1. Template for KyaTera presentations Nelson L. S. da Fonseca Optical Internet Laboratory - OIL Unicamp – IC, Campinas, SP, Brazil nfonseca@ic.unicamp.br

2. Motivations The increasing demand for bandwidth has suggested the development of an all Optical Internet based on WDM technology. However, the efficient use of WDM is only possible with a flexible technology, capable of the burstness of IP traffic. Due to problems of OPS and Circuit switching technologies, OBS has become the best choice in this way.

3. In OBS networks, several packets are transmitted in a single burst, thus changing the statistical properties of the network traffic. Previous research have already investigated the mutual interaction between self-similar traffic and OBS networks, however, these works did´nt take multifractal traffic in account. Understanding the relation between multifractal traffic and OBS networks is also of paramount importance since the use of monofractal models in the characterization of multifractal traffic may result in underutilization of network resources. Motivations

4. Burst assembly in OBS networks CoST. Min T.max  EF5K 4.8ms AF 30K50K 55ms BE 125K 600ms

5. The multifractal nature of IP traffic A self-similar (monofractal) q order process X(t) has statistical moments defined by: A multifractal process has its statistical moments defined by: where  (q) is the scaling function and presents non-linear behavior at different q moments

6. The multifractal nature of IP traffic In the wavelet domain, (2) is represented by: where d X (j,k) is the series of details got obtained by the decomposition of the X(t) process using the discrete wavelet transform. where  qé is the scaling exponent

7. Multiscale Diagram method Determines the occurrence of multifractality in a process by verifying the behavior of  (q) The estimative of  (q) depends on the determination of  q as defined in (4) To determine  q, the logscale diagram method is used. It is defined as the inclination of the curve that is close to the curve generated by relation between  j and 2 j, where the value of  j is given by : where n j is the number of details d X (j,.) in the time scale j, generated by the decomposition of X(t) using a discrete wavelet transform *P. Abry et. Al “The Multscale nature of Network Traffic Dicovery, Analysis and Modeling”, IEEE Signal Processing Magazine, v. 19, p. 28-46, Maio 2002.

8. The cut-off time scale Cutoff time scale (), multifractal measure

9. Numerical results Burst Assembly threshold (time or volume) ( ) - Cutoff time scale ()  >   < 