**3. Traffic characterization**

34 Telecommunications Networks – Current Status and Future Trends

sequence based on the method presented in (Norros, 1995). Each sample of the sequence represents the number of packets to be sent on a time interval of size T. The size of the time

As self-similar models, multifractals are multiscale process with rescaling properties, but with the main difference of being built on **multiplicative** schemes(Incite, 2011). In this way, they are highly non-Gaussian and are ruled by different limiting laws than the additive CLT (Central Limit Theorem). Therefore, multifractals can provide mathematical models to many world situations such as Internet traffic loads, web file requests, geo-physical data, images

In the self similar model, also called as monofractal, the Hurst parameter is a global property that quantifies the process changes according to changes in the scale. For multifractal traffic, however, the Hurst parameter becomes less efficient in this characterization and another metric is needed to perform the scaling analysis of the sample

There are several ways to infer the scaling behavior of traffic, one way is widely used by local singularities of the function. A singular point is defined as a point in an equation, curve, surface, etc., which have transitions or becomes degenerate (Ried et al., 2000). It is quite common that the singular points of the signal containing essential information on

In order to identify the singularities of a signal, it is necessary to measure the regularity of the same point, which will reflect in burst periods occurring at all traffic scales. In (Gilbert & Seuret, 2000) some examples can be found about the point and the exponents of the local

According to Veira, (Veira et al., 2000) the Hölder exponent is capable to describe the degree of a singularity. Considering a function *f : R*→ *R*, with x0 as real number, and **α** a stricted real positive number. It can be assumed that *f* belongs to *C***α(***x***0)** if a polynomial *Pm* with

(2)

As described in (Ludlam, 2004) a multifractal measure P can be characterized by calculating the distribution f ( α ) , known as the multifractal, or singularity, spectrum where α is the local Hölder exponente (Clegg, 2005 ; Castro e Silva, 2004 ; Vieira, 2006 ). This measure can be also shown as a probability density function P ( x ), in this case, the local Hölder

where ℬ ( l , x ) is a box centred at x with radius l , and P ( ℬ ) is the probability density integrated over the box ℬ . It describes the scaling of the probability within a box, centred

α ( x ) = lim l → 0 log P ( ℬ ( l , x ) ) log l (3)

Hölder values making possible to check the degree of uniqueness of network traffic.

interval and the mean of the sequence generated will depend on the traffic rate.

and many others. The Hölder function is defined by the h(t) function.

**2.4 Multifractal traffic** 

regularity.

network traffic packets.

degree **n < α**, as shown in (2).

exponente (; Gilbert & Seuret, 2000) is dened ad in (7).

on a point x , with the linear size of the box.

The process of traffic characterization is a preponderant point of a feasible network project. In this section a traffic characterization framework is described. The characterization intends to describe a step by step procedure, which may be useful to understand the behavior of traffic in large networks using a mathematical model as a tool to achieve good planning. One difficult issue to characterize traffic in IP networks is the changing environment due to new applications and new services that are appearing constantly. This implies that the

Fig. 2. Characterization process.

IP and 3G Bandwidth Management Strategies Applied to Capacity Planning 37

Fig. 4. Downstream traffic "on peak" and "off peak". The rate is normalized, 31 days

Figure 4 and 5 shows the downstream traffic collection results for a 31 days period. The most important source of traffic is the HTTP(Browsing) following by P2P applications(e-Donkey, Bitorrent, Kazaa). In Figure 10, the same analysis is made for a 24 hours period.

Fig. 5. Downstream traffic "on peak" and "off peak". Traffic rate is normalized, 24 hours

02 - 09:00:00

**Day - Time**

TIMESLOT

02 - 11:00:00

02 - 13:00:00

02 - 15:00:00

02 - 17:00:00

02 - 19:00:00

02 - 21:00:00

VoIP P2P E-Mail Browsing

(n = integer)

SERVICE

flows. This happens mainly because of applications such as SKYPE.

Figure 6 shows the packet size probability distribution. Less than 100 Bytes packets have 50% of probability. These samples are from a real network with Internet traffic of 4 million xDSL subscribers, demonstrating the very large use of voice packets even when using http

sampled (De Deus, 2007).

**Mbps / n**

01 - 21:00:00

03 - 03:00:00

04 - 09:00:00

BANDWIDTH SUM

05 - 15:00:00

06 - 21:00:00

08 - 03:00:00

09 - 09:00:00

10 - 15:00:00

11 - 21:00:00

13 - 03:00:00

14 - 09:00:00

15 - 15:00:0

16 - 21:00:0

**Day - Time**

TIMESLOT

18 - 03:00:0

19 - 09:00:0

20 - 15:00:0

21 - 21:00:0

23 - 03:00:0

24 - 09:00:0

25 - 15:00:0

26 - 21:00:0

28 - 03:00:0

29 - 09:00:0

30 - 15:00:0

31 - 21:00:0

VoIP P2P E-Mail Browsing

(n = integer)

SERVICE

sampled (De Deus, 2007).

0

01 - 21:00:00

01 - 23:00:00

02 - 01:00:00

02 - 03:00:00

02 - 05:00:00

02 - 07:00:00

50

100

150

**Mbps / n**

200

250

300

BANDWIDTH SUM

characterization used in real environments shall considerer the evolution and the amount of variation in the types of services, including not well known agents as social behavior and emerging applications.

The efficiency in traffic characterization is given by the model accuracy when compared with real traffic measures. As said by (Takine et al.*,* 2004) a traffic model can only exist if there is a procedure for efficient and accurate inference for the parameters of the same mathematical structure. The traffic characterization is the main information source for the correct mathematical interpretation of network traffic. Once characterized, the traffic may be reproduced in different scales and periods and inserted into network simulators.

Figure 2 shows a complete characterization flow to optimize planning. This procedure was implemented in the GTAR (Barreto, 2007) simulator, developed within our research.
