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

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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.