Elsevier CCDesign and control of the interconnecting network of the access segment of mobile communications systems

8/10/2019 Elsevier CCDesign and control of the interconnecting network of the access segment of mobile communications s

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Design and control of the interconnecting network of the access segmentof mobile communications systemsq

C. Sarantinopoulos, D. Karagiannis, K. Peppas, P. Demestichas*, E. Tzifa, V. Demesticha,M. Theologou

Telecommunications Laboratory, Department of Electrical and Computer Engineering, National Technical University of Athens,

9 Heroon Polytechneiou Street, Zographou, 15773 Athens, Greece

Received 24 October 2000; revised 2 May 2002; accepted 2 May 2002

Abstract

In mobile communication systems, the network segment interconnecting the Base Station (BS) layout with the Base Station Controllers

(BSCs) and the BSCs with the Fixed Network Switches (FNSs) should be carefully designed and controlled. This paper presents techniques

for the efficient design and control (reconfiguration) of this network segment. The corresponding problems are formally defined and

mathematically formulated. Two solutions are presented to the design problem, based on the genetic algorithm and the simulated annealing

paradigms. Additionally, a third solution, based on neural networks, is proposed for the control (reconfiguration) problem. Results are

provided indicating the efficiency of the proposed algorithms.

q 2002 Elsevier Science B.V. All rights reserved.

Keywords: Base station; Base station controller; Simulated annealing; Genetic algorithms

1. Introduction

Mobile communications systems [15] will have to

provide a wide variety of sophisticated services over the

widest possible service area. From the viewpoint of

the users, the success of these systems will depend on the

Quality of Service (QoS) that they will provide, and

especially, on whether it will be comparable to that provided

by fixed systems. From the network providers perspective,

the aim will be to provide QoS in the most cost efficient

manner. An important objective of the design of future

mobile systems is introducing them by minimally impacting

the existing fixed communication infrastructures. In thisrespect, mobile communications systems have been con-

ceived as consisting of the following three segments. First,

the core-network segment (e.g. IP-based) that provides the

switching and transmission functions required. Second, the

intelligent network segment that comprises the logic that

enables the provision of services to mobile users. Third, theaccess-network segment that enables interworking between

the mobile unit and the fixed network. In this paper, we

discuss about the design of the access network segment and

the best distribution of the systems capacity in order to

provide the predefined QoS.

Fig. 1presents the division of the architecture of a mobile

communications system into the three segments described

above. The network elements in the access network segment

are the Base Stations (BSs), which provide radio link

management, the Base Station Controllers (BSCs) and the

Fixed Network Switches (FNSs), which provide switching

functionality, as well as connection and call control [4,5]. In

the UMTS case, a BS is called Node-B, and a BSC is called

Radio Network Controller (RNC). FNSs can be nodes of a

circuit-switched or a packet-switched (e.g. IP-based) net-

work. Typically, the network elements of the intelligent

network segment are called Visited Location Register

(VLR) and the Home Location Register (HLR).

Our aim in this paper is to find the minimum cost

configuration of the interconnecting network, which refers

to the allocation of BSs to BSCs and FNSs. In more detail,

the following topics will be studied. First, given the BS

layout, the derivation of the minimum cost interconnections

of BSs to BSCs, and subsequently, of BSCs to FNSs, that

0140-3664/03/$ - see front matter q 2002 Elsevier Science B.V. All rights reserved.

PII: S 0 1 4 0 - 3 6 6 4 (0 2 )0 0 1 3 5 - 4

Computer Communications 26 (2003) 489497

www.elsevier.com/locate/comcom

qThis work was partially funded by the Commission of the European

Communities, under the Fourth Framework Program, within the ACTS

project Software Tools for the Optimisation of Resources for Mobile

Systems (STORMS).* Corresponding author. Tel.: 30-10-772-14-78; fax: 30-10-772-25-

34.

