A Storage Model with High Rate and Long RangeDependent On / O Sources

We consider a uid queueing problem with an innnite reservoir with output rate C, fed by an innnite superposition of identical On/OO sources with large instantaneous bit rate h C. The On periods have innnite variance, generating Long Range Dependence. It is shown that the distribution of the stationary queue content at embedded time points is heavy tailed with innnite mean. It is explained why this tail behaviour is found rather than Weibullian behaviour which can also arise with heavy On/OO sources. The equilibrium distribution of the maximum queue content during a busy period is shown to be heavy tailed with innnite variance.