Stochastic Network Dynamics: Approximation, Analysis and Control

随机网络动力学：近似、分析和控制

基本信息

批准号：
1712974
负责人：
Ruth Williams
金额：
$ 25万
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：
2017
资助国家：
美国
起止时间：
2017-07-01 至 2022-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1712974&HistoricalAwards=false
关键词：
Stochastic Network Dynamics Approximation Analysis

项目摘要

Stochastic models of complex networks with dynamic interactions arise in a wide variety of applications in science and engineering. Specific instances include biochemical reaction networks, high-tech manufacturing, computer systems, telecommunications, transportation and business service systems. The analysis and control of such complex stochastic networks require solving challenging mathematical problems. This award supports research on solving such mathematical problems. Some of the work involves the development of general theory for broad classes of stochastic networks, while others focus on mathematical problems directly motivated by specific applications. Since the complexity of stochastic networks usually precludes exact analysis of detailed "microscopic" models, the focus is on formulating and analyzing more tractable approximations. New techniques and results will be developed in such a way that they can be used by applied researchers in areas of application. The results of this research will be disseminated through publication in peer reviewed journals, by posting on the University of California's open access website and by presentations at mathematics, science and engineering conferences. The PI will help train new mathematics researchers through collaboration with early career researchers.The research addresses mathematical problems associated with the analysis and control of stochastic network dynamics. Topics to be addressed include rigorous justification of approximations, analyzing and controlling the behavior of the approximate models, and interpreting the results for the original microscopic models. Two levels of approximation are considered: first order approximations called fluid models, and second order approximations which frequently are diffusion models. An important subtheme is understanding the interplay between levels of approximation. Five topics are proposed for study: diffusion approximations for (bio)chemical reaction networks, analysis of processor sharing networks, congestion control and resource entrainment in data networks, networks with random order of service and reneging, and dynamic control of stochastic processing networks. Some stochastic process aspects of these topics include rates of convergence in the approximation of density dependent Markov chains by reflected diffusion processes, analysis of measure-valued processes used to track residual job sizes or ages of jobs in stochastic network models with resource sharing, singular diffusion control problems, foundational questions for reflected processes, and numerical approximation of reflected diffusion processes in non-smooth domains. This award will support the training of early career researchers and underrepresented minorities through direct support of a female graduate student, and through collaboration of the PI with one early career researcher and one female researcher who is at a non-PhD granting institution.

具有动态相互作用的复杂网络的随机模型在科学和工程中的各种应用中都出现。特定实例包括生化反应网络，高科技制造，计算机系统，电信，运输和商业服务系统。对这种复杂随机网络的分析和控制需要解决具有挑战性的数学问题。该奖项支持解决此类数学问题的研究。一些工作涉及开发广泛的随机网络类别的一般理论，而另一些工作则关注直接由特定应用激发的数学问题。由于随机网络的复杂性通常排除了详细的“微观”模型的精确分析，因此重点是制定和分析更多可拖动的近似值。新技术和结果将以这样的方式开发，使应用研究人员可以在应用领域使用它们。这项研究的结果将通过在同行评审期刊上发布，在加利福尼亚大学的开放访问网站和数学，科学和工程会议上的演讲来传播。 PI将通过与早期职业研究人员的合作来帮助培训新的数学研究人员。该研究解决了与随机网络动态的分析和控制相关的数学问题。要解决的主题包括近似值的严格理由，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。考虑了两个近似级别：一阶近似值称为流体模型，而经常是扩散模型的二阶近似值。一个重要的子主题是了解近似水平之间的相互作用。提出了五个主题进行研究：（BIO）化学反应网络的扩散近似，处理器共享网络的分析，拥塞控制和数据网络中的资源夹带，具有随机的服务和重新延误的网络以及对随机处理网络的动态控制。这些主题的某些随机过程方面包括通过反射的扩散过程在密度依赖的马尔可夫链近似中的收敛速率，分析用于跟踪剩余的工作规模的度量值的过程，或者在随机网络模型中的残留工作规模或资源共享，与反射式的差异过程中的基本问题和数字差异的差异过程中，资源共享的工作年龄分析。该奖项将通过直接支持女性研究生的直接支持，并通过与一位早期职业研究员和一名非PHD授予机构的女性研究员合作，支持对早期职业研究人员和代表性少数群体的培训。