The Research Of Two Kind Of M/M/1 Queuing Model With Variable Input Rate And Aplication

Customers are frequently seen in our daily life hesitating about joining the long queue when they find so many people waiting in the line in front of the service desk. Generally speaking, the probability for customers joining the queue changes with the length of it. when k→∞, the probabilityαk→0. Lu Chuanlai discussed the probability ofαk = 1/( k+ 1) andαk = 1/( k + 1)( k+ 2)in article [1]. This paper, by discussing the two kind of M/M/1 queuing model when the customers arrived entering this queuing system by the probability ofαk = 1/(βk+ 1) (hereβ≥0 for constant)andαk = a-k (here a >1for constant),has established the corresponding mathematical model separately, aims at getting the stable distribution and the related indexes of this two modal, and thus extends the application of the results in reference [1]. In addition, the article also has carried out the empirical analysis to the situation ofαk = 1/(βk+ 1).