On the overflow probability asymptotics in a Gaussian queue

Gaussian processes are a powerful tool in network modeling since they permit to capture the long memory property of actual traffic flows. In more detail, under realistic assumptions, fractional Brownian motion (FBM) arise as the limit process when a huge number of on-off sources (with heavy-tailed sojourn times) are multiplexed in backbone networks. This paper studies fluid queuing systems with a constant service rate fed by a sum of independent FBMs, corresponding to the aggregation of heterogeneous traffic flows. For such queuing systems, logarithmic asymptotics of the overflow probability, an upper bound for the loss probability in the corresponding finite-buffer queues, are derived, highlighting that the FBM with the largest Hurst parameter dominates in the estimation. Finally, asymptotic results for the workload maximum in the more general case of a Gaussian input with slowly varying at infinity variance are given.