E-mail address: [email protected] (P. Demestichas).
http://www.elsevier.com/locate/comcomhttp://www.elsevier.com/locate/comcom


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satisfy a set of performance constraints (that derive from the

traffic and mobility patterns in the system). Second, the

recalculation of the minimum cost interconnections

between BSs to BSCs and of BSCs to FNSs subject to the

same set of constraints as the previous calculation but also

depending on the new network condition. The rational for

addressing this problem is based on the belief that the

efficient exploitation of the fixed network infrastructure (inother words, the exploitation of the investment in the fixed

network) will be key factors in the success of future mobile

networks.

The first problem addressed in the context of this study, is

how to find the minimum cost allocation of BSs to BSCs and

of BSCs to FNSs. In the usual problem formulations, there

are three factors contributing to the cost function. Some

consider the cost functions to consist of a factor penalising

the cost of connecting a cell to a switch, and another factor

penalising the handovers that occur among cells that are

connected to different switches. Others consider the cost of

interconnecting BSs to BSCs and BSCs to FNSs and the costof the equipment (namely, BSCs and FNSs) that needs to be

deployed. In the context of this paper we consider an

extension of the problem. More specifically, we include in

the objective function, a factor that enforces load balancing

among BSCs and FNSs. We are based on the assumption

that it is important to optimally balance the load among

BSCs (FNSs), and consequently to provide uniform QoS.

The constraints of the problem derive from the capabilities

of the BSCs (FNSs), expressed in terms of the load they can

handle, and probably, the maximum number of BSs (BSCs)

they can control. The second problem addressed in the

context of this study is associated with the reallocation of

the BSs to BSCs and of the BSCs to FNSs, given the original

distribution and the traffic load.

There are two limitations associated with the first

problem solution. The first is that the computation of the

optimal solution is a computationally intensive task. The

second obstacle is that it does not take into account time

variant traffic loads. Hence, network allocation should be

performed during the system design phase, based on worst-

case estimates regarding the traffic load. However, the traffic

load that a mobile system has to handle is time-variant. Lets

assume that it consists of a set of load vectors, each of which

is valid during a particular time-zone of a day or of a year. In

this perspective, an alternative is to design so as to handle

the more demanding of these vectors, and when the traffic

demand changes, to reconfigure the network allocation so as

to adapt to the traffic variation. There are two advantages

associated with this alternative. First, there can be savings in

the network entity capacity required for providing accep-

table system performance (and consequently mobile user

perceived QoS). Second, the available capacity may beexploited in a more efficient manner, since the allocation is

made with respect to the entities demand. In this paper we

solve this extension to the basic version of the network

allocation problem, in order to handle time variant loads.

The rest of this paper is organised as follows. Section 2

provides a general high level description of the two

problems. Section 3 states the two problems, which are

generally called network design problem and the network

reconfiguration problem. Afterwards, Section 4 mathemat-

ically formulates the two problems. Section 5 describes two

well-known techniques for solving the optimisation pro-

blem of network design. Section 6 describes a neuralnetwork technique for solving the network reconfiguration

problem. Section 7 presents the results of the three methods

and compares them. Finally, Section 8 concludes the paper.

2. High level problem description

This section provides a more detailed description of the

architecture of the interconnecting network of the access

segment. Moreover, it provides the high level definition of

the versions of the interconnecting network design and the

interconnecting network reconfiguration problems

addressed in this paper. To be able to accomplish it we

should define the cost function and specify the constraints

that derive from the requirements of (primarily) the BSs and

the capabilities of the BSCs and FNSs.

The BS requirements derive from the behaviour of the

users in the respective cell. User behaviour may be

characterised in terms of service preferences and mobility.

Service preferences yield the traffic load that will originate

from each BS, which may be expressed in terms of an

associated with each BS level bandwidth value. In essence,

this value corresponds to the bandwidth required by the BS,

so as to adequately provide the services preferred by the

Fig. 1. High level architecture of a mobile communications system.

C. Sarantinopoulos et al. / Computer Communications 26 (2003) 489497490


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users in the cell. The combination of service preferences and

mobility behaviour yields the signalling load. An assump-

tion made in this paper, in order to account for the time

variant traffic demands and mobility conditions, is that the

day may be split in time-zones. Within each time-zone the

traffic demand and the mobility pattern are assumed known.

