The Research Of The Model And Application Of Multi-service Window-M/M/3Queuing With Different Range Of Capacity

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.