**3.4 Pareto-optimal choice of the speech codec**

Proposed theoretical investigations can be used for Pareto-optimal choice of the speech codec used in IP-telephony systems (Bezruk & Skorik, 2010).

For carrying out the comparative analysis of basic speech codec and the optimal codec variant choice there have been used the data about 23 speech codecs described by the set of the technical and economic indicators: coding rate, quality of the speech coding, complexity of the realization, frame size, total time delay, etc. The initial values of the quality indicators are presented in table 3. It is easy to see that presented quality indicators are connected between each other with competing interconnections.

The time delay is increasing with frame size increasing as well as with complexity of the coding algorithm realization. Then, when transferring speech the permissible delay can not be bigger than 250 ms in one direction.

A frame size influences on the quality of a reproduced speech: the bigger is the frame, the more effective is the speech modeled. On other hand, the big frames increase an influence of the time delay on processing the information transferring. A frame size is defined by the compromise amongst these requirements.

Multicriteria Optimization in Telecommunication Networks Planning, Designing and Controlling 269

1 G 711 1 0,851 0,604 0,004 0,515 - 2 G 721 0,5 0,911 1 0,004 1 + 3 G 722 0,75 0,851 0,604 0,004 0,969 - 4 G 722(a) 0,875 1 0,604 0,004 0,969 + 5 G 722(b) 1 0,918 0,604 0,004 0,969 + 6 G 723.1(a) 0,083 0,8 0,439 1 0,818 + 7 G 723.1 0,1 0,867 0,424 1 0,818 + 8 G 726 0,375 0,822 0,748 0,004 1 - 9 G 726(a) 0,5 0,9 0,748 0,004 1 - 10 G 726(b) 0,625 0,866 0,748 0,004 1 + 11 G 727 0,375 0,822 0,727 0,004 1 - 12 G 727(a) 0,5 0,9 0,727 0,004 1 - 13 G 727(b) 0,625 0,866 0,727 0,004 1 - 14 G 728 0,25 0,889 0,281 0,021 1 + 15 G 729 0,125 0,9 0,317 0,333 0,879 + 16 G 729a 0,125 0,878 0,669 0,333 0,879 + 17 G 729b 0,125 0,9 0,309 0,333 0,879 - 18 G 729ab 0,125 0,878 0,626 0,333 0,879 - 19 G 729e 0,125 0,911 0,237 0,333 0,879 - 20 G 729e(a) 0,184 0,915 0,237 0,333 0,879 + 21 G 727(с) 0,25 0,889 0,727 0,004 1 - 22 G 728(a) 0,2 0,911 0,453 0,021 1 + 23 G 729d 0,1 0,889 0,359 0,333 0,879 +

On the base of received results there were considered the practical application features examined methods of the allocation of the Pareto-optimal speech codec variant set taking into account a set of the quality indicators as well as the unique design decision choice. From the initial set of the 23 speech codecs variants there was allocated the Pareto subset

The only one project decision was chosen from the condition of the scalar goal function extreme (9) with two different values of β defined characters of this function changing. In table 5 are presented the values of the given function for Pareto-optimal speech codecs variants at 2 β = and 3. β = It was obtained that an extreme goal function value, depending

Within statement of a problem we have chosen the codec of series G.722b which has following values of the quality indicators: speech coding – 64 kbps, coding quality – 4,13 MOS, complexity of the realization – 11,95 MIPS, the frame size – 0,125 ms, total delay – 31,5 ms.

Paretooptimal choice

№ Codec K1n K2n K3n′ K4n K5n′

Table 4. Transformed quality indicators.

included 12 codecs variants (marked + in table 4).

on β , is reached for the same speech codec G 722 (b).


Table 3. Codecs characteristics.

Complexity of the realization is connected with providing necessary calculations in real time. The coding algorithm complexity influences on the physical size of coding, decoding or combined devices, and also on its cost and power consumption.

