A NEW NETWORK TRAFFIC PREDICTION MODEL IN

COGNITIVE NETWORKS

Dandan Li, Runtong Zhang and Xiaopu Shang

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

Keywords: Cognitive networks, Ant colony algorithm, Neural network, Wavelet, BP (back propagation) neural

network, Network traffic prediction.

Abstract: With the development of the network technology and the increasing demands on communication, more

complex, heterogeneous, and suitable network structures are right on their way to come. Cognitive networks

can perceive the external environment; intelligently and automatically change its behavior to adapt the

environment. This feature is more suitable to provide security for users with QoS. This paper proposes a

hybrid traffic prediction model, which trains BPNN with Ant Colony Algorithm based on the analysis of the

present models, in order to improve the cognitive feature in the cognitive networks. The proposed model

can avoid the problem of slow convergence speed and an easy trap in local optimum when coming up with a

fluctuated network flow. At the beginning, the model rejects the abnormal traffic flow data, and then use

wavelet decomposition, in the following steps, the model predicts the network traffic with the hybrid model.

Thus, the traffic prediction with high-precision in cognitive networks is achieved.

1 INTRODUCTION

A cognitive network (CN) has a cognitive process

that can perceive current network conditions, and

then plan, decide and act on those conditions. The

network can learn from these adaptations and use

them to make future decisions, all while taking into

account end-to-end goals (Thomas et al., 2005).

With the wide application of multi-media on the

Internet, Quality of Service (QoS) of the network

becomes more and more important. The

advancement of CN can improve the user

experience.

The feature of the network traffic reflects the

interaction and influence in the process of data

transmission. By analyzing the traffic data, people

can better learn the interior operation mechanism of

the network and build a mathematical model that can

depict the traffic data flow more accurately.

Designing a traffic prediction model with the

cognitive feature can make networks give a more

reasonable bandwidth assignment, traffic control,

routing control, admission control and error control,

et al (Wang et al., 2005). It is a good method to

improve QoS.

CN has the capacities of self-learning and self-

adaption. Therefore, researching a real-time

prediction model of the traffic based on CN can

better solve the problem of load balancing

hysteresis. And a high-precision traffic prediction

model, especially short-term one, can improve the

cognitive feature of CN. However, current network

traffic prediction models are mostly based on regular

networks, few of them specially research on

cognitive features of networks. Usually, their self-

learning and self-adaption capacities are not so

good, cannot express the cognitive features either, so

it is hard to be applied in CN directly.

By analyzing the advantage and disadvantage of

current network traffic prediction models, and

combining the features of CN, we propose a new

network traffic prediction model. It is a hybrid

model with double-BPNN. BP neural network is

employed twice and Ant Colony Algorithm (ACA)

is employed to train weight values, so it is also

called ACA BP-Double model for short.

This paper is divided into six parts. Section II

gives a summary about current network traffic

prediction models. In section III, we give a brief

introduction of the related theories. A detail

description of the Ant Double-BP model is presented

in section IV. Simulation analysis of the model is

shown in section V. Section VI is the conclusion. the

final formatting of your paper.

427

Li D., Zhang R. and Shang X..

A NEW NETWORK TRAFFIC PREDICTION MODEL IN COGNITIVE NETWORKS.

DOI: 10.5220/0003593504270435

In Proceedings of the 13th International Conference on Enterprise Information Systems (NMI-2011), pages 427-435

ISBN: 978-989-8425-53-9

 2011 SCITEPRESS (Science and Technology Publications, Lda.)

2 BRIEF LITERATURE REVIEW

Current network traffic prediction methods can be

divided into two types: linear prediction and

nonlinear prediction. Linear method, such as (Jin et

al., 2003; Yu and Zhang, 2004; Sang and Li, 2000)

which are in the use of Auto-regressive Integrated

Moving Average Model (ARIMA), is popular. The

precondition to use ARIMA model is that the

network traffic must have feature of linear wide

stationary processes, while the network traffic

always has multi-scale feature in different time

frequency scales (Gao et al., 2001) and the nature of

multi-construct and self-similarity as well (Leland et

al., 1994; Paxson and Floyd, 1995). So it is hard to

express the whole feature of network traffic with

ARIMA singly.

