Discrete event systems are widely used in the production and life, it is difficult to use conventional differential equations, differential equations, and other models to describe, the theoretical analysis method is difficult to obtain analytical solutions, computer simulation techniques to solve these problems provides an effective means. Arrival event is a typical discrete system event; on arrival event handling is always one of the difficulties of computer simulation, in this paper, banking customer arrival system as an example to study. For banks queuing system, customers arrive to obey the parameter of Poisson distribution is, the probability mass function through the distribution curves and cumulative distribution function curves to study the distribution of customer arrival; construction of single-queue multi-server system of customer arrival event subroutine flow chart, and processing steps will be described. Content of this study, it is suitable for the developed area bank to adopt "number ticket machine" approach to service.