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Spectrum of the Operator Corresponding to the M/M/1 Queueing Model with Vacations and Multiple Phases of Operation and Application 被引量:1
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作者 Nurehemaiti YIMING Geni GUPUR 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2020年第10期1183-1202,共20页
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... 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. 展开更多
关键词 M/M/1 queueing model with vacations and multiple phases of operation time-dependent solution C0-SEMIGROUP point spectrum SPECTRUM
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