A NOVEL COMBINED NETWORK TRAFFIC PREDICTION

MODEL IN COGNITIVE NETWORKS

Xiaopu Shang

1

, Xiaomin Zhu

2

1

Institute of Information Systems, Beijing Jiaotong University, Beijing, China

2

School of Mechanical, Beijing Jiaotong University, Beijing, China

Dandan Li

Institute of Information Systems, Beijing Jiaotong University, Beijing, China

Keywords: Cognitive network, Traffic prediction, Neural network, Wavelet, Auto-regression.

Abstract: With the development of the network technology, the concept of Cognitive Network has been proposed and

studied, and various kinds of algorithms and models in Cognitive Networks thus have become an hot topic

of research. This paper proposes a novel model, which includes three stages. The proposed model may

achieve a high-precision traffic prediction in cognitive networks. The model solves some problems in

cognitive networks, such as low adaptive capability and an easy trap in local optimum when coming up with

a fluctuated network flow.

1 INTRODUCTION

The structure of Next Generation Network (NGN) is

becoming complicated and heterogeneous, while

Cognitive Network (CN) (Thomas R W, 2005) is

justly adaptive to the NGN because it has the ability

of autonomous learning and reconfiguration. A CN

can provide, over an extended period of time, better

end-to-end performance than a non cognitive

network. Cognition could be used to improve

resource management, Quality of Service (QoS),

security, access control, or many other network

goals.

In the research area of CN, the design of a

multi-time scale network traffic predication model

with “congnition” will play a key role in the

cognitive performance of the entire network and in

the load-balancing and traffic scheduling algorithm

of the congnitive network. According to the result of

traffic prediction, the CN can allocate the network

resource in advance, make data flow distributes

reasonably in the net, cope with load fluctuation,

reduce network congestion.

In the research of network traffic prediction

model, there are two difficulties (Kasabov N, 2002):

(1) A large scale network contains many complex

nonlinear systems, meanwhile it works under

some periodic fluctuations and trends of

nonlinear rising and falling.

(2) Computer network is subjected to interferences

of many random factors, but traditional single

models have poor adaptive capacity. So we

need combination models to realize traffic

prediction.

We analyze the present situation of network

traffic prediction, improve the wavelet pretreatment

method and BPNN(BP Neural Network) method,

design a network prediction model using combined

NN(Neural Network), and we simulate our model in

the environment of MATLAB to verify and analyze

the model. The conclusion proves the new model

work more precisely than traditional model.

The remainder of this paper is organized as

follows. Section 2 introduces the present research of

network traffic prediction. Section 3 accordingly

describes the related theories of this new model.

Section 4 presents the combination schemes and the

three-stage prediction model. The simulate results of

this new model are presented and analyzed in

section 5. Finally, section 6 makes an overall

conclusion.

205

Li D., Zhu X. and Shang X.

A NOVEL COMBINED NETWORK TRAFFIC PREDICTION MODEL IN COGNITIVE NETWORKS.

DOI: 10.5220/0003268502050211

In Proceedings of the Twelfth International Conference on Informatics and Semiotics in Organisations (ICISO 2010), page

ISBN: 978-989-8425-26-3

Copyright

c

2010 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved

2 A BRIEF REVIEW OF

NETWORK TRAFFIC

PREDICTION

The conception of CN is developed on the basis of

cognitive radios, and current researches mainly

focus on link layer, so research in network traffic

prediction of CN is not enough. However,

fundamentally the algorism of traffic prediction in

CN is to show “cognition”, provide necessary data to

other elements of CN. Thus, from the aspect of time

and data, it demands higher efficiency and precision

than traditional model.

The present technologies of network traffic

prediction can be divided into linear prediction and

nonlinear prediction. ARIMA model (Feng Huifang,

2005) and Kalman Filter model are the examples of

linear prediction model, such as self-adaptive linear

model proposed by Lv Jun (2004). As the linear

model can hardly describe the true features of real

network traffic, nonlinear prediction models are

proposed by scholars. Of course, nonlinear models

sometimes may include linear elements, such as

multi-scale combination predication model proposed

by Khotanzad A (2003). In these kind models, as

nonlinear elements play a more important role than

linear elements, we still call them nonlinear model.

The typical model of nonlinear model is NN model.

The predication model based on NN can be

divided into two kinds. One is to put some algorithm

inside NN, form the scheme as Figure 1 shows.

Figure1: The forcasting model of algorithm inside NN.

WNN (Wavelet Neural Network) proposed by Wang

Peng (2008) just put wavelet decomposition

algorithm into hidden layer of NN. We call this

Prediction Model of NN with Build-in Algorithm.

The other is to separate the data processing and

onefold NN’s prediction as figure 2.

Figure 2: The forecasting model of algorithm outside NN.