Taking into account the aspects outlined above, a generalproblem statement may be the following. Given the BS

layout, the bandwidth requirement (aggregating traffic and

signalling load), the handover rates among neighbouring

BSs, a set of candidate BSC and FNS sites, the cost of each

BSC and FNS, and the cost of inter-connecting BSs to

BSCs, and BSCs to FNSs, find the minimum cost allocation

of BSs to BSCs and of BSCs to FNSs (in terms of the

number of BSCs and FNSs that need to be deployed, the cost

of inter-connecting BSs to BSCs and BSCs to FNSs, and of

the signalling imposed by the arrangement), subject to a set

of constraints, associated with the capabilities of the BSCs

and FNSs.

The cost function for the network reconfiguration

problem may consist of the following factors: first, the

cost for connecting the equipment; second, the penalty for

connecting BSs to different BSCs and BSCs to different

FNSs. The constraints of this problem are the same as in the

network design problem, with one addition. All the network

entities that are deployed in the solution of the network

configuration problem must also be deployed in the solution

of this problem. The second problem may be outlined in

the following statement. Given the network configuration,

the handover rates between neighbouring entities and the

deployed BSCs and FNSs find the minimum cost allocation

of BSs to BSCs and BSCs to FNSs, subject to theconstraints.

The focal points in our work, and in a sense the difference

from pertinent works in the literature [610], are the

following. First, a more general problem version is

considered, since it spans over the information transfer

part of the problem (BSC and FNS deployment). Second, an

extended cost function is introduced, combining factors like

the cost of the equipment, the cost of interconnecting

(cabling) and the cost of signalling (handovers). Third, an

extended set of constraints, related to performance require-

ments and equipment (BSC and FNS) capabilities, is

incorporated. Finally, an optimal formulation comprising

all the desired features and novel computationally efficient

algorithms are presented.

3. Formal problem statements

3.1. Problem 1: interconnecting network design

This section provides the formal statement of the version

of the interconnecting network planning problem addressed

in this paper. Given is the set of BSs, denoted by V;and foreach BS-i i [ V and the capacity (bandwidth) require-

ment,bwi.Crepresents the set of candidate BSC sites and L

represents the set of candidate FNS sites.

Let Cj denote the set of BSs that will be connected to

BSC-j, and Ll; the set of BSCs that will be connected toFNS-l l [ L: The objective is to find the allocations ACandAL;whereAC{Cjlj [ C}Cj # VandAL{Llll [

L} Ll # C: These should minimise a cost function thatmay be represented as fAC;AL: The following factorscontribute to the cost of the allocations. First, the cost of the

BSCs and FNSs that will need to be deployed. These costs

are denoted as CC and CL; respectively. For notationsimplicity it is assumed that the cost of deploying a network

element (of a certain type) is the same in all sites. As an

alternative this cost could be taken variant (depending on

the cost of acquiring and/or maintaining the site, etc.).

Notation may readily be extended. The second cost factor is

that of inter-connecting BSs to BSCs and BSCs to FNSs. We

assume that set PC {PBCi;jli [ V;j [ C} provides the

cost of connecting BS-i to the BSC that may be located atthe candidate site j. In a similar manner, the cost of

connecting the BSC that may be located at candidate sitej,

to the FNS (that may be) located at candidate site l, is

provided by set PL{PCLj; llj [ C; l [ L}: The finalcost factor considered are the handovers among BSs that are

controlled by different BSCs (and subsequently, the hand-

overs among BSCs that are controlled by different FNSs).