In table 4 are presented some transformations results of the initial values of the quality indicators. In particular, there were performed the rationing operations of the indicators to their maximum values <sup>i</sup> iн imax <sup>k</sup> k . <sup>k</sup> <sup>=</sup> These indicators were transformed to a comparable kind where all indicators had the same character depending on the technical codecs characteristics. In particular, for indicators k3n and k5n the transformations 3<sup>н</sup> 3н <sup>1</sup> <sup>k</sup> <sup>k</sup> ′ <sup>=</sup> ,

5н 5н <sup>1</sup> <sup>k</sup> <sup>k</sup> ′ <sup>=</sup> were done.


Table 4. Transformed quality indicators.

268 Telecommunications Networks – Current Status and Future Trends

1 G 711 64 3,83 11,95 0,125 60 2 G 721 32 4,1 7,2 0,125 30 3 G 722 48 3,83 11,95 0,125 31,5 4 G 722(a) 56 4,5 11,95 0,125 31,5 5 G 722(b) 64 4,13 11,95 0,125 31,5 6 G 723.1(a) 5,3 3,6 16,5 30 37,5 7 G 723.1 6,4 3,9 16,9 30 37,5 8 G 726 24 3,7 9,6 0,125 30 9 G 726(a) 32 4,05 9,6 0,125 30 10 G 726(b) 40 3,9 9,6 0,125 30 11 G 727 24 3,7 9,9 0,125 30 12 G 727(a) 32 4,05 9,9 0,125 30 13 G 727(b) 40 3,9 9,9 0,125 30 14 G 728 16 4 25,5 0,625 30 15 G 729 8 4,05 22,5 10 35 16 G 729a 8 3,95 10,7 10 35 17 G 729b 8 4,05 23,2 10 35 18 G 729ab 8 3,95 11,5 10 35 19 G 729e 8 4,1 30 10 35 20 G 729e(a) 11,8 4,12 30 10 35 21 G 727(с) 16 4 9,9 0,125 30 22 G 728(a) 12,8 4,1 16 0,625 30 23 G 729d 6,4 4 20 10 35

Complexity of the realization is connected with providing necessary calculations in real time. The coding algorithm complexity influences on the physical size of coding, decoding

In table 4 are presented some transformations results of the initial values of the quality indicators. In particular, there were performed the rationing operations of the indicators to

kind where all indicators had the same character depending on the technical codecs

characteristics. In particular, for indicators k3n and k5n the transformations 3<sup>н</sup>

<sup>k</sup> <sup>=</sup> These indicators were transformed to a comparable

or combined devices, and also on its cost and power consumption.

imax <sup>k</sup> k .

iн

Complexity of the realization, MIPS

Frame size, ms

Total delay, ms

3н

<sup>1</sup> <sup>k</sup> <sup>k</sup> ′ <sup>=</sup> ,

Coding quality, MOS (1-5)

№ Codec

Table 3. Codecs characteristics.

their maximum values <sup>i</sup>

5н

<sup>1</sup> <sup>k</sup>

5н

<sup>k</sup> ′ <sup>=</sup> were done.

Speech coding, kbps

> On the base of received results there were considered the practical application features examined methods of the allocation of the Pareto-optimal speech codec variant set taking into account a set of the quality indicators as well as the unique design decision choice. From the initial set of the 23 speech codecs variants there was allocated the Pareto subset included 12 codecs variants (marked + in table 4).

> The only one project decision was chosen from the condition of the scalar goal function extreme (9) with two different values of β defined characters of this function changing. In table 5 are presented the values of the given function for Pareto-optimal speech codecs variants at 2 β = and 3. β = It was obtained that an extreme goal function value, depending on β , is reached for the same speech codec G 722 (b).

> Within statement of a problem we have chosen the codec of series G.722b which has following values of the quality indicators: speech coding – 64 kbps, coding quality – 4,13 MOS, complexity of the realization – 11,95 MIPS, the frame size – 0,125 ms, total delay – 31,5 ms.

