Stochastic Networks: Analysis and Control

随机网络：分析与控制

• 批准号: 0305272
• 负责人: Ruth Williams
• 金额: $ 21.52万
• 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: 2003
• 资助国家: 美国
• 起止时间: 2003-07-01 至 2006-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0305272&HistoricalAwards=false
• 关键词: Stochastic; Networks; Analysis; Control

The aim of this project is to study mathematical problems associated with controlling and analyzing the performance of stochastic networks. Since the complexity and heterogeneity of these networks usually preclude exact analysis, the focus here is on approximate models. Two levels of approximation are considered: first order (functional law of large numbers) approximations called fluid models, and second order (functional central limit theorem) approximations, which are frequently diffusion models. The interplay between these two levels is an important subtheme throughout. Three main topics are addressed: (i) Dynamic scheduling for stochastic processing networks, (ii) Analysis of processor sharing networks, (iii) Congestion control for modern communication networks. The stochastic network models considered under these topics are considerably more general than conventional multiclass queueing networks operating under a head-of-the-line (HL) service discipline. Although there is a fairly well developed theory of stability and heavy traffic diffusion approximation for the latter, there are many challenging open problems associated with the control and analysis of the more general stochastic network models being studied here. Some of the stochastic process aspects are that topic (i) involves the analysis and interpretation of the solution of an approximating constrained diffusion control problem, topic (ii) uses measure-valued processes to keep track of residual service times of all jobs in the network, and topic (iii) involves reflected Levy processes when document sizes have heavy tails. This grant funds research on mathematical problems motivated by applications in the disciplines of operations research, computer science and electrical engineering. Specifically, problems associated with the control and analysis of stochastic networks are being studied. Such networks are used as models for complex manufacturing, telecommunications and computer systems. Two fundamental problems for such networks are (a) to understand the effects of common policies on congestion and delay, and (b) to design 'good' controllers for these systems. The networks under study are substantially more general than those that have been rigorously studied to date. Through their complexity and heterogeneity, these networks present challenging mathematical problems. The project involves the development of new theory for stochastic processes and uses techniques from a variety of mathematical disciplines. Collaborations with researchers familiar with areas of application and the training of graduate student researchers are integral parts of the project.

该项目的目的是研究与控制和分析随机网络性能相关的数学问题。由于这些网络的复杂性和异质性通常妨碍精确分析，因此这里的重点是近似模型。考虑两个级别的近似：称为流体模型的一阶（大数函数定律）近似，以及通常是扩散模型的二阶（函数中心极限定理）近似。这两个层次之间的相互作用是贯穿全文的一个重要的子主题。讨论了三个主要主题：（i）随机处理网络的动态调度，（ii）处理器共享网络的分析，（iii）现代通信网络的拥塞控制。这些主题下考虑的随机网络模型比在队头 (HL) 服务规则下运行的传统多类排队网络要普遍得多。尽管后者有相当完善的稳定性和大流量扩散近似理论，但仍存在许多与本文研究的更一般随机网络模型的控制和分析相关的具有挑战性的开放问题。随机过程的一些方面是主题（i）涉及对近似约束扩散控制问题的解决方案的分析和解释，主题（ii）使用测值过程来跟踪网络中所有作业的剩余服务时间，主题 (iii) 涉及当文档大小具有重尾时反映的 Levy 过程。 该拨款资助由运筹学、计算机科学和电气工程学科的应用推动的数学问题的研究。具体来说，正在研究与随机网络的控制和分析相关的问题。此类网络被用作复杂制造、电信和计算机系统的模型。此类网络的两个基本问题是（a）了解常见策略对拥塞和延迟的影响，以及（b）为这些系统设计“良好”控制器。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。由于其复杂性和异质性，这些网络提出了具有挑战性的数学问题。该项目涉及随机过程新理论的发展，并使用各种数学学科的技术。与熟悉应用领域的研究人员的合作以及研究生研究人员的培训是该项目的组成部分。