**4.1 Analysis of an IP network**

The first network to be evaluated is a Brazilian Service Provider in Brazil, with more than ten million PSTN (Public Switched Telephone Network) subscribers and more than one million ADSL as well. The IP network is shown Figure 3 each access layer is a PPPoX router capable called BRAS(Broadband Router Access Server).

Fig. 3. Testbed Network Architecture with 40% of simultaneous attached subscribers at least, all IP/MPLS interface 1 or 10 Gigabit Ethernet, also for long distance. (De Deus, 2007).

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

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

Figure 2 shows a complete characterization flow to optimize planning. This procedure was

The first network to be evaluated is a Brazilian Service Provider in Brazil, with more than ten million PSTN (Public Switched Telephone Network) subscribers and more than one million ADSL as well. The IP network is shown Figure 3 each access layer is a PPPoX router

Fig. 3. Testbed Network Architecture with 40% of simultaneous attached subscribers at least, all IP/MPLS interface 1 or 10 Gigabit Ethernet, also for long distance. (De Deus, 2007).

reproduced in different scales and periods and inserted into network simulators.

implemented in the GTAR (Barreto, 2007) simulator, developed within our research.

emerging applications.

**4. Experimental analysis 4.1 Analysis of an IP network** 

capable called BRAS(Broadband Router Access Server).

Fig. 4. Downstream traffic "on peak" and "off peak". The rate is normalized, 31 days sampled (De Deus, 2007).

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 sampled (De Deus, 2007).

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

IP and 3G Bandwidth Management Strategies Applied to Capacity Planning 39

In Table 1 is shown the estimation of the H parameter for the HTTP (Hyper Text Transfer Protocol) applications. As can be seen, the H relies value between 0.67 and 0.93, which also shows a higher degree of self-similarity, considering that the lower value appears just in one

The estimation of the the Hurst parameter in Table 1 uses three different methods: the Variance-Time Plot Method, the Kettani-Gubner Method (Clegg, 2005), (Barreto, 2007). Also a Chi-squared analysis was made as a non-parametric test of significance (Perlingeiro, 2006), (De Deus, 2007), (Clegg, 2005) due to the fact that it is necessary to verify the distribution similarity. The statistical significance test allows, with a certain degree of confidence, the acceptance or rejection of a hypothesis, as shown in Figure 7. The sampled links had a load,

Figure 7 shows the Hölder calculation for the traffic. The conclusion in fact is that the traffic is self-similar and monofractal, when the measurement is done in a 5 minutes per sample.

Fig. 7. P2P and http 5 minutes samples, Hölder exponent using the local Hölder Oscillation

Figure 8 shows the proposal of a real-time network forecast. First, in the network the samples are collected. Then the traffic is classified per application. The estimation and a characterization of the parameters of collected samples are calculated. These parameters are used as input to a traffic forecast tool based on a mathematical traffic model which intends to find the sub-optimal capacity of the link for that traffic load, considering its self-similarity

The objective is to use these parameters as inputs of a simulation tool to forecast the traffic and feedback in real-time the network to provide a new model to capacity plan in the

Following Figure 8, first the network samples are collected. Thenext step is the execution of classification procedure per application using tools based on protocols (Destination, Source, Port, Payload types). Next phase is to estimate the parameter (e.g. Hurst, Hölder) that will

day. For the P2P applications, the H parameter relies between 0.86 and 0.96.

in the worst case around 70%.

Based method [fraclab].

nature.

backbone.

**4.1.1 Bandwidth control strategies for the IP network** 

Fig. 6. Packet Size Probability Distribution (De Deus, 2007).

Table 1 shows and per application anaylis of traffic in which the Hurst parameter was calculated with two different methods (De Deus, 2007). For real time traffic, the Hurst parameter calculation demands attention because in some cases if statistical process does not have a representative long range dependence characteristic the parameter may be wrongly interpreted. Another issue is the trend present in the periodic traffic. For a more accurate estimation, the cycle regularity is removed to delete all observed trends.


Table 1. HTTP and P2P Hurst parameter estimation for 5 minutes average.

