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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.
MSC:
60K25Queueing theory
60F05Central limit and other weak theorems
60F10Large deviations
60F17Functional limit theorems; invariance principles
60G18Self-similar processes
68U35Information systems (hypertext navigation, interfaces, decision support, etc.)
94C99Circuits, networks