**3.1 Telecommunication network variant choice**

In particular, we considered features of an application of multicriteria optimization methods on the example of the packet switching network. For such a task the mathematical model of full-connected topology of a network was implemented. There was performed the simulation modeling of different variants of data transmission in the indicated network and the quality indicators estimates for each variant were obtained (Bezruk et al., 2008).

Pareto-optimal variants of the network were obtained with the methods of vector optimization and, among them, there was selected the single optimal variant of the network (fig. 1). The results of the optimization were used for the task of the network control when framing optimal control actions.

Thus, the control device collects the information on the current condition of the network and develops Pareto-optimal control actions which are directed to a variation of mechanisms of the arrival requests service and paths of packet transmission through the network.

The structure of the model, realized with a computer, includes simulators of the messages with a Poisson distribution and given intensities, procedures of the messages packing, their

' '' ' '' j j m m ' ' ' ' n nn n 12 m 1 2 m

In this case the components v ,v , ,v 12 m , i.e. the estimates of the system quality indicators k ( ),k ( ),...,k ( ) 12 m ϕϕ ϕ are said to be strictly order in terms of their importance. As the

In determining the lexico-graphical relation a major role is played by the order of enumerating quality indicators. The change in the numeration of quality indicators give rise

Let us consider some practical peculiarities of an application of multicriteria optimization methods within a long-term and short-term planning, designing and controlling. In the examined examples of telecommunication networks operation and estimation of the quality indicators values is probed on mathematical models implemented on a computer using the

In particular, we considered features of an application of multicriteria optimization methods on the example of the packet switching network. For such a task the mathematical model of full-connected topology of a network was implemented. There was performed the simulation modeling of different variants of data transmission in the indicated network and

Pareto-optimal variants of the network were obtained with the methods of vector optimization and, among them, there was selected the single optimal variant of the network (fig. 1). The results of the optimization were used for the task of the network control when

Thus, the control device collects the information on the current condition of the network and develops Pareto-optimal control actions which are directed to a variation of mechanisms of

The structure of the model, realized with a computer, includes simulators of the messages with a Poisson distribution and given intensities, procedures of the messages packing, their

the quality indicators estimates for each variant were obtained (Bezruk et al., 2008).

the arrival requests service and paths of packet transmission through the network.

is satisfied they say that from the lexico-graphical stand point the vector ν′

At m 1 <sup>−</sup> the lexico-graphical relation coincides with the

== − >

............................................................. m) v v , j 1,2,...,m 1,v v , v (v ,v ,...,v ); v (v ,v ,...,v ).

 is

occurs if and only if one the following

Let there be two vectors of estimates <sup>m</sup> ν ν∈ ⊂ , VR ′ . The lexico-graphical relation lex

determined in the following way: the relation lex

' '' 1 1 ' '' ' '' 1 12 2

>

2) v v ;v v

= >

= =

1) v v ;

conditions is satisfied.

relation ' '' v lexv

**3. Practical usage** 

is greater than the vector . ν′

relation on the subset of real numbers.

to a different lexico-graphical relation.

packets of specific simulation modeling.

framing optimal control actions.

**3.1 Telecommunication network variant choice** 

transmission through the communication channels. The procedures of the messages packing have simulated a batch data transmission with a mode of the window load control.

Fig. 1. Choice of Pareto-optimal variants of the telecommunication network.

The procedures of a packet transmission were simulated by the processes of transfer using duplex communication channels with errors. The simulation analysis of the transfer delays was stipulated at a packet transmission in the communication lines connected with final velocity of signals propagation in communication channels, fixed transmission channel capacity and packets arrival time in the queue for their transfer trough the communication channel.

Different variants of the telecommunication network functioning were realized at the simulation analysis, they differed in disciplines of service in the queues, ways of routing in a packet transmission and size of the window of the transport junction. In the considered example thirty six variants of the network functioning were obtained. Network functioning variants were estimated by the following quality indicators: average time of deliveries k T <sup>1</sup> = and average probability of message loss k P <sup>2</sup> = . These quality indicators had contradictory character of interconnection. The obtained permissible set of network variants is presented in a criteria space (fig. 1). The subset of the Pareto-optimal network operation is selected by the exclusion of the inferior variants. The left low bound set of the valid variants corresponds to Pareto-optimal variants. Among Pareto-optimal variants of the network Ф<sup>0</sup> was selected a single variant from the condition of a minimum of the introduced resulting quality indicator k Ck Ck pn 1 1 2 2 = + . For the case C 0,4 <sup>1</sup> = , C 0,6 <sup>2</sup> = the single variant 11 was selected; the discipline service of the requests (in the random order) was established for it as well as the way of routing (weight method) and size of the "transmission window" (equal 8).

