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 

机构地区：[1]College of Mathematics and Systems Science,Xinjiang University,Urumqi 830046,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2020年第10期1183-1202,共20页数学学报（英文版）

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

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 operation.Then 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 quasi-compact.Moreover,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 solution.In addition,we obtain the spectral radius and essential spectral radius of the C0-semigroup.Lastly,we discuss other spectrum of the operator and obtain a set which belongs to the union of its continuous spectrum and residual spectrum.

关 键 词：M/M/1 queueing model with vacations and multiple phases of operation time-dependent solution C0-SEMIGROUP point spectrum SPECTRUM 

分 类 号：O226[理学—运筹学与控制论]