Non-asymptotic Delay Bounds for Networks with Heavy-Tailed Traffic

Abstract

Traffic with self-similar and heavy-tailed characteristics has been widely reported in networks, yet, only few analytical results are available for predicting the delay performance of such networks. We address a particularly difficult type of heavy-tailed traffic where only the first moment can be computed, and present the first non-asymptotic end-to-end delay bounds for such traffic. The derived performance bounds are non-asymptotic in that they do not assume a steady state, large buffer, or many sources regime. Our analysis considers a multi-hop path of fixed-capacity links with heavy-tailed self-similar cross traffic at each node. A key contribution of the analysis is a probabilistic sample-path bound for heavy-tailed arrival and service processes, which is based on a scale-free sampling method. We explore how delays scale as a function of the length of the path, and compare them with lower bounds. A comparison with simulations illustrates pitfalls when simulating self-similar heavy-tailed traffic, providing further evidence for the need of analytical bounds.