Transitory Stochastic Models: Analysis and Optimization

随机模型被广泛用于分析和优化医疗保健，通信，大规模计算和运输系统。现有的理论往往集中在制造商分析同构模型，假设服务需求是相同的所有用户。最近的技术趋势使收集大量数据成为可能，这些数据表明用户的要求往往是多种多样的。因此，非齐次随机模型的理论是必要的。这个项目的目标是开发一个理论的“瞬态随机模型”，明确纳入用户的不均匀性，并同时考虑这些模型的优化和控制。如果成功的话，这个项目将有助于非齐次随机系统的理论理解，和理论结果的应用可能会导致显着的性能增益在许多服务系统的运营管理。此外，从这个项目的想法将被纳入一个新的随机建模课程的本科生，集成理论，数据建模和优化。PI还将利用暑期研究计划，以促进少数民族和女本科生的研究经验。本研究的理论目标是开发随机过程和分析近似的性能分析和优化的瞬态随机模型。所考虑的模型包括系统与许多服务器，嵌入式网络，和系统的重尾服务时间和非平稳，相关的流量。系统是暂时的，在这个意义上，我们感兴趣的预测在一个有限的，但操作上重要的时间范围，和模型需要一个纯粹的瞬态分析，这是不平凡的，即使在简单的情况下。这项研究有两个相关的焦点：首先，这项工作将确定新的缩放制度，其中“通用”的随机过程近似的流量和工作量的过程可以建立，在形式的功能中心极限定理，强近似和条件极限定理。其次，研究还将考虑使用这些随机过程近似的基础系统的最优控制的识别。这里的重点将是发展分析近似的预期成本函数，并确定一个附带的概念渐近最优控制。

Stochastic models are widely used to analyze and optimize healthcare, communication, large-scale computing, and transportation systems. Existing theory has tended to focus on easier-to-analyze homogeneous models that assume that service requirements are identical for all users. Recent technological trends have made it possible to collect large amounts of data that show that users' requirements are often heterogeneous. Thus, a theory of nonhomogeneous stochastic models is needed. The goal of this project is develop a theory of 'transitory stochastic models' that explicitly incorporates users' inhomogeneity and, concomitantly, considers the optimization and control of these models. If successful, this project will contribute to the theoretical understanding of nonhomogeneous stochastic systems, and the application of the theoretical results can potentially result in significant performance gains in the operational management of many service systems. Furthermore, ideas from this project will be incorporated into a new stochastic modeling course for undergraduates that integrates theory, data modeling and optimization. The PI will also leverage summer research programs to facilitate research experiences for minority and female undergraduate students.The theoretical objective of this research is to develop stochastic process and analytical approximations for the performance analysis and optimization of transitory stochastic models. The models considered include systems with many servers, queueing networks, and systems with heavy-tailed service times and non-stationary, correlated traffic. The systems are transitory in the sense that we are interested in predictions over a finite, but operationally significant time horizon, and the models require a purely transient analysis, which is non-trivial even in the simpler cases. The research has twin related foci: first, this effort will identify novel scaling regimes in which "universal" stochastic process approximations to the traffic and workload processes can be established, in the form of functional central limit theorems, strong approximations and conditioned limit theorems. Second, the research will also consider the identification of optimal controls for the underlying systems using these stochastic process approximations. The focus here will be on developing analytical approximations to the expected cost functions and identifying an accompanying notion of asymptotic optimality of controls.