GENETIC ALGORITHM FOR MULTIHOMING CELL ASSINGMENT PROBLEM IN WIRELESS ATM NETWORK

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GENETIC ALGORITHM FOR

MULTI-HOMING CELL ASSINGMENT

PROBLEM IN WIRELESS ATM

NETWORK

R. L. UJJWAL, Dr C. S. RAI, Prof. NUPUR PRAKASH

University School of Information Technology, Guru Gobind Singh Indraprastha University,

Delhi-110075 (INDIA)

Abstract:

In the design of cellular telecommunications networks, the handover and cabling cost management play an important role. In this paper, we propose a cell assignment problem, which assign cells in Personal Communication Service (PCS) to switches in wireless ATM network in an optimal manner. This is a complex integer programming problem and modeled as multi-homing cell assignment problem. Since finding an optimal solution of this problem is NP-hard. The proposed method, based on genetic algorithm, solve this problem. We implement this problem in MATLAB using GA and find better results.

Keyword: cellular network, cell assignment, genetic algorithm, handoff.

1. Introduction

In a cellular network, the area of coverage is often divided into hexagonal shape that is cell. The cells usually communicate through stationary base stations to switches, which route calls either to another base station or to a public switched telephone network [1,2,3]. The two-level hierarchical network is used in network where the lower level network is the PCS network andthe upper level network is the ATM backbone network.

Figure 1. Two level hierarchical network

In the multi-homing cell assignment problem, each cell will be assigned to three switches and they allowed one to reduce the cost of handoff by increasing the cost of cables. If the ATM backbone network is integrated with the PCS network, the handoff cost considered which only depends on the frequency of handoff between two switches is not realistic. Since the switch of ATM backbone is widely spread, the communication cost between two switches should be considered in calculating the handoff cost. . In such a problem, each cell Ci will be assigned to Ki (Ki = 1 and integer) switches and the corresponding Ki disjoint links will be created. If Ki is set as 1 for all cells, the problem is reduced to the cell assignment problem. In this paper, the multi-homing cell assignment problem where Ki was fixed at 3 for all cells is taken under consideration. That is, there are three

assignments of each cell in PCS network, one is the primary assignment and the other is the secondary assignment and the third is tertiary assignment.

2. Problem Description

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for switch sk, k = 1, 2, …, m and (Xci, Yci) for cell ci, i=1, 2, …, n and dkl be the minimal communication cost

between the switches sk and sl.Let fij be the frequency of handoff per unit time that occurs between cells ci and cj



C, (i, j = 1, 2,…,n) is fixed and known. It is assumed that all edges in CG are undirected and weighted; and assume cells ci and cj



C are connected by an edge (ci, cj)



L with weight wij, where wij= fij + fji, wij = wji,

and wii=0. Let lik be the cost of cabling per unit time and between cell ci switch sk, (i = 1, 2,…, n, k = 1, 2,…,m)

and assume lik is the function of Euclidean distance between cell ci and switch sk, that is

2 2

( ) ( )

i

l_{j k} X_c X_s Y_c Y_s

i k k

   

Assume the number of calls that can be handled by each cell per unit time is equal to 1. Let Capk be the number

of cells that can be assigned to switch sk. Our objective is to assign each cell in C to three switches so as to

minimize (total cost) the sum of cabling cost and handoffs cost per unit time of whole system.

Figure 2. The Assignment of two cells ci and cj

Let us define the following variables. Let xik1 = 1 if the primary assignment of cell ci is assigned to switch sk1,

sk1



S; xik1= 0, otherwise. Let xik2 =1 if the secondary assignment of cell ci is assigned to switch sk2, sk2



S;

xik2 = 0; otherwise. Let xik3 = 1 if the tertiary assignment of cell ci is assigned to switch sk3, sk3



S; xik3 = 0;

otherwise.