A s input, in this respect, w e have the set Hb

{hBi; i0l;i; i0 [ V2} that provides the crossing rates

(handovers) among the (neighbouring) BSs i and i 0:The constraints of our problem are the following. First,

each BS should be assigned to one BSC, and each BSC

should be assigned to exactly one FNS. Therefore, Cj1 >

Cj2 B for all j1;j2 [ C2; and Ll1 >Ll2 B for all

l1; l2 [ L2:Second, all BSs should be assigned to a BSC,

and all BSCs should be assigned to an FNS. Hence,Sj[CCj V and

Sl[LLl C: Third, the capacity con-

straints of each BSC and FNS should be preserved. Lets

assume that wmaxBSC; and kC represent the maximum load(bandwidth) and the maximum number of BSs that a BSC

may handle and that and represent the maximum load

(bandwidth) and the maximum number of BSCs that an FNS

may handle. The constraints arewCCj # wmaxBSC; lCjl # kC;

wLLl # wmaxFNS; lLll # kL: The assumption in the previous

constraints is that function wCCj provides the bandwidthrequirements of the BSs assigned to BSC-j and function

wLLl provides the bandwidth requirements of the BSCs

assigned to FNS-l.

The quest for the optimal solution to Problem 1 is

computationally demanding. Nevertheless, this formulation

is effective in handling a certain traffic condition, that is, a

given (time invariant) traffic load. In this respect, an efficient

algorithm for Problem 1 would have significant application

value as discussed in Section 3.2. Then, however, the next

deficiency to be faced is adaptability to the changing with

time traffic conditions.

C. Sarantinopoulos et al. / Computer Communications 26 (2003) 489497 491


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3.2. Problem 2: interconnecting network reconfiguration

(control)

LetACandALbe the allocation of BSs to BSCs, and of

BSCs to FNSs, respectively, that are established throughout

the network at a certain point in time. This allocation

designates the expected QoS levels in each BS and BSC ofthe system. Traffic variations cause QoS degradations, and

hence, a reconfiguration of the allocation is necessary.

Through the reconfiguration mechanism a new allocation of

BSs A0Ck and of BSCs A0

Lk has to be imposed. This

allocation should possess the following properties. First, it

should be compliant with the problem constraints. Second, it

should improve the cost function value, that is for a certain

set of traffic loads Lk;Lk21 and for certain capacity setfk;fk21;the conditionCk , Ck2 1should hold. Third, thealready established allocation should be taken into account.

That is,A0Ckand A0

Lkshould be obtained by using all the

already established BSCs and FNSs. The overall problem

statement has as follows.

The following constitutes the input to the problem. (a)

BS related information, i.e. sets V and Hb; and therequirements bwi ;i [ V: (b) BSC related information,i.e. the set C, and the thresholds kC; w

maxBSC: (c) FNS related

information, i.e. the set L, and the thresholds and wmaxFNS and

kL: (d) The traffic load in the different time-zones Lk: Thecosts of interconnecting BSs to BSCsPC{pBCi;jli [ V;

j [ C} and BSCs to FNSs, PL{pCLj; llj [ C; l [ L}:The objective is to find an allocation of BSs to BSCs

ACk {Cjlj [ C} Cj # V; and of BSCs to FNSs,ALk {Ljll [ L} L# C: The allocations should mini-

mise the cost function fACk; ALk; subject to theconditions Cj1 > Cj2 B ;j1;j2 [ C

2; Ll1 >Ll2 B;l1; l2 [ L

2;S

j[CCj V;S

l[LLl C; wCCj #wmaxBSC; lCjl # kC; ;j [ C wLLl # w

maxFNS; and lLll # kL

;l [ L:

4. Optimal formulation

This section provides the optimal formulation of the

version of the interconnecting network planning and

reconfiguration problem addressed in this paper. In order

to describe the allocation ofAC

BTSs to BSCs we introduce

the decision variablesxBCi;j i [ V; j [ C that take thevalue 1 (0) depending on whether BTS-i is (is not)

connected to BSC-j. In a similar manner, allocation AL is

described by the decision variables xCLj; l; that take thevalue 1 (0) depending on whether BSC-j is (is not)

connected FNS-l. The decision variables YCj and YLl

assume the value 1 (0) depending on whether candidate

BSC-j j [ C or FNS-l l [ L is (is not) deployed. In

addition, we define the set of variables ZBi; i0 ;i; i0 [

V2that take the value 1 (0) depending on whether the BTSs

iand i0 are (are not) connected to the same BSC node. The

variables ZBi; i0are related to variables xBCi;j; xBCi

0;j;

through the relation ZBCi; i0

PlCl

j1xBCi;jxBCi0;j;

which may be turned into a set of linear constraints through

the technique ofRef. [10]. In a similar manner we can define

variables ZCLj;j0 indicating whether BSCs j and j0 are

controlled by the same FNS, respectively.

