Stochastic Convexity in Queueing Networks and Its Application

该提案由J.G. Shanthikumar的 美国加州大学伯克利分校，哈佛的姚明 大学 拟议研究项目的重点是研究 网络的凸性 这些属性通常 它在优化设计和控制配电网中是不可缺少的， 在过去的三十年里， 复杂的随机系统，如计算机系统，通信系统， 网络、数据库系统和制造系统。 PI的提出了一个新的概念，随机凸性，并强调 它在制造系统网络模型中的应用。 这个新概念捕获了二阶（例如，凸出或 网络中随机过程的行为 关于时间和其它参数变化。 排队 他们所关注的网络模型与经典的 例如，它们允许一般的到达间隔和服务时间 分布、有限缓冲区和阻塞。 注意力也集中在 对这些网络的动态行为进行（瞬态）分析。 基于样本路径分析，他们提出了新的方法， 建立某些关键过程的随机凸性， 这些网络。 最近，随机优化方法，基于Monte- Carlo模拟已发展到解决各种优化设计 网络安全的问题。 随机凸性结果提供了 这些方法的二阶最优性条件，因此 对嵌入式网络的理论和应用有重要的贡献。

This proposal is jointly submitted by J.G. Shanthikumar of the University of California, Berkeley, and by D.D. Yao of Harvard University. The focus of the proposed research project is on studying convexity properties in queueing networks. Such properties are often indispensable in the optimal design and control of queueing networks, which for the last three decades have been major tools in studying complex stochastic systems such as computer systems, communication networks, data-base systems, and manufacturing systems. The PI's propose a new concept of stochastic convexity, and highlight its applications in queueing network models of manufacturing systems. This new concept captures the second-order (e.g., convexity or concavity) behavior of the stochastic processes in queueing networks with respect to temporal and other parametric changes. The queueing network models that they focus on are major departures from classical models; for instance, they allow general interarrival and service time distributions, finite buffers and blocking. Attention is also focused on the (transient) analysis of the dynamic behavior of these networks. Based on sample path analysis, they propose new approaches to establish stochastic convexity of certain key processes that underlie these networks. Recently, stochastic optimization approaches that are based on Monte- Carlo simulation have been developed to solve various optimal design problems in queueing networks. Stochastic convexity results provide second-order optimality conditions for those approaches, and hence significantly add to the theory and applications of queueing networks.