Queuing Theory, Applied Research, In The Supermarket Cash Register System

The cash service system of supermarkets is a stochastic service system, the marketing's speed is impacted by the services' speed, the key is the rationality of the supermarket queuing system. In this paper, we construct cash queuing system model at the base of two server, by applying with the theory of Markov skeleton process, gained transient and distribution limit distribution of queue length. The content and main result of the thesis as follows:In chapter 1, the queuing theory research history and the present situation are outlined, simultaneously has listed the thesis structure and the main result.In chapter 2,the preliminary knowledge of Markov skeleton process are introduced, including the concept of Markov skeleton process, backward and forward equation, limit distribution, generalized limit distribution, invariant probability measure and vector Markov process.In chapter 3, we construct a queuing system model for the supermarket with two server, studying the transient distribution and limit distribution of the queue length of this model by applying Markov skeleton process theory.In chapter 4, we study the queuing system of supermarket with two server which is different with chapter 3 and the transient distribution and limit distribution of the queue length of this model by applying Markov skeleton process theory.