Allocations ACand ALmay be obtained by reduction to

the following linear programming problem.

Problem 1. Interconnecting Network Design. Minimise

cCXlClj1

yCj XlVli1

XlClj1

pBCi;jxBCi;j cLXlLll1

yLl

XlClj1

XlLll1

pCLj; lxCLj; l XlVli1

XlVli01

hBi; i0 12zBCi; i

0

XlCl

j1 XlCl

j01

hCj;j0 12zCLj;j

0

1

subject to

XlClj1

xBCi;j 1 ;i [ V; 2

XlVli1

xBCi;j # kCyCj ;j [ C; 3

XlVli1

xBCi;jbwi wCj # wmaxBSCyCj ;j [ C; 4

XlLll1

xCLj; l 1 ;j [ C; 5

XlClj1

xCLj; l # kLyLl ;l [ L; 6

XlClj1

xCLj; lwCj # wmaxFNSyll ;l [ L; 7

Cost function (1) penalises the aspects identified in Section

2 (i.e. cost of the equipment deployed, cost of interconnect-

ing the network elements deployed, and cost of handovers

among BTSs and BSCs controlled by different BSCs and

FNSs, respectively). Constraints (2) and (5) guarantee that

each BTS will be assigned to one BSC, and each BSC will

be controlled by one FNS, respectively. Constraints (3) and

(6) guarantee that BSCs and FNSs will not be assigned more

BTSs and BSCs than allowed by their capacity constraints.

Constraints (4) and (7) guarantee that each BSC and FNS

will not have to cope with more load than that dictated by its

pertinent capacity constraint.

For the description of the allocation of BTSs to BSCs

A0Ck; we introduce the decision variables xBCi;j; k i [V; j [ C; tk[ T that take the value 1 (0) depending on



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whether BTS-i is (is not) connected to BSC-j, at a certain

time-zone tk: In a similar manner, allocation A0

Lk; isdescribed by the decision variables xCLj; l; k that take thevalue 1 (0) depending on whether BSC-j is (is not)

connected FNS-l. Allocations A0Ck; and A0

Lk may be

obtained by reduction to the following linear programming

problem.

Problem 2. Interconnecting Network Reconfiguration.

Minimise

XlVli1

XlClj1

pBCi;jxBCi;j; k XCj1

XlLll1

pCLj; lxCLj; l; k

XlVli1

XlVli01

hBi; i0 1 2zBCi; i

0

XlClj1

XlClj01

hCj;j0

12zCLj;j0 8

subject to

XlClj1

xBCi;j; k 1 ;i [ V; 9

0 ,XlVli1

xBCi;j; k # MC ;j [ C; 10

fCj; k # wmaxBSCyCj ;j [ C; 11

XlLll1

xCLj; l; k 1 ;j [ C; 12

0 ,XlClj1

xCLj; l; k # ML ;l [ L; 13

fLj; k # wmaxFNSyll ;l [ L; 14

Cost function (8) penalises the aspects identified in Section

2 (i.e. cost of the equipment deployed, cost of interconnect-

ing the network elements deployed, and cost of handovers

among BTSs and BSCs controlled by different BSCs and

FNSs, respectively). Constraints (9) and (12) guarantee that

each BTS will be assigned to one BSC, and each BSC will

be controlled by one FNS, respectively. Constraints (10) and

(13) guarantee that BSCs and FNSs will not be assigned

more BTSs and BSCs than allowed by their capacity

constraints. Constraints (11) and (14) guarantee that each

BSC and FNS will not have to cope with more load than that

dictated by its pertinent capacity constraint.

