The M/M/n Queuing System With Variable Input Rate Of Impatient Customers

Lu Chuan-lai studied the M / M/1 queuing system with variable input rate when the new customer join the system with the probability (?)Namely the input rate isλr =λαr,and the service rate u is a constant when the queue length is r in the literature [1];And studied the M / M/n queuing system of impatient customers which the customers leave the intensity of troops isΔr =rδ(δ≥0).And received the stable distribution and key indicators of the system.In this paper, we generalize the above two models in [1]. At first this paper studied the M / M/n queuing system with impatient customers which the leaving intensity of impatient customers isΔr =r2δ(δ≥0) when the queue length is r (NamelyΔr =rδof literature [1] is extended toΔr =r2δ).Secondly, this article discuss the M / M/n queuing system with variable input rate when the new customer join the system with the probabilityαr =1 /(1+r). Namely the input rate isλr =λαr,and the service rate u is a constant when the queue length is r (Namely M / M/1 of literature [1] is extended to M / M/n ). And received the stable distribution and key indicators of the system.Finally, the most important innovation of this article is put the queuing model with impatient customers and variable input rate combined queuing model. Namely this article studes the M / M/n queuing system with variable input rate and impatient customers. In this paper, we consider the situation which input rate and service rate with the change of captain r .That is (?)I established a queuing model which is with variable input rate of impatient customers. And obtained the stable distribution and key indicators of the system. The article also illustrates the application of this model in practical problems .