Multicriteria Optimization in Telecommunication Networks Planning, Designing and Controlling 271

1 21 32 ε = Φ+ σ + σ (K) min(q q (K) q (K)),

1 i

2 i i 1 <sup>1</sup> (K) Z Z ; l-1 <sup>=</sup> σ= −

l

= Φ= ϕ

q1 , q2 , q3 – weight coefficients characterized the traffic balancing cost using standard

i i i 1

x ;

i 1 <sup>1</sup> (K) x x; l 1 <sup>=</sup> σ= − <sup>−</sup>

( ) l 2

( ) 2 l

– standard deviation of channels loading i x , i 1...l <sup>=</sup> ;

(10)

Fig. 6. Considered telecommunication system.

Φ – used routing protocol metric;

<sup>ϕ</sup>i – cost of full used channel ( i i λ = <sup>c</sup> );

metric, agents and channels loading.

<sup>2</sup> σ (K) – standard deviation of agents loading Z , i 1...l <sup>i</sup> = ;

where 1 σ (K)


Table 5. Results of multicriteria optimization.

#### **3.5 Network resources controlling**

Let us consider some features of the short-term planning issues in the telecommunication system. There was shown the important place of multi-service network occupied with models, methods and facilities of network resources controlling in modern and perspective technologies. To the basic network resources facilities belong: channel resources control facilities (channels throughput, buffers size, etc), information resources control (user traffic).

Considered system was presented as the model of a distributed telecommunication system, consisting from a set of operating agents, for each autonomous system (fig 6).

In this model the process of network resources control was carried out by finding the distribution streams vector of the following type (Bezruk & Bukhanko, 2010):

$$\overrightarrow{\mathbf{K}} = (\mathbf{k}\_1, \mathbf{k}\_2, \dots, \mathbf{k}\_l)\_{\prime} \sum\_{\mathbf{i}}^{\mathrm{l}} \mathbf{k}\_{\mathrm{i}} = \mathbf{1}\_{\prime}$$

with next limitation

$$\begin{aligned} 0 \le \mathbf{k}\_{\mathbf{i}} \le \mathbf{1}, \ \mathbf{i} = \overline{\mathbf{1} \dots \mathbf{1}}; \\\\ \lambda\_{\mathbf{i}}^{\text{out}} \mathbf{k}\_{\mathbf{i}} \le \mathbf{c}\_{\mathbf{i}}, \ \mathbf{i} = \overline{\mathbf{1} \dots \mathbf{1}}. \end{aligned}$$

Each element of this vector characterizes a part of outgoing user traffic from autonomous system operating agent transferred by using a corresponding channel. Within a given model, the task of network resources controlling comes to solving the optimization problem connected to function minimization.

Fig. 6. Considered telecommunication system.

270 Telecommunications Networks – Current Status and Future Trends

2 G 721 0,35099 0,24688 4 G 722(a) 0,35039 0,28188 5 G 722(b) 0,35476 0,28532 6 G 723.1(a) 0,31677 0,25791 7 G 723.1 0,32312 0,26308 10 G 726(b) 0,32863 0,26445 14 G 728 0,27801 0,24056 15 G 729 0,26904 0,22785 16 G 729a 0,29103 0,23837 20 G 729e(a) 0,26912 0,22898 22 G 728(a) 0,28812 0,24582 23 G 729d 0,26927 0,22716

Let us consider some features of the short-term planning issues in the telecommunication system. There was shown the important place of multi-service network occupied with models, methods and facilities of network resources controlling in modern and perspective technologies. To the basic network resources facilities belong: channel resources control facilities (channels throughput, buffers size, etc), information resources control (user traffic). Considered system was presented as the model of a distributed telecommunication system,

In this model the process of network resources control was carried out by finding the

12 l i

K (k ,k ,...,k ), k 1, = =

<sup>i</sup> 0 k 1, i 1...l; ≤≤ =

out λ≤ = ii i k c , i 1...l .

