Point Spectra of the Operator Corresponding to the M/M/1 Queueing Model with Working Vacation and Vacation Interruption
Point Spectra of the Operator Corresponding to the M/M/1 Queueing Model with Working Vacation and Vacation Interruption
投稿时间:2017-10-05  修订日期:2018-08-24
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英文关键词:M/M/1 queueing model,C_0-semigroup, eigenvalue, essential growth bound,essential spectral bound
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作者单位E-mail
艾合买提·卡斯木 新疆大学 ehmetkasim@163.com 
艾尼·吾甫尔 新疆大学  
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英文摘要:
      In this paper, we consider point spectra of the operator which corresponding to the M/M/1 queueing model with working vacation and vacation interruption. we will find that the operator has uncountable real eigenvalues and these results describe the point spectrum of the operator. Then, we show that the essential growth bound of the C_0-semigroup generated by the operator is 0 and therefore it is not quasi compact, the essential spectral bound of the C_0-semigroup is equal to 1. Moreover, our results imply it is impossible that the time-dependent solution of the model exponentially converges to its steady-state solution.
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