Table 1 shows and per application anaylis of traffic in which the Hurst parameter was calculated with two different methods (De Deus, 2007). For real time traffic, the Hurst parameter calculation demands attention because in some cases if statistical process does not have a representative long range dependence characteristic the parameter may be wrongly interpreted. Another issue is the trend present in the periodic traffic. For a more

> **Hurst Hurst Chi-Square (***Variance-Time Plot* **) (Kettani-Gubner) (Gaussian Distribution)** 1 0,843 0,895 31,042 2 0,812 0,878 71,299 3 0,901 0,926 38,146 4 0,9 0,934 52,569 5 0,815 0,879 32,549 6 0,816 0,904 62,042 7 0,865 0,906 17,91 8 0,87 0,916 39,653 9 0,907 0,935 28,028 10 0,867 0,919 21,785 11 0,869 0,906 27,167 12 0,671 0,861 35,778 13 0,878 0,909 36,208 14 0,839 0,894 44,604 15 0,874 0,907 30,611 16 0,753 0,85 23,292 17 0,851 0,914 40,299

**Hurst Hurst Chi-Square (***Variance-Time Plot* **) (Kettani-Gubner) (Gaussian Distribution)**

1 0,915 0,948 63,549 2 0,942 0,962 49,771 3 0,937 0,963 45,25 4 0,902 0,935 28,243 5 0,902 0,928 20,708 6 0,901 0,942 30,181 7 0,939 0,964 43,258 8 0,932 0,964 52,354 9 0,937 0,968 39,007 10 0,922 0,948 38,576 11 0,86 0,926 37,5 12 0,904 0,942 33,84 13 0,937 0,965 55,799 14 0,922 0,958 46,972 15 0,935 0,963 46,757 16 0,935 0,967 49,986 17 0,933 0,964 37,285

accurate estimation, the cycle regularity is removed to delete all observed trends.

Table 1. HTTP and P2P Hurst parameter estimation for 5 minutes average.

Fig. 6. Packet Size Probability Distribution (De Deus, 2007).

160

224

288

352

416

**Packet Size** 

480

544

1024

2048

3072

4096

0,000 0,100 0,200 0,300 0,400 0,500 0,600

**Probability** 

0-32

96

**Day**

**Day**

In Table 1 is shown the estimation of the H parameter for the HTTP (Hyper Text Transfer Protocol) applications. As can be seen, the H relies value between 0.67 and 0.93, which also shows a higher degree of self-similarity, considering that the lower value appears just in one day. For the P2P applications, the H parameter relies between 0.86 and 0.96.

The estimation of the the Hurst parameter in Table 1 uses three different methods: the Variance-Time Plot Method, the Kettani-Gubner Method (Clegg, 2005), (Barreto, 2007). Also a Chi-squared analysis was made as a non-parametric test of significance (Perlingeiro, 2006), (De Deus, 2007), (Clegg, 2005) due to the fact that it is necessary to verify the distribution similarity. The statistical significance test allows, with a certain degree of confidence, the acceptance or rejection of a hypothesis, as shown in Figure 7. The sampled links had a load, in the worst case around 70%.

Figure 7 shows the Hölder calculation for the traffic. The conclusion in fact is that the traffic is self-similar and monofractal, when the measurement is done in a 5 minutes per sample.

Fig. 7. P2P and http 5 minutes samples, Hölder exponent using the local Hölder Oscillation Based method [fraclab].

#### **4.1.1 Bandwidth control strategies for the IP network**

Figure 8 shows the proposal of a real-time network forecast. First, in the network the samples are collected. Then the traffic is classified per application. The estimation and a characterization of the parameters of collected samples are calculated. These parameters are used as input to a traffic forecast tool based on a mathematical traffic model which intends to find the sub-optimal capacity of the link for that traffic load, considering its self-similarity nature.

The objective is to use these parameters as inputs of a simulation tool to forecast the traffic and feedback in real-time the network to provide a new model to capacity plan in the backbone.

Following Figure 8, first the network samples are collected. Thenext step is the execution of classification procedure per application using tools based on protocols (Destination, Source, Port, Payload types). Next phase is to estimate the parameter (e.g. Hurst, Hölder) that will

IP and 3G Bandwidth Management Strategies Applied to Capacity Planning 41

Fig. 9. Tunnel selection between two routers using Diffserv and Inteserv to select the specific

The bandwidth estimation most accepted definition, currently known, use a concept introduced by (Kelly et al.,1996), where there is a direct dependency on buffer size and time scales related to the buffer overflow possibility. The concept is shown in (6) where X[0, t] is the amount of bits that arrive in an interval [0, t], considering that X[0, t] has stationary increments. The letter b is the buffer size and t time or scale, BP is the capacity in bits per

Based on this theory, several bandwidth estimators have been proposed and evaluated for its effectiveness and complexity of evaluation. In (Fonseca et al., 2005) an evaluation of the FEP estimator model (Fractal Envelope Process) was developed with good results, for use in

Equation (7) represents the FEP process estimation where the K is the buffer, a is the average, H is the Hurst parameter, ��is the standart devitation and Ploss represents the probability of packet loss when a buffer overflow. This is only valid when 0.5 < H < 1.