Each element of this vector characterizes a part of outgoing user traffic from autonomous system operating agent transferred by using a corresponding channel. Within a given model, the task of network resources controlling comes to solving the optimization problem

l

i

consisting from a set of operating agents, for each autonomous system (fig 6).

distribution streams vector of the following type (Bezruk & Bukhanko, 2010):

Values k ξ for diffrent β

β = 2 3 β =

№ Codec

Table 5. Results of multicriteria optimization.

**3.5 Network resources controlling** 

with next limitation

connected to function minimization.

$$\mathbf{e}(\overline{\mathbf{K}}) = \min(\mathbf{q}\_1 \Phi + \mathbf{q}\_2 \mathbf{e}\_1(\overline{\mathbf{K}}) + \mathbf{q}\_3 \mathbf{e}\_2(\overline{\mathbf{K}})),\tag{10}$$

where 1 σ (K) – standard deviation of channels loading i x , i 1...l <sup>=</sup> ;

$$\sigma\_1(\overrightarrow{\mathbf{K}}) = \sqrt{\frac{1}{1-1} \sum\_{i=1}^{1} \left(\mathbf{x}\_i - \overrightarrow{\mathbf{x}}\right)^2},$$

<sup>2</sup> σ (K) – standard deviation of agents loading Z , i 1...l <sup>i</sup> = ;

$$
\sigma\_2(\overline{\mathbf{K}}) = \sqrt{\frac{1}{1\cdot 1} \sum\_{i=1}^{l} \left( Z\_i - \overline{Z} \right)^2},
$$

Φ – used routing protocol metric;

$$\Phi = \sum\_{\mathbf{i}=1}^{I} \Phi\_{\mathbf{i}} \mathbf{x}\_{\mathbf{i}};$$

<sup>ϕ</sup>i – cost of full used channel ( i i λ = <sup>c</sup> );

q1 , q2 , q3 – weight coefficients characterized the traffic balancing cost using standard metric, agents and channels loading.

Multicriteria Optimization in Telecommunication Networks Planning, Designing and Controlling 273

Below are presented some results of the analytic and imitation modeling within comparative analysis of considered existing and proposed models. These results are shown as dependences of the blocking probability and average delay time from the network loading

Fig. 8. Received dependences of average delay time (a) and blocking probability (b).



The present work deals with the methodology of generating and selecting the variants of information systems when they are optimized in terms of the set of quality indicators. The multicriteria system-optimization problems are solved in three stages. By using the morphological approach a structural set of permissible variants of a system is initially generated. This set is mapped into the space of vector estimates. In this space a subset of Pareto-optimal estimates is selected, defining the potential characteristics of the system on the basis of the set of quality indicators. At the conclusive stage the only variant is selected amongst the Pareto-optimal variants of the system provided there exists an extreme of a certain scalar functional whose form is determined with the use of some additional

The use of the proposed models allows to:

12% (M5) and for 6 – 25% (M6);

information obtained from a customer.

**4. Conclusion** 

(fig. 8).

The considered mathematical model of the distributed network resources controlling uses specific criteria of optimality included standard routing protocol metrics, a measure of channels and agents loading in given telecommunication network.

Obviously, under condition of 1 σ (K) and 2 <sup>σ</sup> (K) absence, function (10) becomes the model of the load balancing under the routes with equal or non-equal metric. However, absence of the decentralized control behind the autonomous system of telecommunication network can finally result in an uncontrollable overload. That fact is defined by the presence of additional minimized indicators leading to the practical value of the proposed model. Thus a choice of the relation of weight coefficients q1 , q2 and q3 is an independent problem demanding some future investigations and formalizations. In this model this task was dared with expert's estimations.

The proposed imitation model included up to 18 agents (fig. 7). Researches for different variants of connectivity between agents have been carried out.

Fig. 7. Used imitation model.

During practical investigation there were analyzed several models of multipath routing and load balancing. These models are listed below:


Below are presented some results of the analytic and imitation modeling within comparative analysis of considered existing and proposed models. These results are shown as dependences of the blocking probability and average delay time from the network loading (fig. 8).

Fig. 8. Received dependences of average delay time (a) and blocking probability (b).

The use of the proposed models allows to:

