On the Effective Envelopes for Fluid Queues with Gaussian Input

Thanks to their flexibility and compact characterization, Gaussian processes have emerged as popular models to describe the traffic dynamics in a wide class of the modern telecommunication networks. A relatively new characterization of traffic flows is based on the effective envelopes, which represent a probabilistic generalization of the arrival curve of Network Calculus. In this paper, we analyse the effective envelopes for a general Gaussian process and use these results to derive non-asymptotic performance bounds for a fluid queuing system. To highlight the effectiveness of the proposed approach, numerical results are shown taking into account heterogeneous traffic flows as well as different correlation structures