Point Spectra of the Operator Corresponding to the M/M/1 Queueing Model with Working Vacation and Vacation Interruption  

作　　者：Ehmet KASIM Geni GUPUR 

机构地区：[1]College of Mathematics and Systems Science, Xinjiang University

出　　处：《Journal of Mathematical Research with Applications》2019年第1期75-88,共14页数学研究及应用（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant No.11801485)

摘　　要：In this paper, we consider point spectra of the operator corresponding to the M/M/1 queueing model with working vacation and vacation interruption. We prove that the underlying operator has uncountable eigenvalues on the left real line and these results describe the point spectra 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.In this paper, we consider point spectra of the operator corresponding to the M/M/1 queueing model with working vacation and vacation interruption. We prove that the underlying operator has uncountable eigenvalues on the left real line and these results describe the point spectra 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.

关 键 词：M/M/1 QUEUEING model working VACATION and VACATION INTERRUPTION C0-SEMIGROUP EIGENVALUE essential spectral bound 

分 类 号：O1[理学—数学]