HEAVY TRAFFIC ANALYSIS OF A STORAGE MODEL WITH LONG-RANGE DEPENDENT ON OFF SOURCES/

We consider a fluid queueing system with infinite storage capacity and constant output rate offered a superposition of N identical On/Off so urces, where the ratio of input to output rate is small. The On and/or Off periods have heavy tailed distributions with infinite variance, g iving rise to Long Range Dependence in the arrival process. In the lim it of a large number of sources and high load, it is shown that the ta il of the stationary queue content distribution is Weibullian, implyin g much larger queue contents than in the classical case of exponential tails. Noting that similar results were recently found by I. Norros f or a storage system input by a Fractional Brownian Motion, we then sho w how the two models are related, thus providing a further physical mo tivation for the Fractional Brownian Motion model.