Steady-state distribution of the buffer content for M/G/infinity input fluid queues

We consider a fluid queue with on periods initiated by a Poisson process an d having a long-tailed distribution. This queue has long-range dependence, and we compute the asymptotic behaviour of the steady-state distribution of the buffer content. The tail of this distribution is much heavier than the tail of the buffer content distribution of a queue which does not possess long-range dependence and which has light-tailed on periods and the same tr affic intensity.