Template for KyaTera presentations

Template for KyaTera presentations

Nelson L. S. da FonsecaOptical Internet Laboratory - OIL

Unicamp – IC, Campinas, SP, Brazilnfonseca@ic.unicamp.br

MotivationsMotivations

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.

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.

MotivationsMotivations

Burst assembly in OBS networksBurst assembly in OBS networks

CoS T. Min T.max

EF 5K 5K 4.8ms

AF 30K 50K 55ms

BE 125K 125K 600ms

The multifractal nature of IP trafficThe 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

)1(|||)1(||)(| qHqq tXEtXE

)2(|||)1(||)(| )(qqq tXEtXE

The multifractal nature of IP trafficThe multifractal nature of IP traffic

In the wavelet domain, (2) is represented by:

where dX (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

)3(2|),(| )( jkjdE qjqX

)4(2

)(q

q q

Multiscale Diagram methodMultiscale 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 2j , where the value of j is given by :

where nj is the number of details dX (j,.) in the time scale j, generated by the decomposition of X(t) using a discrete wavelet transform

)5(|),(||),(|1

1

qX

n

k

qX

jj kjdEkjdn

j

*P. Abry et. Al “The Multscale nature of Network Traffic Dicovery, Analysis and Modeling”, IEEE Signal ProcessingMagazine, v. 19, p. 28-46, Maio 2002.

The cut-off time scaleThe cut-off time scale

Cutoff time scale (), multifractal measure

Numerical resultsNumerical results

Burst Assembly threshold (time or volume) ( ) - Cutoff time scale ()

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