The given task is urgent for practical applications being critical to the delivery time (in telecommunication systems of video and voice intelligences, systems of the banking terminals, alarm installations, etc).

Multicriteria Optimization in Telecommunication Networks Planning, Designing and Controlling 263

4. The number of subscribers under service of the base station, depending on the number

N M int(A / ). aBTS = β 5. The necessary number of the base stations at the given territory of covering, is defined

N int(N /N ). BTS = a aBTS

6. The cell radius, under condition that the load is uniformly distributed over the entire

1,21 S R . N <sup>⋅</sup> <sup>=</sup> <sup>π</sup>

7. The value of the protective distance between BTS with equal frequency channels, is

D R 3C , =

For a choice of optimal design solutions on the basis of multicriteria optimization methods, there was developed the program complex. It includes two parts solving the following

1. Setting initial data and calculation of technical parameters for some permissible set of

Fig. 2 shows, as an example, the program complex interface. Here is shown part of table with values of 14 indicators for 19 CCN variants. There is the possibility to choose («tick off») concrete quality indicators to be taken into account at the multicriteria optimization. Besides, here are given values of coefficients of relative importance of chosen quality

There was selected a subset of Pareto-optimal variants including 71 network variants. Therewith 29 certainly worst variants are rejected. From the condition of minimum conditional criteria of preference as of the Pareto subset, a single variant is chosen (№72). It

2. A choice of Pareto-optimal network variants and narrowing them to a single one.

and other parameters such as the necessary power at the receiver input, the probability of error in the process of communication session, the efficiency of radio spectrum use, etc. Finding the subset of Pareto-optimal network variants is performed in criteria space of the quality indicators estimates. A single variant of CCN was chosen with the use of the conditional criteria of preference by finding the extreme of the scalar criteria function as

where Na is the given number of subscribers to be under service of the cellular

0 BTS

of sectors, permissible telephone load and activity of subscribers

as

defined as

i 1 с , i 1,7 <sup>7</sup> = = .

issues.

indicators.

variants of CCN.

communication network.

zone, is defined by the formula

#### **3.2 Multicriteria optimization in radio communication networks designing**

Let us consider some practical aspects of multicriteria optimization methods when planning radio communication networks, on an example of cellular communication network (CCN). The process of finding CCN optimal variants includes such stages:


In the considered example there was formed a set of permissible variants of CCN (GSM standard), which were defined by different initial data including the following ones: the planned number of subscribers in the network; dimensions of the covered territory (an area); the activity of subscribers at HML (hour of maximum load); the frequency bandwidth authorized for the network organization; sizes of clusters; the permissible probability of call blocking and percentage of the time of the communication quality deterioration.

The following technical parameters of CCN were calculated by a special technique.

1. The general number of frequency channels authorized for deployment of CCN in the given town, is defined as

$$\mathbf{N\_k = \text{int}(\boldsymbol{\omega} \mathbf{F} / \, \mathbf{F\_k})\_\prime}$$

where Fk is the frequency band.

2. The number of radio frequencies needed for service of subscribers in one sector of each cell, is defined as

$$\mathbf{n}\_s = \text{int}(\mathbf{N}\_k \,/ \, \mathbf{C} \cdot \mathbf{M}).$$

3. A value of the permissible telephone load in one sector of one cell or in a cell (for base stations incorporating antennas with the circular pattern) is defined by the following relationships

$$\mathbf{A} = \mathbf{n}\_{\bullet} \left[ 1 - \sqrt{1 - \left( \mathbf{P}\_{\mathrm{sl}} \sqrt{\pi \mathbf{n}\_{\bullet} / \ 2} \right)^{\mathbf{V}\_{\mathrm{n}\_{\bullet}}}} \right] \text{ at } \mathbf{P}\_{\mathrm{sl}} \le \sqrt{\frac{2}{\pi \mathbf{n}\_{\bullet}}};$$

$$\mathbf{A} = \mathbf{n}\_{\bullet} + \sqrt{\frac{\pi}{2} + 2 \mathbf{n}\_{\bullet} \ln \left( \mathbf{P}\_{\mathrm{sl}} \sqrt{\pi \mathbf{n}\_{\bullet} / \ 2} \right)} - \sqrt{\frac{\pi}{2}} \text{ at } \mathbf{P}\_{\mathrm{sl}} > \sqrt{\frac{2}{\pi \mathbf{n}\_{\bullet}}}.$$

where n nn 0 sa = ⋅ ; na is the number of subscribers which can use one frequency channel simultaneously. The value is defined by standard.

