TY - JFULL AU - Quanru Pan PY - 2011/4/ TI - The Research and Application of M/M/1/N Queuing Model with Variable Input Rates, Variable Service Rates and Impatient Customers T2 - International Journal of Mathematical and Computational Sciences SP - 335 EP - 339 VL - 5 SN - 1307-6892 UR - https://publications.waset.org/pdf/15239 PU - World Academy of Science, Engineering and Technology NX - Open Science Index 51, 2011 N2 - How to maintain the service speeds for the business to make the biggest profit is a problem worthy of study, which is discussed in this paper with the use of queuing theory. An M/M/1/N queuing model with variable input rates, variable service rates and impatient customers is established, and the following conclusions are drawn: the stationary distribution of the model, the relationship between the stationary distribution and the probability that there are n customers left in the system when a customer leaves (not including the customer who leaves himself), the busy period of the system, the average operating cycle, the loss probability for the customers not entering the system while they arriving at the system, the mean of the customers who leaves the system being for impatient, the loss probability for the customers not joining the queue due to the limited capacity of the system and many other indicators. This paper also indicates that the following conclusion is not correct: the more customers the business serve, the more profit they will get. At last, this paper points out the appropriate service speeds the business should keep to make the biggest profit. ER -