On the maximum workload of a queue fed by fractional Brownian motion

Consider a queue with a stochastic fluid input process modeled as fractional Brownian motion (fBM).When the queue is stable, we prove that the maximum of the workload process observed over an interval of length t grows like .(logt)1/(2.2H),whereH > ½istheself.similarityindex(alsoknownastheHurstparameter)thatcharacterizesthefBMandcanbeexplicitlycomputed.Consequently,wealsohavethatthetypicaltimerequiredtoreachalevelbgrowslike\exp{b^{2(1-H)}}.We also discuss the implication of these results for statistical estimation of the tail probabilities associated with the steady-state workload distribution.