Proof of a fundamental result in self-similar traffic modeling
ACM SIGCOMM Computer Communication Review
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part III: ICCS 2007
Self-similarity and long-range dependence in teletraffic
MUSP'09 Proceedings of the 9th WSEAS international conference on Multimedia systems & signal processing
A survey on computing Lévy stable distributions and a new MATLAB toolbox
Signal Processing
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We model the workload of a network device responding to a random flux of work requests with various intensities and durations in two ways, a conventional univariate stochastic integral approach ("downstairs") and a higher-dimensional random field approach ("upstairs"). The models feature Gaussian, stable, Poisson and, more generally, infinitely divisible distributions reflecting the aggregate work requests from independent sources. We focus on the fractional Ornstein-Uhlenbeck Lévy process and the Telecom process which is the limit of renewal reward processes where both the interrenewal times and the rewards are heavy-tailed. We show that the Telecom process can be interpreted as the workload of a network responding to job requests with stable infinite variance intensities and durations and that fractional Brownian motion (fBM) can be interpreted in the same way but with finite variance intensities. This explains the ubiquitous presence of fBM in network traffic.