Neural Network (NN) shows its great advantage

in prediction because of its capacities of nonlinear

approximation, self-learning and fitting, for example,

(Husmeier and Taylor, 1998; Hussain, 2001;

Wakurah and Zurada, 2001) achieve ideal results

with NN. Wavelet Transform (WT) is one of the

most effective methods in dealing with non-

stationary time series, so there are nonlinear

researches combined the advantages of NN and WT

representative into Wavelet Neural Network

(WNN), Li et al., 2007). References (Lei and Yu,

2006) and (Peng and Yuan, 2008) employ WT and

three layers BPNN; Reference (Zhao and al., 2005)

employs WNN in Next Generation Network (NGN);

Reference (Yao et al., 2007) uses WT, RBFNN and

Elman NN, then synthesizes outputs with BPNN;

Reference (Tian and Yu, 2008) combines WT with

FIRNN. These applications depict the feature of

network traffic flow very well, and reach high-

precision. Back Propagation (BP) algorithm is the

most popular one nowadays, mainly because it is on

the basis of strong theories and uses widely. But BP

algorithm is based on gradient descent algorithm, so

it needs a long time to train weight values, and easily

falls into local optimum.

ACA (Schoonderwoerd et al., 1996) is a new

evolutionary optimization algorithm from the natural

behavior of ant colony. It possesses characteristics

of high speed, global convergence and heuristic

study. Recent years, there are some models which

combine ACA with BPNN, for example, (Wang et

al., 2003; Yang et al., 2009; Gao, 2008; Pokudom,

2009) determination of appropriate BPNN structure

and weight using ACA. The simulation results show

that extensive mapping ability of CN and rapid

global convergence of ACA can be obtained by

combining ACA with NN. But because network

condition is complex and uncertain, and users who

access network are diverse, data like sudden traffic

appears easily, thus affect the precision of traffic

prediction. First, the data mean nothing to network

traffic prediction. If we use them to train BP NN,

they will increase the complexity of model, and

reduce the accuracy of model. Second, when we deal

with data using WT or normalization, it will affect

the precision because of the abnormal data. So, it is

necessary to deal with the original data first, to reject

abnormal data. In this way，(Wang et al., 2009)

proposes a model using double BPNN. Firstly, it

judges, identifies and rejects abnormal data with

BP1, then inputs them into BP2 to train.

Besides, some researches have proposed to

employ hybrid models to depict the feature of

network traffic flow. For example, (Yao et al., 2007)

combines RBFNN, Elman NN with BPNN.

Reference (Feng et al., 2006) expresses the

interaction and non-stationary of traffic flow by

means of linear NN and Elman NN, and compounds

these outputs from previous models with BPNN to

become final results. This hybrid model obtains a

good effect, and improves fitting and predicting

precision.

But the aforementioned models are mainly based

on regular network, their self-learning and self-

adaptation is not so good, and cannot be employed

in CN directly. According to such considerations, a

traffic prediction model is proposed, which can be

applied in CN. This model applies hybrid NN, and

double BPNN (Wang et al., 2009) as for reference.

The results obtained show that it is more accurate

than other models.

3 RELATED THEORIE

In this section, we review some related theories

which involved the model of Ant Double-BP. Such

as ARIMA, Elman NN, BP NN, WT and ACA.

3.1 ARIMA

ARIMA is a time series prediction model. It is the

typical representative of linear prediction models,

which can supply accurate short term prediction.

Now, we introduce ARMA first. ARMA(p,q) is

given by (1).

011 1122

... ...

ttptptttqtq

yy y

ϕϕεθεθεθε

−

−−−−

=+ ++ ++ + ++

(1)

where y

is an observed value of period t. ε

is an

error or deviation of t period, that’s to say, it is the

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428

random factors which cannot be explained by model.

and θ

are the parameters to be estimated, i

∈

[1,p],

∈

[1,q].