The data pre-processing provides data more

suitable to the input of NN, we call this Prediction

Model of NN with Outside Algorithm. One such

combined NN model is presented by (Feng Hailiang,

2006). This is the main form nowadays. The model

we designed is just based on this.

Considering the character of nonlinear and

multi-scale in network traffic, Lei Ting (2006) gives

the resolution. They demonstrate the traffic and then

forecast the irregular part with ENN. Combine with

linear NN and nonlinear NN, a model that optimize

the forecasting result 4 times is proposed by Feng

Hailiang (2006), the precision is improved, but the

time it needs is not short enough. As for the

traditional problem in prediction model proposed by

Kasabov N (2002), some scholars, such as Wang

Peng (2008) and Cheng Guang (2004) have formed

all kinds of improved models based on NN,. Also,

traditional NN models have the problem of lagging

in learning and are easy to trap in local optimum,

owning limited ability in coping with sudden load in

the net. In order to solve this problem, the main

resolution is put wavelet decomposition algorithm

inside the 3rd layer of BPNN, Han Zhijie (2008)

properly deals with the local suboptimal, but still

spends much time getting a satisfying result.

Combine wavelet decomposition with NN as

prediction model is also a main resolution (Feng

Hailiang, 2006), but after the wavelet

decomposition, only a single kind of NN still have

the problem of rap into local optimum and cannot

develop the advance of multi-scale analysis of

wavelet.

3 RELATED THEORIES

3.1 Wavelet Transform

If square integrable function ψ(t) ε L2(R) meet the

following condition:

21

|()|||d

ψω ω ω

∧

+∞

−

−∞

<+∞

∫

, or

() 0tdt

ψ

+∞

−∞

=

∫

Where Ψ^(ω) is the Fourier

transform of Ψ(ω), than call it mother wavelet.

Through stretching and translation transformation,

the mother wavelet can be changed into wavelet

function:

ψa,b(t)= ψ(at-b),b ε R-{0}

(1)

In our model, we use the form of discrete

wavelet transformation as follows:

ICISO 2010 - International Conference on Informatics and Semiotics in Organisations

206

2

,

() , 2 ( (2 ))

j

j

jjk

D

kf f xkdx

ψψ

+∞

−

−

−∞

≤≥ −

∫

(2)

Where j is frequency domain resolution and k is

time shifting amount. Then we do expansion on time

series.

{f(t), t=1,2,…} is traffic time series, wavelet

function and scaling function can be described as:

1, 1 1,

() () () () ()

jjk j jk

k

f

tAktDkt

φψ

+∞ +∞

−−−

=−∞ −∞

=+

∑∑

(3)

Where

2

,

() 2 (2 )

j

j

jk

ttk

φφ

−

−

=−

and

2

,

() 2 (2 )

j

j

jk

ttk

φψ

−

−

=−

are scale space orthogonal basis and wavelet space

orthogonal basis separately, Aj(k) and Dj(k) are

scale coefficient and wavelet coefficient separately.

1,

() ()

φ

+∞

−

=−∞

∑

jjk

k

A

kt is the part of high frequency in

signal which shows detail signal and usually

contains noisy. And

11,

() ()

ψ

+∞

−−

−∞

∑

jjk

Dk t is the part

of low frequency in signal, it reflects the nature

character of signal, such as the trend of a signal or

the signal period.

As for this thesis, we demonstrate the traffic with

Mallat Algorithm, the algorithm can realize the

demonstrate simply and rapidly, and we have no

need to know the concrete structure of wavelet

function, wavelet decomposition or reconstruction

can be done with just a set of filter coefficients.

0

1

2

11

1

2

11

() ()

( ) 2 [ (2 ) (2 1)], 1,2,...,

() 2 [ (2) (2 1)]

jjj

jjj

Ak fk

A

kAkAkj L

Dk D k D k

−

++

−

++

=

=++=

=++

(4)

L is the number of layer, Aj(k) is approximation

signal, and Dj(k) is the detailed signal.

3.2 Auto-regression Model

Auto-regression (AR) model is a time series model.

Let {X

t

} denote time series, it is the linear function

of prophase expectation and stochastic component:

11 2 2tt t ptpt

XX XLX

φ

φφε

−− −

=+ ++ +

(5)

Where

1

φ

，

2

φ

，L，

p

φ

are autoregressive

coefficients, we use Levinson-Durbin recursive

algorithm (

Burg J P, 1975) to get their specific value.

Stochastic component

t

ε

, is a white noise series,

and it obeys standard normal distribution.

As for this thesis, we use AR model to forecast

the low frequency data that meet the stationary

condition, this may improve the forecasting speed

and promote forecasting efficiency.

3.3 Neural Network Model

Nowadays, BPNN, ENN, HNN, and KNN, etc. are

the popular NN models in use. We just introduce

KNN and BPNN that we used in the novel model.

