Promotion and Application of the M/M/1/N Queuing System

The customers do not necessarily get into the system though arriving at the system in the case of a fixed customer number, which influences sales industry enormously. This paper focuses on the influence of queue length on input rate, and sets up a queuing model with variable input rates, errors service and impatient customers, which are related to the queue length, and get the following conclusions: the customers get into the system in Poisson flow; the number of customers in the system is a birth-death process; the stationary queue length distribution of the model ; 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 service error rate per unit time, the loss probability for the customers not joining the queue due to the limited capacity of the system and so on, and the appropriate service speeds and the capacity the business should keep to make the biggest profit, which provides a valuable reference for the enterprise to improve their sales performance.