Spectrum of the Operator Corresponding to the M/M/1 Queueing Model with Vacations and Multiple Phases of Operation and Application

作     者：Nurehemaiti YIMING Geni GUPUR Nurehemaiti YIMING;Geni GUPUR

作者机构：College of Mathematics and Systems ScienceXinjiang UniversityUrumqi 830046P.R.China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2020年第36卷第10期

页      面：1183-1202页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070105[理学-运筹学与控制论] 0701[理学-数学] 

基　　金：the National Natural Science Foundation of China (Grant No. 11961062) 

主　　题：M/M/1 queueing model with vacations and multiple phases of operation time-dependent solution C0-semigroup point spectrum spectrum 

摘      要：We describe the point spectrum of the operator which corresponds to the M/M/1 queueing model with vacations and multiple phases of *** by using this result we prove that the essential growth bound of the C0-semigroup generated by the operator is 0,the C0-semigroup is not compact,not eventually compact,even not ***,we verify that it is impossible that the time-dependent solution of the M/M/1 queueing model with vacations and multiple phases of operation exponentially converges to its steady-state *** addition,we obtain the spectral radius and essential spectral radius of the ***,we discuss other spectrum of the operator and obtain a set which belongs to the union of its continuous spectrum and residual spectrum.