5. Computationally efficient solutions for the

interconnecting network design problem

This section provides two computationally efficient

solutions for the version of the network design problem

addressed in this paper. The optimal formulation presented

in Section 4 yields that the computation of a feasible

solution is a computationally intensive task. The usual next

step for solving such difficult problems is to devise

computationally efficient algorithms that may provide

good solutions in reasonable time.

The solution methods are influenced by the geneticalgorithm [1114] and the simulated annealing [15,16]

techniques. A step further for reducing the complexity of

Problem 1 is to solve it in a divide and conquer manner. This

approach is facilitated by the fact that the architecture of the

interconnecting network is a multilevel, star one. Hence, the

problem may be solved in phases. Each phase may be

targeted to one level of the architecture, and the output of

each phase may be input to the next. In our case this idea

yields that an algorithm should have two phases, which are

targeted to the computation of the allocations AC(BTSs to

BSCs) and AL (BSCs to FNSs), respectively. The same

technique (division into phases) is applied to the second

problem as well.

5.1. Genetic algorithm

In general, genetic algorithms maintain a set of problem

solutions. A string of genes, also called a chromosome, is

used for representing a solution. During each algorithm

iteration, or generation, the solutions are rated with respect

to their quality, or fitness. Some solutions will be selected

and used for the generation of a new population. This

generation relies on the so-called genetic algorithm

operators. In general, genetic algorithms use the selection,

crossover, mutation and replacement operators. The con-struction of a genetic algorithm requires that the following

points are addressed. First, the aspects that are represented

by the genetic chromosome should be chosen. Second, the

set of genetic operators should be chosen. Third, the fitness

function should be defined. Fourth, the genetic operators

should be configured.

In our case the chromosome is a lVl lCl (or lCl lLl)

matrix of bits indicating whether a BS (BSC) is connected to

a BSC (FNS). Hence, only one gene in each row is set equal

to 1, while the rest genes are set to 0. The fitness function of

a solution is taken as the inverse of the objective function

(5). This is done to straightforwardly express that solutions

that yield lower objective function values are seen as more

fit from the algorithm point of view.

The selection operator aims at selecting the solutions

that will reproduce. The usual choice is to select the

solutions that exhibit the best performance with respect

to the fitness function. The crossover operator is applied

with probability pc after the selection (reproduction)

operator. The basic idea of this phase is to select two

(parent solutions) allocations of BSs (BSCs) to BSCs

(FNSs), from the current set of solutions, and to

combine them to create two children. The mutation

operator is applied after the crossover operator with



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probability pm: The mutation operator produces a newsolution by (slightly modifying one or more gene values

of an existing solution) changing the allocation of a BS

(BSC) to a BSC (FNS). The replacement operator is

finally applied to the population of the already available

and the generated solutions, in order to create the new

population of available solutions.

5.2. Simulated annealing based solution

The development of a simulated annealing-based

procedure means that the following aspects have to be

addressed: configuration space, cost function neighbour-

hood structure and cooling schedule (i.e. manner in which

the temperature will be reduced) [17]. The configuration

space is the set of feasible solutions {xBCi;j; xCLj; l;yCj; yLl} that satisfy the constraints. The cost function

is the one introduced by relation (5). The neighbourhoodstructure of a solution is produced by moving a BTS

(BSC)-i j; from its present BSC (FNS)-j k or l to aneighbouring BSC (FNS)-j0 k0 orl 0:The cooling schedulemay be calculated according to T0 rT; where T is thetemperature and r is usually a number that ranges from

0.95 to 0.99. Other techniques may also be applied. The

algorithm stops when no improvement has been made after

a given number of temperature decreases (in other words

consecutive moves or alterations of the currently best

solution).

6. Neural network solution for the interconnecting

network reconfiguration problem

This section provides a solution for the version of the

interconnecting network reconfiguration problem

addressed in this paper. The solution adheres to the neural

network paradigms inRefs. [1821]. The overall problem

is solved in two phases, targeted to the computation of

allocations AC (BTSs to BSCs) and AL (BSCs to FNSs),

respectively.