KNN’s main idea is to self organize the

information outside into a conception in brain. As

for a system, it is just to organize a corresponding

presentation format in system automatically when

affected by information outside the system. This

includes adjustment of the NN’s weight coefficient.

KNN is a typical self organizing neural network

which is also called SOM. Its input layer is

monolayer and single-dimensional neurons, while

the output layer is two-dimensional neurons. The

format of lateral interaction between neurons in

output layer is Mexican Cap. So in the output layer,

KNN has the feedback character that the neurons are

closer, the effect is stronger. Thus, KNN can be the

detector of mode characteristics and an effective

method to enhance the ability of self adaptivity. In

this view, KNN can be a prompt model in the use of

network traffic prediction.

Based on the original NN, through self-organized

learning to simulate the biological nerve reflex is the

typical character of KNN. In a complex nonlinear

system that changes greatly, KNN can improve the

forecasting precision by the change of the content

and amount of study.

The learning process of KNN is as follows:

(1) Initialize the link weights, each weight can be

initialized from the training data arbitrarily;

(2) X

k

=

（

x

1

,x

2

,…,x

n

）

is input vector, for each input

vector, calculate the Euclidean distance W

ij

which

between X

i

k

and all of the output node N

j

;

(3) N

j*

, which has the minimum distance in

output node, is the winner in competition:

*

{1,2,..., }

min { }

jj

jm

dd

∈

=

;

(4) Adjust the link weights between output node

N

j*

and every input node X

i

k

in geometric

neighborhood: w

i j

=w

i j

+ η(t) (x

i

k

– w

ij

)，

i∈{1, 2, ..., n }，where η(t) is learning rate: 0<η(t)<1

；

(5) As for different t: t=1,2,…, come back to step

(3).

BPNN is a multilayer feed forward network

based on error back-propagation algorithm, which is

one of the broadly used ANN models. BPNN can

learn and restore many input-output mapping

relations without mathematical equations that reveal

A NOVEL COMBINED NETWORK TRAFFIC PREDICTION MODEL IN COGNITIVE NETWORKS

207

the relation between them. The learning rule of

BPNN is to make use of the steepest descent

method, continuously adjust the net weights value

and net threshould value by back propagation in

order to get a minimum square sum of error. The

learning course of BPNN is as figure 3.

As the one of the basic ANN model, BPNN

works on the principle of continuous error feedback:

The error is transmitted through output layer, then to

the hidden layer and input layer, and weight in every

layer can be corrected in the method of gradient

descent algorithm. In cycles of information forward

propagation and error back propagation, weights in

every layer can be modified, and this is the process

of NN’s learning. This process will last until the

output error can be accepted or the set learning times

are met.

Figure 3: The learning course of BPNN.

4 A NOVEL THREE-STAGE

COMBINED NETWORK

TRAFFIC PREDICTION

MODEL

4.1 Basic Thinking of the New Model

The network traffic is generally a kind of

non-stationary time series signal. The non-stationary

of traffic increased the difficulty of prediction, thus

we shall consider the preprocessing of the traffic

signal, so as to achieve relative stationary in-put

signals in the prediction of our model. The

technology of wavelet decomposition (Ardagna C A,

2008) is the best solution. Wavelet decomposition

can decompose non-stationary time series into

several detailed signals and a more stationary signal

via low-pass filter. After decomposition, the traffic

is more unitary in frequency, and thus help improve

the prediction of the model.

AR model has a good performance in the

prediction of relative stationary traffic, and it can

reduce the prediction time and improve the

efficiency of the whole forecasting model.

KNN model can keep the character of wavelet’s

multi-scale analysis, avoid poor adaptive ability of

wavelet coefficient in processing, achieve the aim of

dynamic learning while reduce the NN’s learning

period, avoid being trapped in local optimum, thus

improve the performance of prediction model.

According to Kolmogorov Theory, if the number

of input unit is N, then the unit number of hidden

layer is always 2N+1. In this model, we use the

superposition of traffics which predicted by AR and

KNN model as the input of BPNN. For BPNN’s

excellent ability of function approximation, we can

get a more accurate forecasting result with small

error.

4.2 Describe in Detail of the Novel

Model

Based on the analysis above, we form the structure

of the new model as Figure 4.

Figure 4: Three-stage combined NN model in CN.

In the first stage of the model, decompose the

nonlinear traffic signal with Mallat algorithm

according to formula (4).

In the second stage, in line with formula (5),

forecast the relatively stationary signal by AR

model; as for the nonlinear and non-stationary high

frequency signal, we use KNN model to make the

forecasting. In the last stage, BPNN fit the

superposition of former forecasting results, output a

high precision final result.

