On M/M/n/m Queuing Model With The Different Ability Of The Windows And Variable Input Rate

In the reference one Lu Chuanlai researches the M/M/1 queuing model with variable input rate, and in reference two Chen Yuanyuan discusses the M/M/3 queuing model with the different ability of windows, and also the M/M/n queuing model with the different ability of windows and variable input rate and variable service rate is studied in reference seven. Among these references, the system capacity is assumed to be infinite.Considering the system capacity for m, this paper primarily proposed and studied two queuing models, which are M/M/2/m queuing model and M/M/3/m queuing model with the different ability of the windows and variable input rate. The analysis obtains the K’s algebraic equations in a balance state on the basis of state diagram, and gets a stable distribution of two queuing models and a series of main targets with the solution of equations. Given that with the increase of queue length, the probability of customer join the system might decease, and supposing that the probability is α_k(0<(α_k)<1). This paper discusses the situation ofα_k=1/(k+1)(k+2) And α_k=1/1+1nk with appointing that k<2 And α_k=1. So it is clearly that when k approaches to the infinity, theka will heads toward zero. In the end, this paper illustrates two models in the realistic life, and gets every main targets of examples on the basis of the results of models.In this paper, the most important innovation is to consider the system capacitym is infinite in the queuing model with the different ability of windows and the changeable situations with the input rate α_k following the change of k. And some results are obtained in this paper.