M/M/2Queuing Model With Variable Input、Wrong Service And Different Ability Of The Windows

Liu Chuanlai study the M/M/2queuing model with different ability of the windows in theliterature [1];Tai Wenzhi and Gao Shize study the M/M/1queuing model with variable inputrate in the literature [4];Hou Dongqian and Gao Shize discuss the M/M/2queuing model withability of the windows and variable service rate in the literature [6].They get K’s equations bythe state transition graph according to the regularity, finally find the steady distribution andthe main specifications of the system size.First of all, combining the actual situation, this paper extend the M/M/2queuing modelwith different ability of the windows in the literature [1] to M/M/2queuing model withvariable input and different ability of the windows. Suppose that The longer the system, thesmaller the probability of customers to join the system, consider the probability is k (0k1)and when k, k0,the queue length is k,when k2， k=1.Disscuss the2situation of1kkand b kk (0b1),get the steady distributionand the main specifications of the system size.Second, this paper discuss the M/M/2queuing model with wrong service and differentability of the windows. Suppose that The longer the system, the larger the probability ofwrong service. consider the right probability of service is k (0k1)，kkka1, a1and is real number. Consider that when k2, k1.As a result of all the above situation, discuss the M/M/2queuing model with variableinput、wrong service and different ability of the windows. According to the state transitiongraph and K’s equations, find the steady distribution and the main specifications of thesystem size.The main innovation of this paper is extend the M/M/2queuing model with different ability of the windows in the literature [1] to M/M/2queuing model with variable input、wrong service and different ability of the windows. Then get K’s equations by the statetransition graph according to the regularity, steady distribution and the main specifications ofthe system. When b=1, this model is verified by the literature [1], and this model is moregeneral.