Sample path moderate deviations for a family of long-range dependent traffic and associated queue length processes

Abstract

We consider the long-range dependent cumulative traffic generated by the superposition of constant rate fluid sources having exponentially distributed intra start times and Pareto distributed durations with finite mean and infinite variance. We prove a sample path moderate deviation principle when the session intensity is increased and the processes are centered and scaled appropriately. The governing rate function is known from large deviation principles for the tail probabilities of fractional Brownian motion. We derive logarithmic tail asymptotics for associated queue length processes when the traffic loads an infinite buffer with constant service rate. The moderate deviation approximation of steady-state queue length tail probabilities is compared to those obtained by computer simulations.