Following the specification in Refs. [18 21], thefollowing steps should be conducted, in order to solve

our combinatorial problem with the chosen neural

network model. First, the energy function, which should

have the general form E costglobal constraints;should be defined. Second, the matrix of the weights,

wij; of the connections between the neurons i and j,should be configured. Third, the relations providing the

set of activations aijt; and their update, aijt1;should be provided. Fig. 2 depicts the overall solution

approach.

In our case the energy function is provided by the

following relation:

EAC AXlVli1

XlClj1

pBCi;jxBCi;j; k

BXlVli1

XlVli01

hBi; i0

12zBCi; i0

!

C

XlClj1

xBCi;j; k2 1

!2

DQ

XlVli1

xBCi;j2MC

!2

EQ

fCj; k2 w

maxBSCyCj

!2:

Qxis either equal tox;ifx $ 0;or equal to 0, ifx , 0:Thecoefficients A, B, C, D, E and F denote the importance

(weight) of each term. By minimising the above energy

function is the same as minimising the first three terms and

making the rest three terms equal to zero. However, the last

three terms are equal to zero only when the constraints of the

problem are satisfied.

Each term of the weight matrix can be given by the

following relation.

wij ApBCi;j B

XlVl

i1

hBi; i0 12xBCi

0;j; t

C DE: 15

Furthermore, according toRefs. [18 21], the update of the

activations of the neurons can be conducted through

relations that have the form, aijt1 aijt

daijt=dtdt: The daijt=dt quantity requires thedifferentiation of the energy function EAC with respect

to the decision variables.

7. Results

This section addresses a test case in which the two

problems introduced are solved. The three algorithms

introduced above will be applied to the test case. The

genetic algorithm and the simulated annealing technique

will be used for the instance of Problem 1, while all three

algorithms will be applied to the instance of Problem 2.

The network consists of 25 BTSs, placed in a 5 5

layout.Fig. 3(a) and (b) depict the network layout and the

two load scenarios (total load 9300 erlangs). The maxi-

mum number of BTSs that can be connected to a single BSC

is 7, while the maximum total load that a BSC can handle is

3000 erlangs. The maximum number of BSCs that can be



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connected to a single LE is 2, while the maximum total load

that a FNS can handle is 4500 erlangs.

Fig. 4 depicts the results obtained from the genetic

algorithm.Fig. 4(a)depicts the allocations of BSs to BSCs

in the first load scenario. The number of BSs connected to

each BSC and the total load of each BSC are also shown in

the figure.Fig. 4(b)depicts the allocations of BSCs to FNSs

in the first load scenario. Three FNSs are deployed in the

solution.Fig. 4(c) and (d)depict the allocations of BTSs to

BSCs, and of BSCs to FNSs, in the second load scenario,

given also the BSC and FNS positions. The cost of the

second solution is larger due to the existence of more BTSs

with high requirements.

Fig. 5 depicts the results obtained from the genetic

algorithm.Fig. 5(a) and (b)depict the allocations of BSs to

BSCs, and of BSCs to FNSs, in the first load scenario.Fig.

5(c) and (d)depict the allocations of BSs to BSCs, and of

BSCs to FNSs, in the second load scenario. As anticipated,

the simulated annealing algorithm yields different results

than the genetic algorithm. However, the results areequivalent in terms of their cost (5 BSCs and 3 FNSs

deployed in both load scenarios).

Fig. 6 shows the results from the application of theneural network solution. In Fig. 6(a) and (b) the results

of the genetic algorithm are used as a basis. The neural

network solution is applied for reconfiguring the network

from the first to the second load. The application of the

genetic algorithm has resulted to a solution in which 5

BSCs and 3 FNSs are deployed, at the positions 7, 9, 16,

18, 20, and 9, 16, 20, respectively. Fig. 6(a) shows the

reconfiguration, of the allocation of BTSs to BSCs, for

the second load scenario, proposed by the neural network

solution. The total cost of connecting all the BTSs to the

BSCs is lower than the cost provided by the genetic

Fig. 2. Approach in the neural network based solution.

Fig. 3. Network layout and two load scenarios used in our test case.

