Copula theory and its applications in computer networks




Dong, Fang

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Traffic modeling in computer networks has been researched for decades. A good model should reflect the features of real-world network traffic. With a good model, synthetic traffic data can be generated for experimental studies; network performance can be analysed mathematically; service provisioning and scheduling can be designed aligning with traffic changes. An important part of traffic modeling is to capture the dependence, either the dependence among different traffic flows or the temporal dependence within the same traffic flow. Nevertheless, the power of dependence models, especially those that capture the functional dependence, has not been fully explored in the domain of computer networks. This thesis studies copula theory, a theory to describe dependence between random variables, and applies it for better performance evaluation and network resource provisioning. We apply copula to model both contemporaneous dependence between traffic flows and temporal dependence within the same flow. The dependence models are powerful and capture the functional dependence beyond the linear scope. With numerical examples, real-world experiments and simulations, we show that copula modeling can benefit many applications in computer networks, including, for example, tightening performance bounds in statistical network calculus, capturing full dependence structure in Markov Modulated Poisson Process (MMPP), MMPP parameter estimation, and predictive resource provisioning for cloud-based composite services.



Copula Analysis, Network Calculus, Markov Modulated Poisson Process, Traffic Prediction, Parameter Estimation, Cloud Service Provisioning, Contemporaneous Dependence Modeling, Temporal Dependence Modeling