| 带启动期的M^[x]／M／1／SWV排队系统 |
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| 引用本文： | 曹学云,徐秀丽,李沛.带启动期的M^[x]／M／1／SWV排队系统[J].山东大学学报(自然科学版),2011(7):116-123. |
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| 作者姓名： | 曹学云 徐秀丽 李沛 |
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| 作者单位： | 燕山大学理学院,河北秦皇岛066004 |
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| 基金项目： | 国家自然科学基金资助项目（10671170）;河北省自然科学基金资助项目（F2008000864） |
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| 摘 要： | 针对连续时间带启动期成批到达M^x]／M／1单重工作休假排队系统，建立了模型的三维Markov链，并给出了稳态队长的母函数及其随机分解。利用条件Erlang分布的双参数加法定理，得到了Laplace变换序下的稳态等待时间的上下界以及平均队长、平均等待时间的上下界、平均逗留时间等性能指标。最后通过数值实例验证了所得出的结论。
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| 关 键 词： | 单重工作休假排队 启动期 成批到达 随机分解 Laplace变换序 |
The M^[x]/M/1/SWV queue with start-up time |
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| CAO Xue-yun,XU Xiu-li,LI Pei.The M^[x]/M/1/SWV queue with start-up time[J].Journal of Shandong University(Natural Science Edition),2011(7):116-123. |
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| Authors: | CAO Xue-yun XU Xiu-li LI Pei |
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| Institution: | (College of Science, Yanshan University, Qinhuangdao 066004, Hebei, China) |
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| Abstract: | A batch arrival M^X]/M/1 with start-up time and single working vacations is considered. A model of a three- dimensional Markov chain is established. Then, the PGF and the stochastic decomposition of the stea-dy-state are given. The two parameters addition theorem of condition Erlang distribution are obtained, with which the upper and lower bounds of steady-state waiting time is given under Laplace transform order. The mean queue length, the mean waiting time of the upper and lower bounds, and the mean sojourn time are also given. Finally, some numerical examples to verify the conclusions are presented. |
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| Keywords: | single working vacations start-up period batch arrival stochastic decomposition Laplace transform order |
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