Exact Overflow Asymptotics for Queues with Many Gaussian Inputs

摘要

In this paper we consider a queue fed by a large number n of independent continuous-time Gaussian processes with stationary increments. After scaling the buffer exceedance threshold B and the (constant) service capacity C by the number of sources (i.e., B identical with nb and C identical with nc), we present asymptotically exact results for the probability that the buffer threshold is exceeded. We both consider the stationary overflow probability, and the (transient) probability of overflow at a finite time horizon Tau. We give detailed results on the practically important cases in which the inputs are fractional Brownian motion processes or integrated Gaussian processes.