Spatio-Temporal Dependence and Extremes with Applications to Networking and the Environment

该项目的目标是在时空计算机网络流量和环境数据的背景下开发模型和统计推断技术。pi建议通过多变量时空过程扩展他们在全球网络流量建模方面的联合工作，并解决网络克里格、预测和最佳监测设计问题。还将讨论涉及计算机网络流量极端依赖以及环境数据的新问题。为此，pi建议使用已建立的技术以及开发涉及最大稳定过程、多变量、功能和隐藏规则变化的新工具。该提案的主要主题之一是理解和模拟计算机网络中流量传播的统计方面。这项研究将有助于以更有原则的方式预测、检测、监控和管理计算机网络流量。拟议的方法侧重于描述空间和时间上的全球统计行为，这将提供整个网络的更全面的情况，即所有链路、路线在同时以及不同时间点上的交通负荷。这可以使从业者通过监视一组选定的链路或路由来预测未观察到的链路或路由上的流量负载。该研究的另一个方面涉及应用极值理论来理解和模拟计算机网络中极端延迟和流量负载的统计依赖性。这可以帮助识别瓶颈和？薄弱环节?当异常极端的交通量出现时。在环境应用中出现了相关的重要问题，其中极端因素起着关键作用。例如，对在不同空间位置同时发生极端降水事件的概率进行充分建模，对于能够量化洪水风险至关重要。拟议的研究将有助于模拟和估计这些同时发生的极端事件的概率，并评估重要的环境风险，如污染、洪水、干旱、高温期等。

The goal of the project is to develop models and statistical inference techniques in the context of space-time computer network traffic and environmental data. The PIs propose to extend their joint work on global network traffic modeling via multivariate spatio-temporal processes and to address the network kriging, prediction, and optimal monitoring design problems. New problems involving extremal dependence in computer network traffic as well as environmental data will be also addressed. To do so, the PIs propose to use established techniques as well as to develop new tools involving max-stable processes, multivariate, functional, and hidden regular variation.One of the main themes of the proposal is to understand and model the statistical aspects of traffic propagation in computer networks. This research would help predict, detect, monitor, and manage computer network traffic in a more principled way. The proposed methodology focuses on characterizing the global statistical behavior in both space and time, which would provide a more comprehensive picture of the entire network, namely the traffic loads on all links, routes, at concurrent as well as different points of time. This could enable the practitioners to predict the traffic load on an unobserved link or route by monitoring a select set of links or routes. Another aspect of the proposed research involves applying the Extreme Value Theory to understand and model the statistical dependence of extreme delays and traffic loads in computer networks. This could help identify bottlenecks and ?weak links? when unusually extreme traffic volumes arise. Related important problems arise in environmental applications, where extremes play a critical role. For example, the adequate modeling of the probability of extreme precipitation events to occur at the same time over different spatial locations is essential to be able to quantify the risk of floods. The proposed research would help model and estimate such probabilities of concurrent extremes and evaluate important environmental risks such as pollutions, floods, droughts, hot-spells, etc.