J4 ›› 2011, Vol. 46 ›› Issue (7): 116-123.
• 数学 • 上一篇 下一篇
曹学云,徐秀丽,李沛
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基金资助:
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)
CAO Xue-yun, XU Xiu-li, LI Pei
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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。
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
Abstract:
A batch arrival M［X］／M／1 with start-up time and single working vacations is concerned. A model of three-dimensional Markov chain is established. Then, the PGF and the stochastic decomposition of stea-dy-state are given. The two parameters addition theorem of condision Erlang distribution is obtained, with which the upper and lower bounds of steadystate waiting time is given under Laplace transform order. The mean queue length, the mean waiting time of the upper and lower bounds, the mean sojourn time are also given. Finally, some numerical examples to verify the conclusions.
Key words: single working vacations; start-up period; batch arrival; stochastic decomposition; Laplace transform order
曹学云,徐秀丽,李沛. 带启动期的M［x］／M／1／SWV排队系统[J]. J4, 2011, 46(7): 116-123.
CAO Xue-yun, XU Xiu-li, LI Pei. The M［X］／M／1／SWV queue with start-up time[J]. J4, 2011, 46(7): 116-123.
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