  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.
