Asymptotic Behavior of the Time-Dependent Solution of the M/G/1 Queueing Model with Second Optional Service

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Abstract

By studying the spectral properties of the underlying operator corresponding to the M / G / 1 queueing model with second optional service, we obtain that the time-dependent solution of the model strongly converges to its steady-state solution. We also show that the time-dependent queueing size at the departure point converges to the corresponding steady-state queueing size at the departure point.

Keywords

The M / G / 1 queueing model with second optional service  Eigenvalue Resolvent set 

Mathematics Subject Classification

47A10 60K25 
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Notes

Acknowledgments

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 Natural Science Foundation of Xinjiang (No: 2015211C279).

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Copyright information

© Malaysian Mathematical Sciences Society and Universiti Sains Malaysia 2015

Authors and Affiliations

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

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