Compared with the traditional single NN model, this

model avoid the problem of trapping in local

optimum. And compared with ENN model proposed

by Wang Peng (2008) and put wavelet

ICISO 2010 - International Conference on Informatics and Semiotics in Organisations

208

decomposition inside the hidden layer of BPNN, the

new model resolve the problem of long learning

period and poor self-adaptivity under a sudden load.

Figure 7: Wavelet decomposition of network traffic.

The speed of wavelet decomposition and linear

forecasting can make up the delay of NN’s learning,

improve the efficiency of the whole model. In reality

application, regular learning cycle can be written

into protocol and save the net resource in CN. As a

NN with good output performance, BPNN makes

the forecasting result more accurate. Also, its ability

in learning can make up the defect of long time

learning and poor self-regulation mentioned above.

Meanwhile, as a non-stationary model, BPNN is

suitable to depict the non-stationary traffic.

Because this novel model can reduce the

forecasting time, improve the forecasting precision,

and receive a result with high precision under wide

traffic fluctuation. So in the aspect of time and

precision, this new model shows the meaning of

cognition. It can work in the net under the condition

of multi-background traffic or multi-scale time

variation, provide a timely, accurate, steady

cognitive platform to the high level algorithms in

CN.

5 SIMULATION AND ANALYSIS

We simulate in the environment of MATLAB (Liu

Linhui, 2008). MATLAB is an advanced computing

language and interactive environment which is

widely used in algorithm development, data

visualization, data analysis and data computing.

As figure 5 shows, we collect the network traffic

from a core router in the backbone network. The

sampling interval is an hour, we gathered 900

samples, each sample is the average traffic value in

an hour, and the last 100 samples have been used to

test the forecasting result. Figure 6 is the curve line

of traffic.

Figure 5: Collection of network traffic data.

Figure 6: Curve line of network traffic.

For the traffic above, according formula (4), use

Mallat algorithm to decompose it. In order to

improve the precision without loss of generality, we

A NOVEL COMBINED NETWORK TRAFFIC PREDICTION MODEL IN COGNITIVE NETWORKS

209

set scale coefficient L=5. Thus we can get series{

D1(k), D2(k), D3(k), D4(k), D5(k), A5(k)} after

wavelet decomposition, the original signal

S=d1+d2+d3+d4+d5+a5. The result of wavelet

decomposition is as figure 7.

Then we input the low frequency a5 into AR

model to forecast. At the same time, normalize the

high frequency d1, d2, d3, d4, d5, and input them

into KNN to forecast. The weight values and

threshold values of KNN are determined by

self-learning. We set the start learning rate on 0.95,

the minimum learning rate on 0.001, the maximum

step of training on 5000. At last, composite the AR

model’s forecasting result and KNN model’s

forecasting result, make it as the input of BPNN.

According the Kolmogorov algorithm mentioned

above, there are 3 hidden layers in BPNN.

Figure 8 is one-step forecasting result of the 100

data samples, and we compare the real traffic with

the prediction result in one Figure.

Figure 8: One-step forecasting result compared with real

traffic.

Figure 9 is the comparison of two-step

forecasting result and the real traffic. And figure 10

is the forecasting result of WNN model which has

put wavelet decomposition into BPNN as described

earlier in the thesis.

Figure 9: Two-step forecasting result compared with real

traffic.

Figure 10: WNN forecasting result compared with real

traffic.

By the contrast of forecasting result and real

traffic, and the contrast of new model and WNN

model, the simulation proves the high precision of

the novel model. And we have expatiated earlier the

advantage of efficiency and time cost of this model.

Some data of the model’s performance are listed

in Table 1. We make a contrast between statistic

data of one-step, two-step forecasting result and the

statistic data of WNN model. In table 1, SSE means

Squared Sum Error, MSE means Mean Squared

Error, MAE means Mean Absolute Error and MRE

means Mean Relative Error.

Table 1: Comparison of forecasting performance.

Method

SSE

%

MSE

%

MAE

%

MRE

%

WNN 10.79 1.84 7.60 21.17

One-step 5.12 0.98 4.50 16.02

Two-step 7.01 1.38 5.04 18.98

6 CONCLUSIONS

Taking into account the multi-scale and non-linear

characters of the network traffic, combined with the

wavelet decomposition, AR model and NN models,

the thesis proposes a novel network forecasting

model that suitable in CN. The main idea of the

model are as follows: In stage one, the traffic signal

is decomposed into low-frequency part and

high-frequency part. In stage two, two kinds of the

signals are predicted with AR model and KNN

model respectively. To enhance the prediction

accuracy and merge the traffic characters captured

by individual models, the output of the previous

models are combined using BPNN. At the end of the

thesis, the simulation and comparison suggest that

the proposed model has better performance than

WNN model, and may achieve a high-precision

traffic prediction result, thus can work satisfactorily

in the use of CN.

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