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

论文摘要

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 C0-semigroup generated by the operator is 0 and therefore it is not quasi compact, the essential spectral bound of the C0-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.

论文目录

文章来源

类型: 期刊论文

作者: Ehmet KASIM,Geni GUPUR

来源: Journal of Mathematical Research with Applications 2019年01期

年度: 2019

分类: 基础科学

专业: 数学

单位: College of Mathematics and Systems Science, Xinjiang University

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

分类号: O226

页码: 75-88

总页数: 14

文件大小: 193K

下载量: 15

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