Heath, David; Resnick, Sidney; Samorodnitsky, Gennady Heavy tails and long range dependence in on/off processes and associated fluid models. (English) Zbl 0981.60092 Math. Oper. Res. 23, No. 1, 145-165 (1998). 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. Cited in 44 Documents MSC: 60K25 Queueing theory (aspects of probability theory) 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 90B22 Queues and service in operations research Keywords:long range dependence; heavy tails; on/off models; G/G/1 queue; fluid models PDFBibTeX XMLCite \textit{D. Heath} et al., Math. Oper. Res. 23, No. 1, 145--165 (1998; Zbl 0981.60092) Full Text: DOI Link