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

这个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包括制造业、服务业、电信、计算机系统和生化反应。正在研究的一些问题涉及到广泛类别随机网络的一般理论的发展，而其他问题则集中在由特定应用直接激发的数学问题上。以下五个主题被考虑：(i)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）输入排队交换机，以及(v)生化反应网络。与这些主题相关的随机网络模型比传统的多类排队网络在队列首（HL）服务规则下运行要普遍得多。尽管对于后者有一个相当发达的稳定性理论和大流量扩散近似，但与更一般的随机网络的控制和分析相关的许多具有挑战性的开放问题。这个项目的一些随机过程方面包括奇异扩散控制问题的研究，使用测量值过程来跟踪剩余作业大小，反映Levy过程的基础问题，以及使用无限服务器队列来模拟非指数反应时间的生化反应。本基金资助由运筹学、计算机科学、电子工程及生物化学等学科的应用所引发的数学问题的研究。所研究的具体问题涉及随机网络的控制和分析，随机网络是涉及受不确定性影响的动态相互作用的复杂系统的模型。这类网络的两个基本问题是(a)理解这些系统在自然控制策略下的行为，以及(b)为这些系统设计“好的”控制器。研究中的网络比迄今为止严格研究过的网络要普遍得多。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，并使用了各种数学学科的技术。与熟悉应用领域的研究人员合作，研究生研究人员的培训，以及通过在同行评审期刊上发表研究成果和在跨学科研究会议上发表报告来传播研究成果是该项目的组成部分。

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.