第二种服务可选的M/M/1排队模型的主算子的点谱  

On the Point Spectrum of the Operator Associated with the M/M/1 Queueing Model with Optional Second Service

作　　者：买哈巴.乃扎木 艾尼.吾甫尔[1] NAIZHAMU Maihaba;GUPUR Geni(College of Mathematics and Systems Science,Xinjiang University,Urumqi 830046,China)

机构地区：[1]新疆大学数学与系统科学学院,乌鲁木齐830046

出　　处：《应用泛函分析学报》2019年第1期8-34,共27页Acta Analysis Functionalis Applicata

基　　金：国家自然科学基金(11371303)

摘　　要：当顾客的到达率λ,第一种服务的服务率μ_1,第二种服务的服务率μ_2,顾客选择第二种服务的概率θ满足μ_1(1-θ)>λ,μ_2>λ时,证明第二种服务可选的M/M/1排队模型的主算子的点谱包含区间(-λ,0).由此推出:(i)该模型的主算子生成的C_0-半群不是拟紧算子.(ii)该模型的时间依赖解不可能指数收敛于其稳态解.We prove that if the arrival rate of customers λ, the service rate of the first essential service μ1, the service rate of the second optional service μ2 and the probabilityθ that customers opt the second optional service satisfy μ1(1-θ)>λ,μ2 >λ,then the point spectrum of the generator of the Co-semigroup associated with the M/M/1 queueing model with optional second service contains the interval(-λ, 0). From this we verify:(i) the Co-semigroup is not quasi-compact,(ii) it is impossible that the time-dependent solution of the M/M/1 queueing model with optional second service converges exponentially to its steady-state solution.

关 键 词：第二种服务可选的M/M/1排队模型 点谱 C0-半群 

分 类 号：O177.7[理学—数学]