[1] SONG Shi-ying;HUANG Jing-xue;GUPUR Geni(College of Mathematics and Systems Science,Xinjiang University,Urumqi 830017,China)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830017

出　　处：《数学的实践与认识》2023年第10期178-187,共10页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11961062);新疆维吾尔自治区大学生创新项目(S202210755094)。

摘　　要：研究偏微分方程形式的M/M/1排队模型的主算子在左半复平面中的谱,证明集合{γ∈C|R_(γ)≤-(λ+μ)}包含于该模型主算子的连续谱与剩余谱的并集.由此指出偏微分方程形式的M/M/1排队模型和常微分方程形式的M/M/1排队模型的本质区别.This paper studies spectrum of the underlying operator,which corresponds to the M/M/1 queueing model described by partial differential equations,on the left half complex plane and proves that{γ∈C|R_(γ)≤-(λ+μ)}belongs to union of its continuous spectra and residual spectra,thus points out the essential difference between the M/M/1 queueing model described by partial differential equations and the M/M/1 queueing model described by ordinary differential equations.

关 键 词：M/M/1排队模型 谱 特征值 

分 类 号：O226[理学—运筹学与控制论]