If a time series is non-stationary, we handle data

with zero-mean and difference stationary to make it

become a stationary time series. After processing,

ARMA becomes ARIMA. ARIMA(p,d,q) is given

by (2).

() ()

By B

δθ ε

Δ=+

(2)

Where

( ) 1 ...

BBBB

φφφφ

=− − − −

(3)

() 1 ...

BBBB

θθθθ

=− − − −

(4)

△

is difference.

△

is d-order difference. B

is k-

steps shift operator, it means

ttk

Bx x

−

= . φ(B) is

autoregressive operator. θ(B) is shift mean operator.

From the analysis we can see that, ARMA is a

special example of ARIMA when d=0. It means both

non-stationary and stationary time series could be

expressed with ARIMA(p,d,q).

3.2 Wavelet Transform

Wavelet Transform is one of the most effective

methods in dealing with non-stationary time series.

Generally speaking, for an arbitrary continuous

variable function or signal f(t), continuous WT is

given by (5), and we call it WT for short.

1/ 2

[](,)| | ()( )

Wfab a ft dt

∞

−

−∞

−

∫

(5)

While discrete WT is given by (6).

000

[](,)| | ()( )

Wfmn a ft atnbdt

∞

−−

−∞

=−

∫

(6)

where a is scale parameter. b is step parameter.

(t)

is a basic wavelet, which is positive and negative

shocks, its mean is zero. f(t) is a square integrable

function, f(t)

∈

(R). a=a

，

b=nb

（m, n

∈

Z）.

In this paper, we decompose network traffic with

Mallat algorithm (Zhang, 2008). It is an easy

recursion formula for wavelet and scale parameter,

based on (7).

1/2

1/ 2

() ()

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

jjj

Ak fk

Ak AkAk

Dk D k D k

−

⎧

⎪

=++

⎨

⎪

=++

⎪

⎩

(7)

where j

∈[1,L], L is steps of layer. A

(k) and D

(k)

are approximate and detailed signal.

3.3 Elman Neural Network

Elman NN is proposed by Elman in 1990,which is

based on the basic structure of BPNN with dynamic

mapping by storing inside situation. The system can

hence, adapt to time-variant characteristics through

Elman NN. Elman NN is four layers which are

input, output, intermediate (or called hidden) and

connection layer. The structure shows in Fig. 1.

Figure 1: Stucture of Elman NN.

Its nonlinear expression is given by (8).

() ( ())

() ( () (( -1)))

() ( -1)

yk gwxk

xk f wx k w uk

xk xk

⎧

⎪

⎨

⎪

⎩

(8)

where y is a m-dimension output node vector. x

is a

n-dimension intermediate layer node element vector.

u is r-dimension input vector. x

is n-dimension

feedback state variable. w

is connection weight

value between connection layer and intermediate

layer. w

is connection weight value between input

layer and intermediate layer; w

is connection weight

value between output layer and intermediate layer.

g(x) is both transmit function of output neurons and

linear combination of intermediate output. f(x) is

transmitting function of intermediate neurons.

3.4 Ant Colony Algorithm

An ant always can find the shortest path between

food source and formicary. That is because when

ants cross the road, they leave something volatile,

we call it pheromone. So the more ants walk across

the road, the more pheromone will be left; while the

more pheromone, the more ants follow it on this

path. If there is no ant on the path, the path

pheromone volatilizes itself, which is called positive

feedback effect. The steps of ACA show in Fig.2.

A NEW NETWORK TRAFFIC PREDICTION MODEL IN COGNITIVE NETWORKS

429

Figure 2: Steps of ACA.

3.5 BP Neural Network

BPNN is a multilayer feedforward neural network

which trains network with error back-propagation

algorithm. If we input a pair of training samples into

BPNN, neuron value will transmit from input layer

to output layer visa all intermediate layers, and

obtain reflection of network at output layer neurons.

Then according to direction of the error between real

and object output, it changes connection weight

values reversely from output to input layer.

