Copula-based Dependence Modeling for Computer and Communication Networks

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With the fast advance of network technologies, the Internet has become an indispensable part of modern society. In less than 50 years, the Internet has become not only the major platform for entertainment, communication, and social networking, but also the main driving force for many new business services. Under the hood of diverse applications over the Internet are core mathematical models and algorithms that support their smooth operation. Improving the core models and algorithms will create a significant impact on the whole ecosystem of the Internet. We are thus motivated to investigate fundamental models that are critical to the future success of many internet applications. Looking back at history, we find that various dependence models have been proposed in every stage of research and development in the Internet. In theory, Internet traffic dependence models, together with queueing theory, lay the foundation for theoretical performance analysis of modern computer networks. In practice, dependence models are the basis for traffic engineering, network capacity planning, and prediction-based resource provisioning. Overall, the Internet essentially relies on various dependence models. While extensive work has been done on dependence modeling for computer and communication networks, the rich dependence structures in network traffic, particularly those beyond the scope of linear dependence, have not been fully explored. The goal of this NSERC discovery proposal is to push the state-of-the-art by exploring the power of copulas. Copulas are dependence models that are able to capture the functional dependence between/within network traffic flows and have shown promising results in traffic prediction, automatic resource adjustment, and network sampling. With mathematical analysis, simulation, and real-world experiments, the project will address two interweaving research themes: copula-based network performance tomography, and copula models for interdependent networks. In the first theme, we will develop a reliable network tomography method which can infer the network performance based on observations from a small number of monitoring points. In the second theme, we will study the system of interdependent networks, where the performance of one network depends on the performance of other networks. The research will enrich the toolset of dependence modeling for computer and communication networks and will benefit many real-world applications, including for example real-time multimedia delivery, performance monitoring for large-scale online broadcasting, and smart grid communication. By applying the theoretical results into our existing projects with industrial partners in Canada, our research results can benefit Canadian IT industries with more effective algorithms for data dependence analysis.