大型并行排队网络的随机负载平衡策略及其超市模型研究

项目名称： 大型并行排队网络的随机负载平衡策略及其超市模型研究

项目编号： No.71271187

项目类型： 面上项目

立项/批准年度： 2013

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： 58万元

中文摘要： 近年来，云计算与云制造已经广泛地应用于企业产供销的各项服务业务中，资源整合与优化、任务调度与分配已经成为提高企业运营效率的两个重要手段。这些需求在国际上极大地推动了大型并行排队网络的研究工作；同时大型排队网络也有许多非常重要的理论问题迫切需要解决。本项目旨在解决大型并行网络中的两个重要问题：建立"系统级渐近独立性"来研究无穷维非线性的微分差分方程组的唯一全局解；提供固定点的有效算法来实现系统的性能评价。基于此，本项目的研究内容包括：（1）利用算子半群提供大型并行排队网络的平均场逼近，实现网络的系统级渐近独立性；（2）提供无穷维泛函的Lipschitz条件来研究无穷维非线性微分差分方程组的唯一全局解；（3）提供固定点的超指数解及其有效算法，实现对大型网络的性能评价及其模拟实验平台的开发。本项目的研究成果为企业的资源配置与任务调度提供重要的理论支持，也是目前排队论研究领域中最热点的发展方向。

中文关键词： 并行排队网络；超市模型；平均场理论；非线性马氏过程；渐近独立性

英文摘要： Recently, the service of cloud computing and cloud manufacturing is being offerred to enterprises from various areas such as production, supply and sales. Integration and optimization of available resourses，and scheduling and assigning of tasks are two important ways of every enterprise who ia improving its operations efficiency. These requirements greatly promote investigation of large scale parallel queueing networks which also have of their own interesting. This project will deal with two important issues: Seting up the asymptotic independence of systemical level, and then give the unique and global solution to the systems of limiting differential equations; providing effective algorithms of the fixed points, and then analyze performance measures of these parallel queueing networks by means of algorithmic and/or simulation ways. Based on this, the contents of this project contains three points: (1) Applying the operator semigroup to provide the mean field approximation of the sequences of Markov processes describing the parallel queueing networks, and then set up the asymptotic independence of systemical level for these networks. (2) Developing the Lipschitz conditions for the infinite-dimensional functions, and obtain the unique and global solution to the systems of limiting differential equations. (3) Provi

英文关键词： Parallel queueing network；Supermarket model；Mean-field theory；Nonlinear Markov process；Asymptotic independence