Figure 3: Structure of BP NN with several layers.

Fig.3 is the structure of BPNN with one input

layer, one output layer and two hidden layers, the

network is fully connected. BPNN is based on

gradient descent algorithm. Its efficiency is low

because the use of complex optimization functions.

Besides, BP is a local optimization searching

algorithm hence, the possibility of failure is very

large. Thirdly, the weight values of BPNN are

mostly based on training data. So considering the

processing of training weight value is similar to the

way of ants finding food, we determine BP structure

and weight values by ACA.

4 ACA DOUBLE-BP MODEL

The goal of CN is to optimize the end-to-end

performance of QoS which is for the whole network

not any nodes. CN can learn by itself in the process

of dynamic adaptation, and accumulate experience

for the future acting and deciding. Otherwise, CN

has the foreseeing ability, and its adjustments

happen before what will happen not after that. In this

section, a new network traffic prediction model

which has the features of CN is proposed. It is a

high-prevision model which can be employed in CN

better, and realizes optimization of end-to-end’s

QoS.

4.1 The Basic Idea

The training data are from real network, so there are

some abnormal data in them. They are caused by

artificial factors and other reasons related to

network. Before using them to train weight values,

we must reject these abnormal data first because it

means nothing for traffic prediction. If we do not

reject them, the complexity of model will be

increased, and the precision will be lowered. So, in

this paper, we reject the abnormal data using

abnormal data rejecting network called BP1.

Network traffic flow has the features of multi-

scale, multi-construct, non-stationary and self-

similar. In order to make it stationary, WT is

employed. After that, the data are decomposed to the

scaling coefficient series and wavelet coefficient

series. And the coefficient series is taken as input of

ARIMA and Elman NN. At last, we fit data with

BP2, and output network traffic of prediction.

From the mathematical point of view, BPNN is

based on gradient descent algorithm which is a local

optimization searching algorithm. But the problem

that resolved is global extreme value of complex

nonlinear function, it easily falls into local optimum

and fails the training. Besides, the approximation

and extension capacity of network is closely related

to training samples. It shows that how to choose

typical samples become the key problem of network.

So, in this paper, we determine BP structure and

weight value using ACA. It can avoid the problem

of local optimum and lower the speed of

convergence while the weight value has no business

of training samples.”

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430

4.2 Procedure

According to the considerations, ACA Double-BP

model is proposed to be employed in forecasting

network traffic flow, which uses ACA to determine

BP structure and weight value. Framework of the

proposed model shows in Fig. 4.

Figure 4: Framework of ACA Double-BP model.

According to Kolmogorov theorem ， regular

nonlinear function only needs three layers BP NN.

So in ACA Double-BP model there are three layers

in both BP1 and BP2: one input layer, one hidden

layer and one output layer. In order to express it

clearly, we divide proposed model into four stages.

Stage 1: Rejecting abnormal data. In this stage,

abnormal data are rejected from original data with

BP1. The framework of BP1 is similar to Fig.3

except one hidden layer. There is one node in input

layer and two nodes in output layer. The output is 1

when signal is effective or is 0.

Stage 2: Wavelet transmission. Data which

output 1 are transmitted with Mallat algorithm (7),

multi-scale, multi-construct, non-stationary and self-

similar data are divided into two parts: scaling

coefficient series with feature of stationary and

wavelet coefficient series with high-frequency.

Stage 3: Forecasting traffic flow. ARIMA and

Elman NN are combined to predict stationary

wavelet scaling coefficient series with (2) and

wavelet coefficient series with high-frequency with

(8).

Stage 4: Integrating data and reducing errors.

Outputs which from stage 3 are Integrated with BP2.

It is to fit data by using the function approximation

ability of BP NN, and to reduce errors which caused

by single model. The outputs are predicted results.

