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

本计画研究与随机网络的控制与分析有关的数学问题，这些随机模型的应用领域包括制造业、服务业、电信、计算机系统和生物化学反应。正在研究的一些问题涉及广泛的随机网络类的一般理论的发展，而其他人则专注于直接由特定应用激发的数学问题。审议了以下五个专题： 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头的线（HL）服务纪律下运行更一般。虽然有一个相当发达的理论稳定性和重型交通扩散近似后者，有许多具有挑战性的开放问题与控制和分析更一般的随机网络。一些随机过程方面，这项目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，反射Levy过程的基础问题，以及使用无限服务器模型来模拟具有非指数反应时间的生化反应。该基金资助数学问题的研究，这些问题的动机是在运筹学，计算机科学，电气工程和生物化学。正在研究的具体问题涉及随机网络的控制和分析，随机网络是涉及不确定性动态相互作用的复杂系统的模型。这种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，和（B）为这些系统设计“好的”控制器。所研究的网络比迄今为止已经严格研究的网络更一般。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的新理论的发展，并使用各种数学学科的技术。与熟悉应用领域的研究人员合作，培训研究生研究人员，通过在同行评审的期刊上发表和在跨学科研究会议上介绍来传播研究成果，这些都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.