It is important to note that if a cell is to be connected to the same switch in primary, secondary and tertiary assignments, its cabling cost should not be double or triple [4,6]. In order to ensure that the cabling costs are not double or triple in the event that a cell is connected to the same switch in two and three assignments, variables xik, I = 1, 2,…, n; k = 1, 2,…,m are defined as: xik = xik1 V xik2 V xik3 ; for i = 1, 2,… n and k = 1, 2,…m;

where the ‘ V ‘ symbol means the ‘or’ operation [2]. Since each cell should be assigned to at most three switches, we have the constraints





 m

k

ik

x 1 1

1 1

for i=1,2,…..,n

1

1 2

2







m

k i

k

x

for i=1,2,…n





m

k i

k

x

1 3

3

1

for i=1,2,…n

Further, since we allow the three assignments of the cell can be the same, the constraint on the call handling capacity of switch is



    

   

 



 

n

i

k i

n

i i n

i

i n

i i n

i

k i

n

i i n

i

n

i

k

cap k

x k

x

capk k

x k

x

cap k

x k

x

cap xik

xik

1

3 1 2 1 1 1

3 1 1 1

3 1 2

1 1

2 1

(3)

Thus, the sum of cabling costs can be formulated as:









  

 

 m

k

i i i ik n

i m

k

n

i ik

ikx l xk xk xk

l

1

3 2 1

1 1 1

(

To formulate the handoff cost, define variables zijk1 =xik1xjk1 ; for i; j = 1; 2;…; n and k1 = 1; 2;…;m: Thus, zijk1

equals 1 if both the primary assignments of cells ci and cj are connected to a common switch sk1; otherwise it is

zero. Further, let yij =





m

ki ij

k

z

1

1 I, j = 1, 2,…, n:

Thus, yij takes a value of 1, if both the primary assignments of cells ci and cj are connected to a common switch;

0, otherwise [3].

With this definition, it is easy to see that the cost of handoffs per unit time between the primary assignment of cell ci and cj is given by

 



  





m

k m

l

l k jl ik j j

n

j n

i

d

x

yi

wi

1 1 1 1 1

1

1 1 1 1

)

1 (

Assume cell ci is assigned to sk1, sk2 and sk3, cj is assigned to switches sl1, sl2 and sl3.

To formulate the handoff cost, several variables are introduced as follows: There are nine possible communication cases between cells ci and cj. They are:

a) from sk1to sl1

b) from sk1 to sl2

c) from sk1 to sl3

d) from sk2 to sl1

e) from sk2 to sl2

f) from sk2 to sl3

g) from sk3 to sl1

h) from sk3 to sl2

i) from sk3 to sl3

Thus, the handoff cost should be computed by the summation (or average) of these cases. To formulate the handoff cost, several variables are introduced as follows:

 zijk1 =xik1xjl1 , for i,j = 1,2,…….,n and k= k1 = l1= 1,2,…..,m

 yij =





m

k1

1

zijk ,i,j = 1,2,…n..

 z1ijk1 =xik1xjl2 , for i,j = 1,2,…….,n and k= k1 = l1= 1,2,…..,m

 y1ij =





m

k1

1

z1ijk1 ,i,j = 1,2,…n..

 y2ij =





m

k1

1

z2ijk ,i,j = 1,2,…n..

 y3ij =





m

k1

1

z3ijk ,i,j = 1,2,…n..

 y4ij =





m

k1

1

z4ijk ,i,j = 1,2,…n..

 y5ij =





m

k1

1

z5ijk ,i,j = 1,2,…n..

 y6ij =





m

k1

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 y7ij =





m

k1

1

z7ijk ,i,j = 1,2,…n..

 y8ij =





m

k1

1

z8ijk ,i,j = 1,2,…n..

