Dynamic Stochastic Networks: Analysis, Control and Applications

动态随机网络：分析、控制和应用

基本信息

批准号：
1206772
负责人：
Ruth Williams
金额：
$ 53.09万
依托单位：
University of California-San Diego
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2012
资助国家：
美国
起止时间：
2012-07-01 至 2019-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1206772&HistoricalAwards=false
关键词：
Dynamic Stochastic Networks Analysis Control

项目摘要

Stochastic dynamic models of complex networks arise in a wide variety of applications in science and engineering. Specific instances include high-tech manufacturing, telecommunications, computer systems, service systems and biochemical reaction networks. This project involves the study of a number of mathematical problems stemming from the challenges of analyzing and controlling such dynamic stochastic networks. A balance of topics is proposed. Some topics involve the development of general theory for broad classes of networks, while others focus on mathematical problems directly motivated by specific applications. Since the complexity of these networks usually precludes exact analysis of detailed microscopic models, the focus here is on approximate models. Mathematical questions to be addressed include rigorous justification of these approximations, analyzing and controlling the behavior of the approximate models and interpreting the results for the original microscopic models. Four topics are proposed for study:(i) Dynamic control of stochastic processing networks,(ii) Analysis of processor sharing networks,(iii) Congestion control and resource entrainment in data networks,(iv) Stochastic systems with delayed dynamics and state constraints.Some stochastic process aspects of these topics include study of singular diffusion control problems, analysis of measure-valued processes, foundational questions for reflected processes, and the asymptotic properties of functional stochastic differential equations with natural state constraints.Dynamic stochastic networks are used as mathematical models in a wide variety of applications in science and engineering, particularly in operations management, computer science, electrical engineering and bioengineering. This grant funds research to develop new results and techniques for addressing mathematical problems stemming from the need to analyze and control such dynamic stochastic networks. The networks under study are substantially more general than those that have been rigorously studied to date. The results will be of fundamental mathematical interest as well as of interest for applied researchers in relevant areas of science and engineering. The training of mathematics PhD students, dissemination of results through publication in peer-reviewed journals and presentations of the research at cross-disciplinary conferences, are all integral parts of the project.

复杂网络的随机动态模型出现在科学和工程领域的各种应用中。具体实例包括高科技制造、电信、计算机系统、服务系统和生化反应网络。该项目涉及对因分析和控制此类动态随机网络的挑战而产生的许多数学问题的研究。建议平衡主题。一些主题涉及广泛类别网络的一般理论的发展，而另一些主题则侧重于由特定应用直接激发的数学问题。由于这些网络的复杂性通常妨碍对详细微观模型的精确分析，因此这里的重点是近似模型。要解决的数学问题包括对这些近似的严格论证、分析和控制近似模型的行为以及解释原始微观模型的结果。提出了四个研究主题：（i）随机处理网络的动态控制，（ii）处理器共享网络的分析，（iii）数据网络中的拥塞控制和资源夹带，（iv）具有延迟动态和状态约束的随机系统。这些主题的一些随机过程方面包括奇异扩散控制问题的研究、测值过程的分析、反射过程的基本问题以及具有自然状态约束的函数随机微分方程的渐近性质。动态随机网络是作为数学模型广泛应用于科学和工程领域，特别是在运营管理、计算机科学、电气工程和生物工程领域。该赠款资助研究开发新的结果和技术，以解决因分析和控制此类动态随机网络的需要而产生的数学问题。正在研究的网络比迄今为止经过严格研究的网络要普遍得多。结果将具有基本的数学意义以及相关科学和工程领域的应用研究人员的兴趣。数学博士生的培训、通过在同行评审期刊上发表论文来传播研究成果以及在跨学科会议上展示研究成果，都是该项目的组成部分。