运筹学学报 >
2021 , Vol. 25 >Issue 4: 15 - 30
DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2021.04.002
两类具有N-策略和单重休假的M/G/1排队系统的最优控制策略
收稿日期: 2020-01-31
网络出版日期: 2021-12-11
基金资助
国家自然科学基金(71571127)
Optimal control strategies for two types of M/G/1 queueing systems with N-strategy and single vacation
Received date: 2020-01-31
Online published: 2021-12-11
唐蓓蕾, 唐应辉 . 两类具有N-策略和单重休假的M/G/1排队系统的最优控制策略[J]. 运筹学学报, 2021 , 25(4) : 15 -30 . DOI: 10.15960/j.cnki.issn.1007-6093.2021.04.002
This paper considers two types of M/G/1 queueing systems with N-strategy and single vacation, one of which is uninterruptible on vacation and the other is of interruptible on vacation. Using the stochastic decomposition of the steady-state queue length, the expressions of the probability generating function of the steady-state queue length are obtained. And the sensitivity of the system's idle rate and the additional average queue-length towards system parameters is discussed. Furthermore, the explicit expressions of the long-run expected cost per unit time are derived under a given cost structure. At the same time, numerical calculation examples are used to determine the control strategy N* for minimizing the long-run expected cost per unit time as well as the combined control strategy (N*, T*) when the vacation time is fixed duration T.
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