4.3 Determination of Appropriate BP

NN Weight Value using ACA

In this section we take (Pokudom, 2009) for

reference. The parameter table is a set of parameters

on each route, represent by PTB

. Where n is a

sequence of route in network. Which is consist

group of the parameters for an ant choose from

PTB

, each parameter in PTB

represent by pa

where i = 1,2,…, P (P is the number of parameter in

PTB

). The pa

consist pheromone (τ

), connection

) and weight (w

), shows in Table I.

Table 1: The parameter table (ptbn) on route n.

mber

Phero

mone

Conne

ction

eight

…

……

…

Detailed steps are as following.

Step 1: Initialization. Give an initial value for

for all PTB

on the routes. Set τ

=τ

, where τ

the initial value of the pheromone. The rest

parameters are random. Take 2

×2×1 BP NN for

example, Fig.5 is the framework of ant k=1.

Figure 5: The parameter table (PTBn) on every route.

Step 2: Route traversal. An ant k starts from

arbitrary route, selects pa

from PTBn is given by

(9) and (10). It depends on a random variable q

uniformly distributed over [0,1], and a parameter q

∈

[0,1]). Mmean square error (MSE) is calculate.

An ant k which traversals all routes decodes the

parameters shows in Fig.6. Then BP structure is

determined shows in Fig.7.

arg max { },

ip ni

pelse

≤

⎧

⎪

⎨

⎪

⎩

(9)

ni ni nj

∑

(10)

Step 3: Updating local pheromone. An ant k

applies this step only to the pa

choosed form all

A NEW NETWORK TRAFFIC PREDICTION MODEL IN COGNITIVE NETWORKS

431

Figure 6: The parameter of ant k.

Figure 7: The structure of ant k.

PTBn in the routes, then it updates the pheromone

(τ

) level is performed by applying (11).

(1 )

ni ni

ϕτ ϕτ

=− +

(11)

where

∈

φ (0,1], and φ is the pheromone decay

coefficient.

Step 4: Repeat step2-step4, for every ant.

Step 5: Updating global pheromone. A global

update is applied to the pheromone on the pa

belonging to the best solution or least MSE using

(12) and (13).

(1 ) ,

ni ni best

iMSE

otherwise

ρτ ρ τ

−+Δ∈

⎧

⎨

⎩

(12)

And

ni best

Δ=

(13)

where ρ

∈

(0,1), and ρ is the evaporation rate, Δτ

additional pheromone and MSE

best

is the least MSE

of the tour ant.

Step 6: Judging end condition. If the maximum

number of iteration is run or it reaches the error

precision that is given before, go step 7; else go step

Step 7: Determination of BP structure and weight

value. Use c

to determine BP structure, it means

deleted connections which c

=0, and left

connections which c

=1. The weight value is the

result that is convergence by ACA.

Step 8: The end.

From this algorithm we can see that it does not

completely depend on original data using ACA, and

makes the whole model posses better self-learning

and self-organization ability. It embodies the feature

of CN well, and more suitable in CN.

5 SIMULATION AND ANALYSIS

In this section, MATLAB (Liu et al., 2008) is

employed to simulate and analyze ACA Double-BP

model. The structure of BP1 is 9

×10×1 with three

layers, and BP2 is 9

×10×2 with three layers. The

learning rate is set to 0.01, the number of ants is 30,

the maximum iteration is 100, p=60, q

=0.9, ρ=0.9,

=0.9.

The simulated data are history data from a core

router of backbone of 1 hour intervals. The number

is 1,040, and the last 140 is for detecting fitting

results. The curve of the network traffic flow shows

in Fig. 8.

0 200 400 600 800 1000

500

1000

1500

Figure 8: The curve of original data.

In Fig. 8, abscissa represents time, and ordinate

represents traffic data. The unity is hour and kb/sec.

Range is [0,1816.73].

5.1 Reject Abnormal Data using BP

There are abnormal data in original data caused by

artificial factors or other reasons related to network,

for example, the moment traffic is 0kb/sec. The

curve of the network traffic which has rejected

abnormal data shows in Fig.9 .

0 200 400 600 800 1000

500

1000

1500

Figure 9: The curve of data which reject abnormal one.

