Upper-bounds for tail probability of a queue with long-range dependent input

We consider the performance analysis of a queueing system with a LRD process as input. The LRD input is modeled by a fractional Gaussian noise (FGN), and the performance measure considered is the tail probability of the queue. Due to the lack of any Markovian structure of the FGN, the only exact analytical results available concerning the performance measure are a lower-bound and a large deviations result. We improve the understanding of this queueing system by deriving a transient upper-bound for the performance measure, for all values of buffer threshold. This transient upper-bound is then shown to be very tight, compared to the existing lower-bound; hence it compliments existing results well. We also propose two upper-bounds for the steady-state performance measure. One is obtained empirically, based on the derived transient upper-bound, while the other is obtained by using a Markov approximation technique.