4. The number of subscribers under service of the base station, depending on the number of sectors, permissible telephone load and activity of subscribers

$$\mathbf{N}\_{\text{aBIS}} = \mathbf{M} \operatorname{int}(\mathbf{A} \,\prime \, \beta).$$

5. The necessary number of the base stations at the given territory of covering, is defined as

$$\mathbf{N\_{BTS}} = \text{int}(\mathbf{N\_a} \,/\, \mathbf{N\_{aBTS}}).$$

where Na is the given number of subscribers to be under service of the cellular communication network.

6. The cell radius, under condition that the load is uniformly distributed over the entire zone, is defined by the formula

$$\mathbf{R} = \sqrt{\frac{1,21 \cdot \mathbf{S}\_0}{\pi \mathbf{N}\_{\text{BTS}}}}.$$

7. The value of the protective distance between BTS with equal frequency channels, is defined as

$$\mathbf{D} = \mathbf{R}\sqrt{3C\_{\text{\textdegree C}}}$$

and other parameters such as the necessary power at the receiver input, the probability of error in the process of communication session, the efficiency of radio spectrum use, etc.

Finding the subset of Pareto-optimal network variants is performed in criteria space of the quality indicators estimates. A single variant of CCN was chosen with the use of the conditional criteria of preference by finding the extreme of the scalar criteria function as

$$\mathbf{c}\_{\mathrm{i}} = \frac{1}{\mathcal{T}} \quad \mathrm{i} = \overline{1, \mathcal{T}} \quad \text{.}$$

262 Telecommunications Networks – Current Status and Future Trends

Let us consider some practical aspects of multicriteria optimization methods when planning radio communication networks, on an example of cellular communication network (CCN).



In the considered example there was formed a set of permissible variants of CCN (GSM standard), which were defined by different initial data including the following ones: the planned number of subscribers in the network; dimensions of the covered territory (an area); the activity of subscribers at HML (hour of maximum load); the frequency bandwidth authorized for the network organization; sizes of clusters; the permissible probability of call

1. The general number of frequency channels authorized for deployment of CCN in the

N int( F /F ), k k =

2. The number of radio frequencies needed for service of subscribers in one sector of each

n int(N /C M). s k = ⋅

3. A value of the permissible telephone load in one sector of one cell or in a cell (for base stations incorporating antennas with the circular pattern) is defined by the following

( ) <sup>0</sup>

where n nn 0 sa = ⋅ ; na is the number of subscribers which can use one frequency

 = −− π

π π =++ π − at sl

<sup>n</sup> A n 1 1 P n /2 <sup>O</sup> sl <sup>О</sup>

An 2 <sup>O</sup> пО ln P n / 2 ( ) sl <sup>О</sup> 2 2

channel simultaneously. The value is defined by standard.

1

at sl

o

<sup>2</sup> P , n

> π

o

<sup>2</sup> P ; n

≤ π

structure and parameters, limitation on the value of the quality indicators;

blocking and percentage of the time of the communication quality deterioration. The following technical parameters of CCN were calculated by a special technique.

**3.2 Multicriteria optimization in radio communication networks designing** 

The process of finding CCN optimal variants includes such stages:

the parameter of radio wave attenuation, etc;



given town, is defined as

cell, is defined as

relationships

where Fk is the frequency band.

For a choice of optimal design solutions on the basis of multicriteria optimization methods, there was developed the program complex. It includes two parts solving the following issues.


Fig. 2 shows, as an example, the program complex interface. Here is shown part of table with values of 14 indicators for 19 CCN variants. There is the possibility to choose («tick off») concrete quality indicators to be taken into account at the multicriteria optimization. Besides, here are given values of coefficients of relative importance of chosen quality indicators.

There was selected a subset of Pareto-optimal variants including 71 network variants. Therewith 29 certainly worst variants are rejected. From the condition of minimum conditional criteria of preference as of the Pareto subset, a single variant is chosen (№72). It

Multicriteria Optimization in Telecommunication Networks Planning, Designing and Controlling 265

Fig. 3. MPE of the quality indicators (the number of subscribers serviced by one base station

We have a set of permissible solutions (routes) on the finite network graph G (V,X), = where V {v} = – set of nodes, E {e} = – set of network lines. Each route X is defined by a subset of the nodes and links. The goal task is presented by the model \* {X,F} x , <sup>→</sup> where X {x} <sup>=</sup> – set of permissible solutions (routes) on the network graph G (V,E); = F(x) – objective function of choice of the routes; \* x – optimal solution of the routing problem. The multicriteria approach of a choice of the best routes relies to perform decomposition of the function F(x) to set (vector) partial choice functions. In this case on