Using (7) and correcting with (8) and (9), some curves are plotted in different time scales in Figure 10 (FEP Estimator and FEP Model). The best results are with 5 and 1 minutes, achieving the most next to average but still providing a good service with no delay, jitter or packet loss. The "Modelo FEP" *f*op means the dynamic calculation per hour, the "Tunel P2P constante" and "Tunel HTTP constant"means the estimation with a Poisson Distribution

*<sup>H</sup> loss <sup>H</sup>*

\* 2\*ln( \*

*EN <sup>a</sup> <sup>K</sup> <sup>P</sup> <sup>H</sup> <sup>H</sup>* <sup>−</sup> <sup>−</sup> <sup>=</sup> <sup>+</sup> <sup>−</sup> <sup>−</sup> <sup>1</sup> <sup>1</sup> )

( ) ( ) *<sup>H</sup>*

σ\* 1

�� � � �� � � � (6)

*H*

√��� �� ��5 � � � ��� (8)

(7)

����� �� <sup>=</sup> ��� � ����������

Estimator, the P2P and HTTP means the dynamic bandwidth calculation.

*H*

1

��� <sup>=</sup> <sup>2</sup> 5 ��

tunnel.

second.

high speed networks.

be used as input to a traffic forecast tool based on valid models (Norros *at al.*, 2000). The next step is to insert the parameter to a tool that will take a decision of how the autoconfiguration will be done and a configuration of the element abstracting the vendor (e.g. Juniper, Cisco, Huawei). In figure 7 the example of application of the feedback process is described using the auto configuration tool to change the tunnel characteristics, that will use the proposed framework in Figure 8, as an example of setting up an outstream traffic marked as Diffserv.

If the traffic can be characterized as asymptotical self-similar or monofractal or multifractal some ready prediction models based (e.g. fBm, MWM, MMW) can be used. The core idea is that using only some parameters the mathematical calculus can be feasible at real time, as shown in Figure 14.

Fig. 8. Proposal of a network real-time forecast framework with bandwidth estimation.

In this case, the tunnels are configured using the self-similarity bandwidth estimators, as described in (Carvalho, 2007). The traffic needs to be marked as the DiffServ and will be injected per tunnel as the auto configuration tunnel selection.

There are several methods used to estimate bandwidth. The method used in our example is the FEP(Fractal Envelope Process). This model has a good performance for long range dependence with a high degree of confidence in the quasi-Real Time estimation (De Deus, 2007).

be used as input to a traffic forecast tool based on valid models (Norros *at al.*, 2000). The next step is to insert the parameter to a tool that will take a decision of how the autoconfiguration will be done and a configuration of the element abstracting the vendor (e.g. Juniper, Cisco, Huawei). In figure 7 the example of application of the feedback process is described using the auto configuration tool to change the tunnel characteristics, that will use the proposed framework in Figure 8, as an example of setting up an outstream traffic

If the traffic can be characterized as asymptotical self-similar or monofractal or multifractal some ready prediction models based (e.g. fBm, MWM, MMW) can be used. The core idea is that using only some parameters the mathematical calculus can be feasible at real time, as

Fig. 8. Proposal of a network real-time forecast framework with bandwidth estimation.

injected per tunnel as the auto configuration tunnel selection.

In this case, the tunnels are configured using the self-similarity bandwidth estimators, as described in (Carvalho, 2007). The traffic needs to be marked as the DiffServ and will be

There are several methods used to estimate bandwidth. The method used in our example is the FEP(Fractal Envelope Process). This model has a good performance for long range dependence with a high degree of confidence in the quasi-Real Time estimation (De Deus,

marked as Diffserv.

shown in Figure 14.

2007).

Fig. 9. Tunnel selection between two routers using Diffserv and Inteserv to select the specific tunnel.

The bandwidth estimation most accepted definition, currently known, use a concept introduced by (Kelly et al.,1996), where there is a direct dependency on buffer size and time scales related to the buffer overflow possibility. The concept is shown in (6) where X[0, t] is the amount of bits that arrive in an interval [0, t], considering that X[0, t] has stationary increments. The letter b is the buffer size and t time or scale, BP is the capacity in bits per second.

$$BP(b, t) = \frac{\log E\left[e^{bX[0, t]}\right]}{bt} \; 0 < b, t < \infty \tag{6}$$

Based on this theory, several bandwidth estimators have been proposed and evaluated for its effectiveness and complexity of evaluation. In (Fonseca et al., 2005) an evaluation of the FEP estimator model (Fractal Envelope Process) was developed with good results, for use in high speed networks.

