traffic 6.4.2.2 Self-Similarity of Elastic IP Traffic In the last decade, many investigations focused on the characterization of measured IP traffic in local and wide area networks. The most important result of these studies is that the IP traffic has fractal-like behavior, which indicates the burstiness, long-range dependence and self-similarity. Self-similarity means, the measured traffic rates are statistically the same in all time scales, i.e. small and large time scale [WPT98]. Usually, the degree of self similarity is mathematically measured in the light of the Hurst parameter H. The detailed definition of self-similarity and the Hurst parameter is given in Appendix A.7. If 0.5<H<1, the traffic is considered as self-similar. This is the so-called Hurst effect. The self similarity of IP traffic can be caused by the heavy tail file size distributions at the application layer, other possible reasons are the TCP congestion control and TCP retransmission scheme for reliable transport. When transferring the elastic IP traffic in the UMTS network, the IP packets are converted into corresponding shaped FP PDU streams. For each TCP round trip time, one or several TCP packets are sent in a time, which cause the burst of the traffic. It is expected that the aggregated UMTS lub traffic, i.e. the superposition of FP PDU streams of all users, inherit the burstiness and self-similarity property of the IP traffic. This can be proven by the following example. Figure 6.46 shows the Cumulative Distribution Function (CDF) of the FP PDU inter-arrival time in case of carrying pure elastic IP traffic (all users transmit with RAB 128 kbps). It can be seen that the CDF curve has several abrupt steps instead of a smooth curve. Figure 6.47 plots the property of the given aggregated UMTS traffic. The value of the Hurst parameter H is obtained by the skewness of the linear regression. In this figure, its value equals to 0.69 (i.e. H>0.5). This demonstrates that the aggregated UMTS traffic indeed has the self-similarity property. 6 Dime