排队论在超市收银系统中的应用研究

【作者】 王连球；

【导师】 侯振挺；

【作者基本信息】 中南大学 ， 概率论与数理统计， 2007， 硕士

【摘要】 超市的收银服务系统是一个随机服务系统,收银台的服务效率直接影响超市的营销效率,其关键在于超市内收费排队系统的合理性问题。本文以两个收银台为基础,应用马尔可夫骨架过程理论研究了两个收费排队系统的队长的瞬时状态和极限状态。论文的主要内容和结构安排如下:第一章概述了排队论的历史和研究现状,同时给出了论文的结构和主要结果。第二章介绍了马尔可夫骨架过程的理论,包括马尔可夫骨架过程的主要概念,向后和向前方程,有限维分布和极限分布,广义极限分布与不变测度以及向量马氏过程。第三章针对恰有两个收银台的超市,构建了一个排队系统模型,应用马尔可夫骨架过程的理论研究了这个模型队长的瞬时状态和极限状态。第四章考虑了与第三章有所不同的两个收银台的排队系统,仍应用马尔可夫骨架过程的理论研究了这个模型队长的瞬时状态和极限状态。更多还原

【Abstract】 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.更多还原