AMC-SS: Stochastic Networks - Control, Analysis and Applications

AMC-SS：随机网络 - 控制、分析和应用

• 批准号: 0604537
• 负责人: Ruth Williams
• 金额: $ 25.77万
• 依托单位: University of California-San Diego
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-07-01 至 2009-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0604537&HistoricalAwards=false
• 关键词: AMC; SS; Stochastic; Networks; Control

This project involves the study of mathematical problems associated with the control and analysis of stochastic networks.Examples of application domains for these stochastic models include manufacturing, the service industry, telecommunications,computer systems and biochemical reactions. Some of the problems being studied involve the development of general theory for broad classes of stochastic networks, while others focus on mathematical questions directly motivated by specific applications. The following five topics are considered:(i) dynamic scheduling for stochastic processing networks,(ii) analysis of processor sharing networks,(iii) congestion control for data networks,(iv) input-queued switches, and(v) biochemical reaction networks.The stochastic network models associated with these topics areconsiderably more general than conventional multiclass queueingnetworks operating under a head-of-the-line (HL) service discipline.Although there is a fairly well developed theory of stabilityand heavy traffic diffusion approximation for the latter,there are many challenging open problems associated withthe control and analysis of more general stochastic networks.Some stochastic process aspects of this project include thestudy of singular diffusion control problems, the use of measure-valued processes to keep track of residual job sizes,foundational questions for reflected Levy processes,and the use of an infinite server queueto model biochemical reactions with non-exponential reaction times.This grant funds research on mathematical problems motivated byapplications in the disciplines of operations research, computer science, electrical engineering and biochemistry.The specific problems being studied concern thecontrol and analysis of stochastic networks which are models forcomplex systems involving dynamic interactions subject to uncertainty.Two fundamental problems for such networks are(a) to understand the behavior of these systems under naturalcontrol policies, and(b) to design 'good' controllers for these systems.The networks under study are substantially more general thanthose that have been rigorously studied to date. Through theircomplexity and heterogeneity, these networks present challengingmathematical problems. The project involves the development of new theory for stochastic processes and uses techniques from a variety ofmathematical disciplines. Collaborations with researchers familiar withareas of application, the training of graduate student researchers,and the dissemination of research results through publication in peer reviewed journals and presentations at cross-disciplinary research conferences are integral parts of the project.

该项目涉及与随机网络的控制和分析相关的数学问题的研究。这些随机模型的应用领域的示例包括制造业，服务行业，电信，计算机系统和生化反应。所研究的一些问题涉及开发广泛的随机网络类别的一般理论，而另一些问题则关注直接由特定应用程序动机的数学问题。考虑了以下五个主题：（i）进行随机处理网络的动态调度，（ii）处理器共享网络的分析，（iii）数据网络的拥塞控制，（iv）输入式的开关以及（v）生物化反应网络与这些主题相关联的随机反应网络。服务纪律。尽管有一个相当发达的稳定性和交通繁重的交易扩散近似理论，但与对更通用的随机网络的控制和分析有关的挑战性开放问题。该项目的一些随机过程方面。无数服务器模型的生物化学反应具有非指数反应时间。这项授予的数学问题基金在运营研究，计算机科学，电脑科学，电气工程和生物化学的学科中促成了byapplications的动机。所研究的特定问题关注的问题和依赖于动态的网络的分析，这些问题涉及动态互动，并涉及动态的互动。是（a）了解这些系统下这些系统在这些系统下的“良好”控制器下的行为。所研究的网络比迄今为止对已进行了严格研究的更一般性。通过它们的复杂性和异质性，这些网络带来了挑战性的数学问题。该项目涉及为随机过程开发的新理论，并使用各种各样学科的技术。与研究人员熟悉应用程序的合作，研究生研究人员的培训以及通过在同行评审的期刊和跨学科研究会议上发表的研究结果传播研究结果是该项目不可或缺的一部分。