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.
M/G/1 queueing model with optional deterministic server vacations \(C_0\)-semigroup Dispersive operator Resolvent set Eigenvalue
Mathematics Subject Classification
60K25 47D03 47A10
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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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