F(x) (W x),...,W (x),...,W (x) , = 1 jm ( )

The route variant \* x X ∈ is Pareto-optimal route if another route x X ∈ doesn't exist, order to perform inequality \* F (x ) F (x), j j ≤ = j 1,...,m, where at least one of the inequalities is strict. We propose to solve the problem of finding Pareto-optimal routes by using weight method. It is used for finding extreme values of the objective route function as a weighted sum of the

> ( ) <sup>m</sup> j j var x X j 1 extr F(x) W (x). <sup>∈</sup> <sup>=</sup> = =λ

Pareto-optimal routes have some characteristic features. Particularly, Pareto-optimal alternative routes corresponds to the Pareto coordinated optimum partial objective functions () () () W x ,…,W x ,…,W x 1jm . When selecting a subset of the Pareto-optimal routes there was dropped a certainly worst variant in terms of the absolute criteria of

the set X it is given the vector of the objective function (Bezruk & Varich, 2011):

partial choice functions for all possible values of the weighting coefficients j λ :

where components determine the values of quality routes indicators.

(a), the load, the activity of subscribers (b)) for CCN of GSM standard.

**3.3 Features of a choice of Pareto-optimal routes** 

preference.

is characterized by the following initial and calculated parameters: the number of subscribers is 30000; the area under service is 320 km2; activity of subscribers is 0.025 Erl; the frequency bandwidth is 4 MHz; the permissible probability of call blocking is 0.01; percentage of the connection quality deterioration time is 0.07; the density of service is 94 active subscribers per km2; the cluster size is 7; the number of base stations in the network is 133; the number of subscribers serviced by one BS is 226; the efficiency of radio frequency spectrum is 1.614·10-4 active subscribers per Hz; the telephone load is 3.326 Erl; the probability of error is 5.277·10-7; the angle of antenna radiation pattern is 120 degrees.


Fig. 2. Interface of program complex.

As results of Pareto-optimization, there were obtained multivariate patterns of exchange (MPE) of the quality indicators, being of antagonistic character. For illustration, some MPE are presented at fig. 3. Each MPE point defines the potentially best values of each indicator which can be attained at fixed but arbitrary values of other quality indicators. MPE also show how the improvement of some quality indicators is achieved at the expense of other.

Fig. 3. MPE of the quality indicators (the number of subscribers serviced by one base station (a), the load, the activity of subscribers (b)) for CCN of GSM standard.

#### **3.3 Features of a choice of Pareto-optimal routes**

264 Telecommunications Networks – Current Status and Future Trends

is characterized by the following initial and calculated parameters: the number of subscribers is 30000; the area under service is 320 km2; activity of subscribers is 0.025 Erl; the frequency bandwidth is 4 MHz; the permissible probability of call blocking is 0.01; percentage of the connection quality deterioration time is 0.07; the density of service is 94 active subscribers per km2; the cluster size is 7; the number of base stations in the network is 133; the number of subscribers serviced by one BS is 226; the efficiency of radio frequency spectrum is 1.614·10-4 active subscribers per Hz; the telephone load is 3.326 Erl; the

probability of error is 5.277·10-7; the angle of antenna radiation pattern is 120 degrees.

As results of Pareto-optimization, there were obtained multivariate patterns of exchange (MPE) of the quality indicators, being of antagonistic character. For illustration, some MPE are presented at fig. 3. Each MPE point defines the potentially best values of each indicator which can be attained at fixed but arbitrary values of other quality indicators. MPE also show how the improvement of some quality indicators is achieved at the

Fig. 2. Interface of program complex.

expense of other.

We have a set of permissible solutions (routes) on the finite network graph G (V,X), = where V {v} = – set of nodes, E {e} = – set of network lines. Each route X is defined by a subset of the nodes and links. The goal task is presented by the model \* {X,F} x , <sup>→</sup> where X {x} <sup>=</sup> – set of permissible solutions (routes) on the network graph G (V,E); = F(x) – objective function of choice of the routes; \* x – optimal solution of the routing problem. The multicriteria approach of a choice of the best routes relies to perform decomposition of the function F(x) to set (vector) partial choice functions. In this case on the set X it is given the vector of the objective function (Bezruk & Varich, 2011):

$$\mathbf{F}(\mathbf{x}) = (\mathbf{W}\_1(\mathbf{x}), \dots, \mathbf{W}\_j(\mathbf{x}), \dots, \mathbf{W}\_m(\mathbf{x}))\_{\prime\prime}$$

where components determine the values of quality routes indicators.

