【作者】 陈媛媛；

【导师】 高世泽；

【作者基本信息】 重庆师范大学 ， 系统理论， 2012， 硕士

【摘要】 陆传赉在文献[1]中提出了窗口能力不等的多服务窗M/M/n排队模型.在该模型中，假定顾客陆续到达，且他们之间的间隔时间服从参数为λ的指数分布.各服务窗对顾客服务的时间分别服从参数是μi的指数分布，其中下标i表示第i个服务窗.顾客到达系统的时间间隔与顾客接受服务的时间是相互独立的.在文献[1]中，作者只对模型中服务窗个数n=2的情形进行了研究，并运用系统状态转移图得到了K氏方程组.通过把正则性与K氏方程组相结合，得到了系统队长的平稳分布及各项指标.本文最重要的创新之处是推广了文献[1]的模型，将窗口的个数n=2推广到n=3，讨论了窗口能力不等的多服务窗M/M/3排队模型.本文运用系统状态转移图得到了K氏方程组，再通过把正则性与K氏方程组相结合，得到了系统队长的平稳分布及各项指标.同时通过在模型中令μ1=μ2=μ3=μ，φ1=φ2=φ3=1/3，获得了与多服务窗等待制排队模型M/M/3完全相同的结果.这一方面说明本文结果也是多服务窗等待制M/M/n模型的推广，另一方面也在一定程度上验证了本文结果的正确性.最后通过举例说明了该模型在生活实际中的应用并根据模型结果得到了实例的各项指标.更多还原

【Abstract】 Lu Chuanlai once put forward the model of multi-service window-M/M/3queuing with different range of capacity in literature[1]. This model assumed that theinterval between the customers’ arrival obeyed parameters forλof exponentialdistribution; the service time of each window for customers obeyed parameters forμiof exponential distribution and the “i” stands for the number of the servicewindow. The interval between customers’ arrival at the system and the service timeare independent. In the literature[1], the author only had a research on the case thatthe number of the service window was two, that is “n=2”, and got the K’s equationsthrough the system state transition diagram. It got the stationary distribution and theindexes of the queuing length through the combination of K’s equations andregularity.In this paper, the most important innovation is to promote the model of theliterature[1]: the number of the window from2to3, that is “n=2” to “n=3”;discussing the model of the multi-service window-M/M/3queuing. In the paper, ituses the system state transition diagram to get the K’s equations and it gets thestationary distribution and the indexes of the queuing length through the combinationof the K’s equations and regularity. At the same time, it gets the same result as themodel of multi-service window-M/M/3waiting-queuing through settingμ1=μ2=μ3=μ, φ1=φ2=φ3=1/3in the model. On one hand, it indicatesthat it is the promotion of the model of multi-service window-M/M/nwaiting-queuing in the paper; on the other hand, it also checks, to some extent, theveracity of the result in the paper. Finally, it shows the application of the model inreal life through the examples and it gets the indexes of the examples through theresult of the model.更多还原