Heavy Tails and Long Range Dependence in On/Off Processes and Associated Fluid Models

On/off models are common inputs for a variety of communication network models as well as storage and inventory models. A stationary renewal process alternating periods of activity active transmission, fluid buildup, etc with periods of inactivity silence, no transmission, inputs off, etc induces a stationary indicator process which indicates if the system is active or not. Heavy tails for the on periods induces a covariance function for the indicator process which decreases slowly at a rate characteristic of long range dependence. This has dramatic consequences for fluid models where fluid flows in at constant rate and there is a constant rate of release.