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Heavy tails and long range dependence in on/off processes and associated fluid models. (English) Zbl 0981.60092
Summary: 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 induce 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 a constant rate and there is a constant rate of release.

60K25 Queueing theory (aspects of probability theory)
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
90B22 Queues and service in operations research
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