| The analysis of Gaussian queues, i.e., queues fed by Gaussian traffic, has been attracting increasing attention in the applied probability and queueing research communities, motivated by their wide-spread use in many application domains. Focusing on the field of communication networking, the intrinsic flexibility of the Gaussian traffic model has proven to be particularly useful. Its capability of covering a broad range of highly relevant correlation structures has made it one of the leading paradigms in traffic modelling. Notably, the class of Gaussian models contains long-range dependent processes such as fractional Brownian motion (fBm). Despite the substantial research effort spent, and the considerable number of useful results obtained, there are still many open challenging problems. The main goal of the proposed research is to gain a deeper understanding of the occurrence of rare events (particularly buffer overflow) in Gaussian queues. The research topics include: (A) assessment of methods for retrieving traffic characteristics from samples of the buffer content distribution; such methods have proven to work well for (purely) Gaussian traffic, but it is unclear whether these carry over to traffic aggregates that tend to a Gaussian limit in a heavy-traffic regime; (B) large buffer asymptotics for concatenations of queues (tandem networks) fed by Gaussian input (for instance fBm); (C) many-sources asymptotics of infinite intersections of events, with emphasis on the impact of the 'smoothness' of the underlying Gaussian model on the nature of the solution. |
