Small and Large Time Scale Analysis of a Network Traffic Model
 Krishanu Maulik,
 Sidney Resnick
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Empirical studies of the internet and WAN traffic data have observed multifractal behavior at time scales below a few hundred milliseconds. There have been some attempts to model this phenomenon, but there is no model to connect the small time scale behavior with behavior observed at large time scales of bigger than a few hundred milliseconds. There have been separate analyses of models for high speed data transmissions, which show that appropriate approximations to large time scale behavior of cumulative traffic are either fractional Brownian motion or stable Lévy motion, depending on the input rates assumed. This paper tries to bridge this gap and develops and analyzes a model offering an explanation of both the small and large time scale behavior of a network traffic model based on the infinite source Poisson model. Previous studies of this model have usually assumed that transmission rates are constant and deterministic. We consider a nonconstant, multifractal, random transmission rate at the user level which results in cumulative traffic exhibiting multifractal behavior on small time scales and selfsimilar behavior on large time scales.
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 Title
 Small and Large Time Scale Analysis of a Network Traffic Model
 Journal

Queueing Systems
Volume 43, Issue 3 , pp 221250
 Cover Date
 20030301
 DOI
 10.1023/A:1022894627652
 Print ISSN
 02570130
 Online ISSN
 15729443
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 M/G/∞ queue
 heavy tails
 long range dependence
 multifractal
 Hausdorf dimension
 Lévy process
 transmission schedule
 data networks
 infinite source Poisson model
 selfsimilarity
 weak convergence
 Industry Sectors
 Authors

 Krishanu Maulik ^{(1)}
 Sidney Resnick ^{(2)}
 Author Affiliations

 1. Department of Statistical Science, Cornell University, Ithaca, NY, 14853, USA
 2. School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY, 14853, USA