During the last decade packet traces collected from both Local Area Networks (LAN) and Wide Area Networks (WAN) have been extensively analysed in the framework of self-similar processes. Not only is there ample empirical evidence supporting the existence of self-similarity in network traffic data, but also mathematical models have been established which suggest physical explanations for observed self-similarity. Of course in practice self-similarity can only hold over a finite range of scales, whence the need for a statistically founded test for determining the scaling range. A further difficulty that arises when modelling packet traces is distinguishing long-range correlation from trends in the mean packet arrival rate.

In this talk we present a non-parametric statistical test for self-similarity and use it both to determine scales over which we have a constant scaling regime and to determine time intervals wherein the intensity process appears to be stationary. The method is then applied to some publicly available LAN and WAN traces. These traces all exhibited self-similarity over a range of around 5 seconds to 5 minutes. The change in scaling below 5 seconds is most likely due to the effect of the network protocols used to transmit packets. Above 5 minutes we may be seeing the effect of finite network capacity, which puts an upper limit on the traffic intensity. Some of the traces we looked at also showed changes in the mean packet arrival rate and/or scaling behaviour over time. The length of stationary periods varied from 5 minutes to 120 minutes (the longest trace we considered).
 

Convenor:Kais Hamza