Delay Bounds for Networks with Heavy-Tailed and Self-Similar Traffic

Abstract

We provide upper bounds on the end-to-end backlog and delay in a network with heavy-tailed and self-similar traffic. The analysis follows a network calculus approach where traffic is characterized by envelope functions and service is described by service curves. A key contribution of this paper is the derivation of a probabilistic sample path bound for heavy-tailed self-similar arrival processes, which is enabled by a suitable envelope characterization, referred to as `htss envelope'. We derive a heavy-tailed service curve for an entire network path when the service at each node on the path is characterized by heavy-tailed service curves. We obtain backlog and delay bounds for traffic that is characterized by an htss envelope and receives service given by a heavy-tailed service curve. The derived performance bounds are non-asymptotic in that they do not assume a steady-state, large buffer, or many sources regime. We also explore the scale of growth of delays as a function of the length of the path. The appendix contains an analysis for self-similar traffic with a Gaussian tail distribution.