Busy periods of fractional Brownian storage: A large deviations approach

A storage with constant service rate and fractional Brownian input is considered. It is shown how large deviation asymptotics of the buffer occupancy and the ongoing busy period can be obtained applying a generalized Schilder's theorem. The crucial point of the method is to identify the "most probable path" satisfying some criterion. Whereas this turns out to be very simple in the case of achieving a given buffer occupancy, the case of achiev-ing a given length of the ongoing busy period remains an open problem. Instead, tight bounds are obtained in this latter case.