实时排队控制下超市网络的非线性马氏过程与超指数结构

项目名称： 实时排队控制下超市网络的非线性马氏过程与超指数结构

项目编号： No.71471160

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 管理科学

项目作者： 李泉林

作者单位： 燕山大学

项目金额： 62万元

中文摘要： 当今的超市网络已经成为人们生活的重要场所，也是体现我国经济腾飞的重要标志。本项目旨在构建能够定量分析超市网络的关键数学模型体系，发展超市网络中两个重要的数学理论：非线性马氏过程；超指数结构。基于此，本项目的研究内容包括：（1）利用排队网络描述超市网络中顾客的购物行为、货物的寿命、保鲜期、变质率、自然灾害发生过程等重要因素；（2）在规模增长下，建立超市网络的随机模型理论：非线性马氏过程、非线性马氏报酬过程和非线性马氏决策过程，研究这些马氏过程序列的流逼近与扩散逼近，讨论它们在局部集之间的相依性与渐近独立性；（3）提出集中推式与分散拉式的实时排队控制策略，发展超市网络的性能优化与实时控制的理论与方法，实现系统资源的实时优化配置与综合利用；（4）在超市网络中，提出并发展一套崭新的非线性马氏过程理论及其计算技术。本项目的研究成果将为提高我国超市企业的管理水平提供一些重要的理论依据与实践指导。

中文关键词： 排队网络；超市网络；非线性马氏过程；实时排队控制；超指数结构

英文摘要： Today's supermarket networks are a major place in People's daily life, and it is also an important symbol of fast development of China's economics. This project aims to build a key system of mathematical models based on quantitative analysis of the supermarket networks, and develop two important theories in the study of the supermarket networks: nonlinear Markov processes and super-exponential structure. Based on this, the objective of the research contents include: (1) queuing networks are used to describe customer shopping behavior in the supermarket networks, involving the service life of the goods, freshness, deterioration rate and emergent disaster events and other important factors. (2) With growing scale in the supermarket networks, we need to establish nonlinear Markov processes, nonlinear Markov reward processes and nonlinear Markov decision processes, study their limiting processes through the fluid approximation and the diffusion approximation, and discuss their asymptotic independence. (3) In a large-scale supermarket network, we need to develop the centralized as well as distributed real-time queue control policies, which are used to provide the real-time optimal resource allocation and comprehensive utilization with respect to a number of customer resource and various goods in this system. (4) For the large-scale supermarket networks, we will develop a new and original class of nonlinear Markov processes with effective computational techniques and associated computer simulation platforms. The main results of this project will provide important theoretical basis and practical guidance in order to improve the management level of supermarket enterprises in China.

英文关键词： Queueing networks;supermarket networks;nonlinear Markov processes;real-time control of queues;super-exponential structure