| 具有不同到达率的带有启动时间的多级适应性休假M^ξ／G／1排队模型 |
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| 引用本文： | 孙微,;李世勇,;田乃硕.具有不同到达率的带有启动时间的多级适应性休假M^ξ／G／1排队模型[J].运筹学杂志,2007(1):55-65. |
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| 作者姓名： | 孙微 ;李世勇 ;田乃硕 |
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| 作者单位： | [1]燕山大学信息科学与工程学院,秦皇岛066004; [2]燕山大学理学院,秦皇岛066004 |
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| 基金项目： | This research is supported by National Science Foundation of China（No. 10271102）. |
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| 摘 要： | 本文研究具有不同到达率的带有启动时间的多级适应性休假M^ξ/G/1排队模型，应用嵌入马尔可夫链方法推导出了稳态队长和等待时间（先到先服务规则）分布，并验证了稳态队长和稳态等待时间具有随机分解性，而且给出了忙期分布．许多关于M^ξ/G/1的排队模型都可以看作是此模型的特例．
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| 关 键 词： | 运筹学 多级适应性休假 嵌入马尔可夫链 随机分解 到达率 启动时间 |
The Queue M^ξ/G/1 with Different Arrival Rates on the Multiple Adaptive Vacations and Setup Times |
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| Institution: | Sun Wei,Li Shiyong, Tian Naishuo(College of Information Science and Engineering, Yanshan University, Qinhuangdao 066004, China; College of Science, Yanshan University, Qinhuangdao 066004, China) |
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| Abstract: | In this paper, we discuss the queue M^ξ/G/1 with different arrival rates on the multiple adaptive vacations and setup times. We derive the probability generating function （p.g.f.）of the steady-state queue length by the method of embedded Markov chain and the Laplace-Stieltjes transform （LST）of the steady-state waiting time （FCFS）. From the results, we obtain the conclusion that the steady-state queue length and waiting time have the property of stochastic decomposition. And we also get the LST of busy period and give several special cases. Many discussed models as to M^ξ/G/1 are special cases of the model. |
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| Keywords: | Operations research multiple adaptive vacations embedded Markov chain stochastic decomposition arrival rates setup times |
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