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