With these definitions, it is easy to see that the cost of handoffs per unit time for the best case is given by

Handoff =                  



                                    m k m l l k jl ik ij ij n i n j m k m l l k jl ik ij ij n i n j m k m l l k jl ik ij ij n i n j m k m l l k jl ik ij ij n i n j m k m l k jl ik ij ij n i n j m k m l l k jl ik ij ij n i n j m k m l l k jl ik ij ij n i n j m k m l l k jl ik ij ij n i n j m k m l l k jl ik ij n i n j d x x y w d x x y w d x x y w d x x y w d x x y w d x x y w d x x y w d x x y w d x x yij w 1 1 8 1 1 1 1 7 1 1 1 1 6 1 1 1 1 5 1 1 1 1 4 1 1 1 1 3 1 1 1 1 2 1 1 1 1 2 1 1 1 1 1 1 1 3 3 3 3 3 3 3 2 2 3 2 3 3 1 1 3 1 3 3 2 3 1 3 2 2 2 12 2 2 2 1 1 2 1 2 1 3 3 1 3 1 1 2 1 2 1 1 1 1 1 1 1 ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( 1 ) 1 ( ) 1 ( ) 1 ( ) 1 ( { 

This together with our earlier statement about the sum of cabling costs gives us the objective function: Minimize:

1 1

n m

i k i k

i k

l x

h a n d o f f

 



 

where



is the ratio of the cost between cabling and network costs. That is, our objective is to assign each cell to three switches so as to minimize (total cost) the sum of cabling costs and handoffs cost per unit time.

3. Genetic algorithm for multi homing cell assignment problem

In this section, the details of GA developed to solve the multi-homing assignment problem of optimum assignment of cells in PCSs to switches in the ATM network are discussed. The development of GA requires:

1) a chromosomal coding scheme, 2) genetic crossover operators, 3) mutation operators,

4) fitness function and penalty function

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3.1Chromosomal coding

Since our problem involves representing connections between cells and switches, A coding scheme that uses positive integer numbers is designed [7,8]. Cells are labeled from 1 to n (the total number of cells), and switches are labeled from 1 to m (the total number of switches). The cell-oriented representation of chromosome structure shown in Fig.3 (a) consists of three parts. The first part is the primary assignment of cells, where the ith cell belongs to the vi

th

switch, the second part is the secondary assignment, where the ith cell belongs to the v (i+n) th

switch, and the third part is the tertiary assignment, where the ith cell belongs to the v (i+2n) th

switch Since each cell will be assigned to three switches on ATM network, So 3 x n array is used to represent the assignment of cells. If cell ci is assigned to switches sk1, sk2 and sk3, then vi= k1 ,v(i+n) =k2 and v(i+2n) =k3: For example, the

chromosome of as shown in Fig 3. It is worth noting that, the cell-oriented representation of chromosome structure can be divided into three sets which represent the primary assignment, the secondary assignment of cells and tertiary assignment of cells, respectively.

3.2 Genetic crossover operator

This operator selects two chromosomes randomly for crossover from previous generations and then by using a random number generator, an integer value i is generated in the range [1, n]. The offspring are generated by swapping of characters between i+1 and n of two parents.

3.3 Mutations

Crossover can generate a very large amount of different strings. However, depending on the initial population chosen, there may not be enough variety in the strings to ensure the GA covers the entire problem space. Or the GA may find itself converging on strings that are not quite close to the optimum it seeks due to a bad initial population. Some of these problems are overcome by introducing a mutation operator into the GA. The GA has a mutation probability, which dictates the frequency at which mutation occurs. Mutation can be performed either during selection or crossover. For each string element in each string in the mating pool, the GA checks to see if it should perform a mutation [11]. If it should, it randomly changes the element value to a new one. In our binary strings, 1s are changed to 0s and 0s to 1s.

The mutation probability should be kept very low (usually about 0.001%) as a high mutation rate will destroy fit strings and degenerate the GA algorithm into a random walk, with all the associated problems.

3.4 Fitness function definition

Generally, GAs use fitness functions to map objectives to costs to achieve the goal of an optimally designed two-level wireless ATM network[9,10]. If cell ci is assigned to switch sk1 ; and sk2 ; then vi in the chromosome is

set as k1 and v(i+n) is set as k2 and v(i+2n) is set of k3

Let d(vi ,vj), d(vi ,v(j+n)), d(vi, vj+2n),d(v(i+n),vj),d(v(i+n),v(j+n)), d(v(i+n),v(j+2n)), d(v(i+2n),vj),d(v(i+2n),v(j+n)),

d(v(i+n),v(j+2n)), be the minimal communication cost between switches

Sk1 and sl1; sk1 and sl2 ; sk1 and sl3

Sk2 and sl1; sk2 and sl2 ; sk2 and sl3

Sk3 and sl1; sk3 and sl2 ; sk3 and sl3 in G respectively

An objective function value is associated with each chromosome, which is the same as the fitness measure. If vi=v i+n = v i+2n then qi=0; otherwise qi= 1:

