We consider a fluid queue with sessions arriving according to a Poisson process. A long-tailed distribution of session lengths induces long range dependence in the system and causes its performance to deteriorate. The deterioration is due to occurrence of load regimes far from average ones. Nonetheless, the extent of this performance deterioration is shown to depend crucially on the average values of the system parameters.
"How system performance is affected by the interplay of averages in a fluid queue with long range dependence induced by heavy tails." Ann. Appl. Probab. 9 (2) 352 - 375, May 1999. https://doi.org/10.1214/aoap/1029962746