Exact overflow asymptotics for queues with many Gaussian inputs

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., $Bequiv nb$ and $Cequiv nc$), 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 $T$. We give detailed results on the practically important cases in which the inputs are fractional Brownian motion processes or integrated Gaussian processes.