Fig. 4. Results from the genetic algorithm. (a) Allocation of BTSs to BSCs

in the first load scenario. (b) Allocation of BSCs to FNSs in the first load

scenario. (c) Allocation of BTSs to BSCs in the second load scenario. (d)

Allocation of BSCs to FNSs in the second load scenario.



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algorithm. Fig. 6(b) shows the allocation of BSCs to

FNSs, for the second load scenario. The results in this

case are the same as those provided by the genetic

algorithm.

InFig. 6(c) and (d)the results of the simulated annealing

algorithm are used as a basis. The solution consists of 5

BSCs and 3 RNSs, deployed at the positions 3, 9, 12, 19, 22

and 3, 12, 22, respectively. Fig. 6(c) and (d) show the

reconfiguration, of the allocation of BTSs to BSCs, and of

BSCs to FNSs, for the second load scenario, proposed by the

neural network solution. The BTS to BSC allocation

corresponds to lower cost with respect to that of the

simulated annealing algorithm.

In the rest of this section the behaviour and performance

of the three algorithms is discussed and compared. The

genetic and the simulated annealing algorithms have been

applied to Problem 1. All algorithms have been applied to

Problem 2.The algorithms have been coded in the C

programming language, executed in a PC/Windows

environment having a 1 GHz processor. The algorithms

solve the selected test cases in less than a minute.

The genetic and the simulated annealing algorithm

exhibit similar performance in the solution of Problem 1,

which is considered to be more difficult than the second one

since the positions of the elements have to be found, apart

from the need of finding the equipment interconnections.

The fact that two independent algorithms converge to

equivalent solutions is a strong indication on the efficiency

of the algorithms.

The strategy based on neural networks seems better

suited for Problem 2. In other words, the method exhibits

Fig. 5. Results from the simulated annealing algorithm. (a) Allocation of

BTSs to BSCs in the first load scenario. (b) Allocation of BSCs to FNSs in

the first load scenario. (c) Allocation of BTSs to BSCs in the second load

scenario. (d) Allocation of BSCs to FNSs in the second load scenario.

Fig. 6. Results from the neural network algorithm, in the second load

scenario. (a) Reconfiguration of the initial allocation, of BTSs to BSCs,

proposed by the genetic algorithm. (b) Reconfiguration of the initial

allocation, of BSCs to FNSs, proposed by the genetic algorithm. (c)

Reconfiguration of the initial allocation, of BTSs to BSCs, proposed by the

simulated annealing algorithm. (c) Reconfiguration of the initial allocation,

of BSCs to FNSs, proposed by the simulated annealing algorithm.



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slightly better performance when the optimisation criterion

depends on the cost of the inter-connection of the

equipment, while the number of the elements deployed

and their position is given. It should also be noted that the

neural network algorithm required less computation time

than the other algorithms for finding a better solution.

Inherently, the neural network model chosen converges tosolutions rapidly. This leaves some room for applying

techniques that verify the overall quality of the solution, and

therefore, avoid local optima. Typically, these techniques

result to running the algorithm many times with different

initial conditions. The algorithm should converge to

equivalent solutions. However, in order to achieve the

improved performance, there is an important aspect that

should be addressed, that of finding the proper combination

of the coefficients of all the terms participating into the

energy function. However, the fact that the three different

methods converge to equivalent solutions is again a strong

indication on the efficiency of the schemes.

8. Conclusions

This paper started from the identification of the

importance of efficiently designing and controlling

(reconfiguring) the interconnections of BSs with BSCs

and of BSCs with FNSs. In this respect, two problems

targeted to the design and the control of these

interconnections were formally defined and formulated.

Two solutions to the design problem were proposed,based on the genetic algorithm and simulated annealing

paradigms. Additionally, a third solution to the control

(reconfiguration) problem was based on neural net-

works. A first set of results shows the efficiency of the

genetic and simulated annealing schemes in solving the

design problem . A second set of results shows

the efficiency of the genetic, simulated annealing and

neural network schemes in solving the control (reconfi-

guration) problem. Issues for further study can include

the experimentation with larger test cases, and the

integration of the algorithms in an overall network

planning tool.

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