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Self-similar communication models and very heavy tails. (English) Zbl 1083.60521
Summary: Several studies of file sizes either being downloaded or stored in the World Wide Web have commented that tails can be so heavy that not only variances are infinite, but so are means. Motivated by this fact, we study the infinite node Poisson model under the assumption that transmission times are heavy tailed with infinite mean. The model is unstable but we are able to provide growth rates. Self-similar but nonstationary Gaussian process approximations are provided for the number of active sources, cumulative input, buffer content and time to buffer overflow.

60K25 Queueing theory (aspects of probability theory)
60F05 Central limit and other weak theorems
60F10 Large deviations
60F17 Functional limit theorems; invariance principles
60G18 Self-similar stochastic processes
68U35 Computing methodologies for information systems (hypertext navigation, interfaces, decision support, etc.)
94C99 Circuits, networks
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