On the correlation structure of Gaussian queues
In this paper we study Gaussian queues (that is, queues fed by Gaussian processes, such as fractional Brownian motion (fBm) and the integrated Ornstein-Uhlenbeck (iOU) process), with a focus on the correlation structure of the workload process. The main question is: to what extent does the workload process inherit the correlation properties of the input process? We first present an alternative definition of correlation that allows (in asymptotic regimes) explicit analysis. For the special cases of fBm and iOU we analyze the behavior of this metric under a many-sources scaling. Relying on (the generalized version of) Schilder's theorem, we are able to characterize its decay. We observe that the correlation structure of the input process essentially carries over to the workload process.