Abstract The queuing theory (called stochastic service system) is an important branch of operational research. It is a mathematics subject which studies the crowded phenomenon affected by random factors. It studies different kinds of service system’s probability characteristic in the queue of waiting, to guide the systems optimal design and optimal operating strategies. With the development of the society, queuing has been close with our daily life. People will feel depressed when they are at the checkout counters after shopping. It will make people cancel the shopping sometimes because they have to wait for a long time. It is necessary and crucial for the managers of the supermarkets and emporiums to provide best service with the lowest cost to save customers’ time. Therefore, the optimization of supermarket’s queueing system according to the knowledge of queueing theory has the practical significance. puter simulation is to simulate the studied system’s internal structure , function and the behavior puter. Because of wide application of the queueing theory and because of the characteristics and rules of queueing and anization being more and plex, the analytic method has bee n unable to solve. But puter simulation is a very effective method to solve th e queueing system and to analyze queuing system’s performance. And puter simulation has advantages of low cast, fast speed and high accuracy. bination of queueing theory puter simulation is the inevitable trend o f queueing theory in future. In the preliminary knowledge part, the thesis introduced four kinds of probability distribution, two kinds of stochastic process and basic knowledge related to statistical test and the queuing theory. Then, the thesis applied some theories related to the queuing theory and it abstracted the Checkout Counter Service Syst em as a mathematical model which is the M / M / c / ¥ queuing system. The model which meets some certain conditions is the optimal one. It also analyzed t
