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

这个项目涉及与随机网络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。一些正在研究的问题涉及广泛类别的随机网络的一般理论的发展，而另一些问题则专注于直接由特定应用驱动的数学问题。考虑了以下五个主题：(I)随机处理网络的动态调度，(Ii)处理器共享网络的分析，(Iii)数据网络的拥塞控制，(Iv)输入排队交换机，和(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运行在队头(HL)服务规则下的多类排队网络要普遍得多。尽管对于后者有相当发展的稳定性理论和大流量扩散近似，与更一般的随机网络的控制和分析有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研究奇异扩散控制问题，使用测量值过程来跟踪剩余的作业大小，反射的Levy过程的基本问题，以及使用无限服务队列来模拟具有非指数反应时间的生化反应。这项资助用于研究数学问题，这些问题是由运筹学、计算机科学、电子工程和生物化学。正在研究的具体问题涉及随机网络的控制和分析。随机网络是复杂系统的模型，涉及动态相互作用，具有不确定性。这类网络的两个基本问题是：(A)了解这些系统在自然控制政策下的行为，(B)为这些系统设计‘好的’控制器。所研究的网络比迄今严格研究的网络要普遍得多。由于它们的复杂性和异构性，这些网络提出了具有挑战性的数学问题。该项目涉及发展随机过程的新理论，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、对研究生研究人员的培训，以及通过在同行评议的期刊上发表研究成果和在跨学科研究会议上发表演讲来传播研究成果，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.