In Fig. 9, abscissa represents time, and ordinate

represents traffic data. The unity is hour and kb/sec.

After rejecting abnormal data, there is 1001 left,

range is [159.79, 1765.24].

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432

5.2 Wavelet Transmission

For traffic data in Fig. 9, transmit them by (7). L=5,

wavelet coefficient series after transmitting is {

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

t=d1+d2+d3+d4+d5+a5, the result shows in Fig.

10.

0 200 400 600 800 1000

1000

2000

Wavelet Decomposition(db4 at level 5:s=a5+d5+d4+d3+d2+d1)

Kb/s

0 200 400 600 800 1000

500

1000

1500

0 200 400 600 800 1000

-500

500

0 200 400 600 800 1000

-500

500

0 200 400 600 800 1000

-500

500

0 200 400 600 800 1000

-500

500

0 200 400 600 800 1000

-1000

1000

Figure 10: The result of data WT.

In Fig. 10, the first one is original data, the

second one a5 is low-frequency data, from the third

to the seventh are high-frequency data d1, d2, d3, d4

and d5.

5.3 Traffic Prediction

Input a5 to ARIMA, input d1, d2, d3, d4 and d5 to

Elman NN. Then combine outputs of ARIMA and

Elman as inputs, input them to BP2 to predict.

The fitting result by last 140 signals shows in Fig.

11, it is a short time prediction for one hour.

0 20 40 60 80 100 120 140

200

400

600

800

1000

1200

1400

1600

1800

traffic:kb/s

time:hour

original value

predicted value

Figure 11: Proposed model one hour prediction.

Fig. 12 is the fitting result by last 140 signals

which is a short time prediction for two-hour. And

Fig. 13 is 24-hour. The proposed model ACA

Double-BP compared with WNN shows in Fig. 14.

From Fig. 11-12, we can see that ACA Double-

BP model reaches high precision and fitting degree

0 20 40 60 80 100 120 140

200

400

600

800

1000

1200

1400

1600

1800

traffic:kb/s

time:hour

original value

predicted value

Figure 12: Proposed model two-hour prediction.

0 20 40 60 80 100 120 140

200

400

600

800

1000

1200

1400

1600

1800

ffi

kb/

time:hour

original value

predicted value

Figure 13: Proposed model 24-hour prediction.

0 20 40 60 80 100 120 140

200

400

600

800

1000

1200

1400

1600

1800

traffic:kb/s

time:hour

original value

Ant Double-BP

WNN

Figure 14: The proposed model compared with WNN.

in short term prediction. Although in Fig.13 24-hour

prediction is not good as Fig. 11-12, its error is so

small, and it does not influence the effective of

model. It shows its obvious advantage from

comparing with WNN in Fig.14.

In order to express the advantage of ACA

Double-BP model clearly, the performance

parameters compared with WNN and shows in table

II. Where SSE is square sum of error, MRE is mean

relative error, MAE is mean absolute error.

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433

Table 2: Ant Double-B model performance parameter.

6 CONCLUSIONS

This paper is based on CN, through analyzing the

advantage and disadvantage of current network

traffic prediction models. And points out that they

are hard to be applied in CN directly. Then a new

model named ACA Double-BP model is proposed

which has great self-learning and self-adaptation

ability. Comparing with other models, ACA Double-

BP solves the problem of low speed convergence

and local optimum, improves the prevision by means

of rejecting abnormal data. BP does not depend on

training samples using ACA at all. Meanwhile, using

hybrid model obtains high fitting and prediction

prevision. It is applied in CN by using self-

organization and self-learning algorithm. The

Simulation in MATLAB and comparison with WNN

shows that performance of the novel model is better.

But ACA Double-BP is very complex, so how to

improve the efficiency with high-precision character

is the researching trend of this paper.

ACKNOWLEDGEMENTS

This work is partly supported by the Fundamental

Research Funds for the Central Universities of China

under Grant No.2009YJS034, and Beijing Nature

Science Foundation of China (No.4112044).

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