Empirical Testing Of The Infinite Source Poisson Data Traffic Model

Abstract

The infinite source Poisson model is a fluid queue approximation of network data transmission that assumes that sources begin constant rate transmissions of data at Poisson time points for random lengths of time. This model has been a popular one as analysts attempt to provide explanations for observed features in telecommunications data such as self-similarity, long range dependence and heavy tails. We survey some features of this model in cases where transmission length distributions have (a) tails so heavy that means are infinite, (b) heavy tails with finite mean and infinite variance and (c) finite variance. We survey the self-similarity properties of various descriptor processes in this model and then present analyses of four data sets which show that certain features of the model are consistent with the data while others are contradicted. The data sets are 1) the Boston University 1995 study of web sessions, 2) the UC Berkeley home IP HTTP data collected in November 1996, 3) traces collected in end of 1997 at a Customer Service Switch in Munich, and 4) detailed data from a corporate Ericsson WWW server from October 1998.

^#Research supported by the Gothenburg Stochastic Centre, by the EU TMR network ERB-FMRX-CT96-0095 on “Computational and statistical methods for the analysis of spatial data” and by the Knut and Aline Wallenburg Foundation. Sidney Resnick's research was also partially supported by NSF grant DMS-97-04982 and NSA Grant MDA904-98-1-0041 at Cornell University.

Keywords:

• Data transmission modelling
• Internet traffic
• Heavy tails
• Regular variation
• Pareto tails
• Self-similarity
• Scaling
• Primary 62N09
• Secondary 60K250

Acknowledgment

We are very grateful to Helmut Gogl, for providing us with the Munich lo and Munich hi data sets, and to P. Abry, for letting us use his wavelet estimation program, and to both for illuminating discussions. We also want to thank M. Greiner,Å. Arvidsson, P. Abry, W. Willinger, Steve Gribble, and J. Istas for useful conversations and help with details and references.

Notes

^#Research supported by the Gothenburg Stochastic Centre, by the EU TMR network ERB-FMRX-CT96-0095 on “Computational and statistical methods for the analysis of spatial data” and by the Knut and Aline Wallenburg Foundation. Sidney Resnick's research was also partially supported by NSF grant DMS-97-04982 and NSA Grant MDA904-98-1-0041 at Cornell University.