Minimize OBJ =





 



n

i m

k

n

wij

n

i

qiliv

n

i

qiliv

livi

1 1 1

}

2n)),

v(j

n),

d(v(i

n))

v(j

2n)

d(v(i

vj)

2n),

d(v(i

2n))

v(j

n),

d(v(i

n))

v(j

,

n)

d(v(i

vj)

n),

d(v(i

2n)

vj

d(vi,

n)),

v(j

,

d(vi

vj)

,

d(vi

{

)

2 (

)

(



4. Implementation and Results

This section presents the experimental result of the GA that is implemented in MATLAB, and experiments were run on windows-xp with a Pentium-IV processor and 1GB RAM. The following graph showing that our experimental results are best.

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Figure: 4 Graph between Generation vs Fitness

Figure: 5 Graph showing fitness value of each individual

Figure: 6 Score histogram graph

5. Conclusion

In this paper, the multi-homing cell assignment problem which optimally assigns each cell in PCS to three switches on ATM network is investigated. This method is very helpful to design wireless mobile communication system. Since finding an optimal solution of this problem is NP-hard, a stochastic search method based on a genetic approach is proposed to solve it. GA is used to find optimal solution so as reduce the cost. The cost involves the inter-switch handoff cost that involves three different switches and the cost of cabling that connects cells to switches of ATM network.

References

[1]. Arif Merchant and Bhaskar Sengupta, Assignment of Cells to Switches in PCS Networks. IEEEIACM Transactions on networking, vol. 3, NO. 5, October 1995 521

[2]. D.-R. Din, S.S. Tseng . Genetic algorithm for solving dual-homing cell assignment problem of the two-level wireless ATM network. Elsevier, Computer Communications 25 (2002) 1536–1547 .

0 20 40 60 80 100

0 2 4 6 8 10

12 Fitness of Each Individual

Individual

F

it

ness

0 100 200 300 400 500

4 5 6 7 8 9 10

Generation

Fit

n

e

s

v

a

lu

e

Best: 4.2143 Mean: 5.0659

4 6 8 10 12

0 10 20 30 40 50 60 70 80

Score Histogram

Score

Num

ber of

Individu

al

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[3]. Der –Rong in and s.S Tseng, Heuristic Algorithm for optimal Design of Two level wireless ATM network. Journal of Information Science and Engineering 17, 647-665 (2001).

[4]. C.B.Akki,S.M.Chachan, The Survey of Handoff Issues in Wireless ATM Networks International journal of Nonlinear Science. Vol.7(2009) No.2.pp.

[5]. Der-Rong Din, Shian–Shyong Tseng, and Mon-Fong Jiang,Genetic Algoritm for extended Cell Assignment problem in wireless ATM Network. ASIAN 2000, LNCS 1961, pp. 69–87, 2000.

[6]. F. Akyildiz , W. Su , Y. Sankarasubramaniam , E. Cayirci, Wireless sensor networks: a survey, Computer Networks: The International Journal of Computer and Telecommunications Networking, v.38 n.4, p.393-422, 15 March 2002.

[7]. Anderson, L.G., A simulation study of some dynamic channel assignment algorithms in a high capacity mobile telecommunications system. IEEE Transactions on Communications. v21 i11. 1294-1301.

[8]. Beckmann, D. and Killat, U., A new strategy for the application of genetic algorithms to the channel assignment problem. IEEE Transactions on Vehicular Technology. v48 i4. 1261-1269.

[9]. Chakraborty, G., An efficient heuristic algorithm for channel assignment problem in cellular radio systems. IEEE Transactions on Vehicular Technology. v50 i6. 1528-1539.