Fractional Lévy motion and its application to network traffic modeling

We introduce a general non-Gaussian, self-similar, stochastic process called the fractional Lévy motion (fLm). We formally expand the family of traditional fractal network traffic models, by including the fLm process. The main findings are the probability density function of the fLm process, several...

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Bibliographic Details
Published in:Computer networks (Amsterdam, Netherlands : 1999) Netherlands : 1999), 2002-10, Vol.40 (3), p.363-375
Main Authors: Laskin, N., Lambadaris, I., Harmantzis, F.C., Devetsikiotis, M.
Format: Article
Language:English
Subjects:
Communications networks
Fractal queueing theory
Heavy-tailed distribution
Probability
Scalability
Scaling
Self-similarity
Stochastic models
Studies
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Summary:We introduce a general non-Gaussian, self-similar, stochastic process called the fractional Lévy motion (fLm). We formally expand the family of traditional fractal network traffic models, by including the fLm process. The main findings are the probability density function of the fLm process, several scaling results related to a single-server infinite buffer queue fed by fLm traffic, e.g., scaling of the queue length, and its distribution, scaling of the queuing delay when independent fLm streams are multiplexed, and an asymptotic lower bound for the probability of overflow (decreases hyperbolically as a function of the buffer size).
ISSN:1389-1286
1872-7069
DOI:10.1016/S1389-1286(02)00300-6