Self-similar communication models and very heavy tails

Sidney I. Resnick · Holger Rootzén

71 citations0/0 files storedThe Annals of Applied Probability

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Advanced Queuing Theory Analysis Stochastic processes and statistical mechanics Probability and Risk Models

Abstract

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 are variances 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.

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References

1987Extreme Values, Regular Variation and Point Processes 1987Applied Probability and Queues 1987Brownian Motion and Stochastic Flow Systems.1996Tail Index Estimation, Pareto Quantile Plots Regression Diagnostics 1996The qq-estimator and heavy tails 1997Smoothing the Hill Estimator 1999Asymptotic results for multiplexing subexponential on-off processes 1999Stochastic Storage Processes: Queues, Insurance Risk, Dams and Data Communication

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