The route variant \* x X ∈ is Pareto-optimal route if another route x X ∈ doesn't exist, order to perform inequality \* F (x ) F (x), j j ≤ = j 1,...,m, where at least one of the inequalities is strict. We propose to solve the problem of finding Pareto-optimal routes by using weight method. It is used for finding extreme values of the objective route function as a weighted sum of the partial choice functions for all possible values of the weighting coefficients j λ :

$$\mathop{\mathrm{ext}\, \mathrm{r}}\_{\mathrm{var}\, \mathrm{x} \in \mathrm{X}} = \left(\mathrm{F}(\mathbf{x})\right) = \sum\_{\mathbf{j}=1}^{\mathrm{m}} \lambda\_{\mathbf{j}} \mathbf{W}\_{\mathbf{j}}(\mathbf{x}) .$$

Pareto-optimal routes have some characteristic features. Particularly, Pareto-optimal alternative routes corresponds to the Pareto coordinated optimum partial objective functions () () () W x ,…,W x ,…,W x 1jm . When selecting a subset of the Pareto-optimal routes there was dropped a certainly worst variant in terms of the absolute criteria of preference.

Multicriteria Optimization in Telecommunication Networks Planning, Designing and Controlling 267

Network analysis shows that for each destination node there are many options to choose the

Fig. 5 shows the set of the alternative routes between nodes 0 and 8 in the space of the quality indicators k1 and k2 . Subset of the Pareto-optimal alternatives routes corresponds to the left lower border which includes three variants, they are marked (▲). This subset

> 01234 k1

The resulting subset of the Pareto-optimal alternative routes can be used for organizing multipath routing when using MPLS technology. It will allow to provide a load balancing and a traffic management and to provide given quality-of-service taking into account the set

Proposed theoretical investigations can be used for Pareto-optimal choice of the speech

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

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

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

route directly. For example, between node 0 and node 8 there are 22 routes.

corresponds to be coordinated in Pareto optimum of the quality indicators.

0 0,5 1 1,5 2 2,5 3 3,5 4

Fig. 5. Set of the routes between nodes 0 and 8.

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

between each other with competing interconnections.

be bigger than 250 ms in one direction.

compromise amongst these requirements.

codec used in IP-telephony systems (Bezruk & Skorik, 2010).

k2

of the quality indicators.

Pareto-optimal alternatives of the routes are equivalent to the Pareto criteria and could be used for organizing multipath routing in the multi-service telecommunication networks.

Network model consists of twelve nodes; they are linked by communication lines with losses (fig. 4).

Fig. 4. The structure of the investigated network.



Table 2. Network quality indicators.

Network analysis shows that for each destination node there are many options to choose the route directly. For example, between node 0 and node 8 there are 22 routes.

Fig. 5 shows the set of the alternative routes between nodes 0 and 8 in the space of the quality indicators k1 and k2 . Subset of the Pareto-optimal alternatives routes corresponds to the left lower border which includes three variants, they are marked (▲). This subset corresponds to be coordinated in Pareto optimum of the quality indicators.

Fig. 5. Set of the routes between nodes 0 and 8.

266 Telecommunications Networks – Current Status and Future Trends

Pareto-optimal alternatives of the routes are equivalent to the Pareto criteria and could be used for organizing multipath routing in the multi-service telecommunication networks.

Network model consists of twelve nodes; they are linked by communication lines with

losses (fig. 4).

The link

Table 2. Network quality indicators.

Fig. 4. The structure of the investigated network.

The delay time of packets transmission k1

The quality indicators normalized to maximum values are presented in table 2.

0-1 0.676 1 0.333 0-2 1 0.25 1 0-3 0.362 1 0.333 0-4 0.381 0.25 1 0-5 0.2 1 0.333 0-6 0.19 1 0.333 0-7 0.571 0.25 1 7-6 0.4 0.25 0.333 7-8 0.362 0.25 0.667 8-6 0.314 0.5 0.5 8-5 0.438 0.25 0.333 8-9 0.248 0.5 0.333 9-5 0.257 0.25 1 9-11 0.571 0.25 0.667 11-10 0.762 0.25 0.333 5-4 0.381 0.25 0.667 2-10 0.457 0.25 0.333 3-10 0.79 0.25 0.333 4-3 0.286 0.25 0.333 1-2 0.448 0.25 0.333

The level of packet loss k2

The cost of using the line k3

The resulting subset of the Pareto-optimal alternative routes can be used for organizing multipath routing when using MPLS technology. It will allow to provide a load balancing and a traffic management and to provide given quality-of-service taking into account the set of the quality indicators.