Equation (7) represents the FEP process estimation where the K is the buffer, a is the average, H is the Hurst parameter, ��is the standart devitation and Ploss represents the probability of packet loss when a buffer overflow. This is only valid when 0.5 < H < 1.

$$EN = \overline{a} + K^{\frac{H-1}{H}} \ast \left(\sqrt{-2^\* \ln(P\_{\text{loss}})} \ast \sigma\right)^{\frac{1}{H}} \ast H (1 - H)^{\frac{1-H}{H}} \tag{7}$$

Using (7) and correcting with (8) and (9), some curves are plotted in different time scales in Figure 10 (FEP Estimator and FEP Model). The best results are with 5 and 1 minutes, achieving the most next to average but still providing a good service with no delay, jitter or packet loss. The "Modelo FEP" *f*op means the dynamic calculation per hour, the "Tunel P2P constante" and "Tunel HTTP constant"means the estimation with a Poisson Distribution Estimator, the P2P and HTTP means the dynamic bandwidth calculation.

$$f\_{op} = \frac{2}{5} \frac{EN}{\sqrt{b'L}} \text{ if } 0.5 < H \le 0.7 \tag{8}$$

IP and 3G Bandwidth Management Strategies Applied to Capacity Planning 43

the difference will be minimum. In the other hand, when going to small time scales .05, .5 or 1 seconds, there is a trend in super estimation, proportional to the diminishing of the Hurst

As shown in many works (Leland et al., 1994), (Abry et al., 2002), (Carvalho et al., 2009), the Hurst parameter can show an accurate and single way to determinate the self-similarity. The Erlang model is very useful because its simplicity. A traffic engineer only needs to have some little information about service demand such as Retention time, blocking Probability, Number of Calls in the maximum usage hour to have the traffic and number of channels or

The curves in Figure 10 show the possibility to have something, not so easy as Erlang model, but also possible to be achieved as a traffic model when a self-similar characterization is feasible. Also, the multi fractal model can also help to understand this same traffic in smaller

The second evaluated network is a brazilian 3G network. This network runs with more than 1 million attached 3G costumers with national coverage. The traffic samples were collected in July, 2009 in three different locations (Leblon, Barra da Tijuca and Centro) in Rio de Janeiro.

> Monitor 2

> > Physical RNC

The main objective in this section is to investigate planning and project deployment phases based on traffic characterization. The first step is to classify the traffic per application. The second is to characterize the traffic using a procedure based on self-similarity (Clegg, 2005)

Ethernet MPLS - BFD ATM

Tellabs 8600

IuB ATM

Figure 12 shows the network topology for the Ethernet physical node B (ATM node) with an ATM-IP router which is responsible to convert ATM to Ethernet(IP). The same situation is found in RNC side where a Tellabs ATM-IP router aggregates all node B physical uplinks,

Two monitors were located in the network to collect the traffic, as shown in Figure 11.

Metro

parameter.

resource needed.

**4.2 Analysis of a 3G network** 

Fig. 11. 3G Network.

Node B

or multifractal analysis (Carvalho *et al*, 2009).

Physical Ethernet

IuB Ethernet

Monitor 1

scales, or in some case depending the traffic nature.

$$f\_{op} = \frac{2}{75} \frac{EN}{\sqrt{b'L}} \text{ if } 0.7 < H < 1\tag{9}$$

The *fop* is calculated based on (Perlingeiro & Ling, 2005) study as shown in (8) and (9), where *EN* is from (7) and *b'* is the normalized buffer (*b'*=*b*/*b0*), where *b* is the buffer and *b0* minimum possible buffer size, L is the burst factor.

Fig. 10. Bandwidth estimation curves using the FEP method.

The FEP Model shown in Figure 10 uses a dynamic tunnel configurator as shown in Figure 9, denoting a better usage of the total available bandwidth. In the figures it appears that when a constant calculated bandwidth is used, more bandwidth is required. In the same way, the FEP Estimator shows that as much aggregated the traffic will be in any time scale, the difference will be minimum. In the other hand, when going to small time scales .05, .5 or 1 seconds, there is a trend in super estimation, proportional to the diminishing of the Hurst parameter.

As shown in many works (Leland et al., 1994), (Abry et al., 2002), (Carvalho et al., 2009), the Hurst parameter can show an accurate and single way to determinate the self-similarity. The Erlang model is very useful because its simplicity. A traffic engineer only needs to have some little information about service demand such as Retention time, blocking Probability, Number of Calls in the maximum usage hour to have the traffic and number of channels or resource needed.

The curves in Figure 10 show the possibility to have something, not so easy as Erlang model, but also possible to be achieved as a traffic model when a self-similar characterization is feasible. Also, the multi fractal model can also help to understand this same traffic in smaller scales, or in some case depending the traffic nature.
