Copula analysis for statistical network calculus

The tightness of stochastic performance bounds has been a lingering issue in the theory and practical applications of stochastic network calculus (SNC). More often than not, inappropriate stochastic traffic arrival models and/or service models lead to loose stochastic bounds. In practice, loose bounds occur due to inaccurate a-prior assumption on traffic arrivals and/or the obliviousness to possible correlation between arrivals. To alleviate this problem, this paper uses copula analysis to capture the correlation in traffic flows and introduces a statistical method to infer traffic arrival models. Using copula theory, we show the range of performance bounds that SNC can achieve. With concrete numerical examples and real-world experiments, it is demonstrated that copula analysis offers a new opportunity for extending SNC research and augmenting its impact in practice.