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On existence and asymptotic behavior of the time-dependent solution of the M/G/1 queueing model with optional deterministic server vacations

  • Ehmet KasimEmail author
  • Geni Gupur
Article
  • 11 Downloads

Abstract

In this paper, we consider the M/G/1 queueing model with optional deterministic server vacations. Firstly, we convert the system into an abstract Cauchy problem, then we prove well-posedenss of the system by using the operator semigroup methods. Next, we investigate asymptotic behavior of its time-dependent solution by studying spectral properties of the corresponding operator. Therefore, we conclude that the time-dependent solution of the model strongly converges to its steady-state solution.

Keywords

M/G/1 queueing model with optional deterministic server vacations \(C_0\)-semigroup Dispersive operator Resolvent set Eigenvalue 

Mathematics Subject Classification

60K25 47D03 47A10 

Notes

Acknowledgements

The authors would like to express their sincere thanks to the anonymous referees and associated editor for his/her careful reading of the manuscript. The author’ research work was supported by the National Natural Science Foundation of China (no: 11801485).

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Copyright information

© African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2019

Authors and Affiliations

  1. 1.College of Mathematics and Systems ScienceXinjiang UniversityUrumqiPeople’s Republic of China

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