Bandwidth allocation in ATM Networks using Novel Particle approach / Performance Analysis of ATM networks using modified particle approach

International Conference on Intelligent Information Systems and Management (IISM’2010), June10-12, 2010

Abstract──This paper presents generalized particle approach to

optimize the bandwidth allocation and QoS parameters in ATM

networks. The generalized particle approach algorithm (GPAA)

transforms the network bandwidth allocation problem into dynamics

and kinematics of numerous particles in a force-field. In ATM

networks optimization, the GPA deals with a variety of random and

emergent phenomena, like congestion, failure, and interaction. The

bandwidth allocated, success rate and the shortest path determined by

GPAA are compared with the same parameters determined using

Max-Min fairness (MMF) algorithm. The comparison among the

algorithms gives the effective performance analysis of ATM

networks.

I. INTRODUCTION

TM network is to support multiple classes of traffic (e.g.

video, audio, and data) with widely different

characteristics and Quality of Service (QoS) requirements.

The major challenges are guaranteeing the QoS required for

all the admitted users and dynamically allocating appropriate

resources to maximize the resource utilization. Many

algorithms and evaluation criteria for the bandwidth allocation

have been proposed are based on maximizing an aggregate

utility function of users, an average priority or average

reliability of traffics; minimizing the overhead of data

transmission and the highest call blocking Probability of all

source-destination pairs. In some duality models the network's

optimization problem can be solved by a primal Parallel

algorithm for allotted rates and a dual parallel algorithm for

shadow prices or congestion signals [1].

In this paper GPAA is used to determine bandwidth to be

allocated based on pricing and shortest path. MMF is used to

determine bandwidth to be allocated based on fairness and

pricing. The success rate, shortest path are also calculated

using both methods separately and compared.

II. GENERALIZED PARTICLE APPROACH

The GP model consists of numerous particles and forces,

with each particle having its own dynamic equations to

represent the network entities and force having its own time-

varying properties to represent various social interactions

among the network entities. Each particle in GP has four main

characteristics [2]:

M. Dhivya is with the Department of Electrical and Electronics

Engineering, Anna University, Coimbatore, India. e-mail:

[email protected].

M. Sundarambal is with the Department of Electrical and Electronics

Engineering, Coimbatore Institute of Technology, Coimbatore, India.

L. Nithissh Anand is with the Department of Mechanical Engineering,

Anna University, Coimbatore, India

Digital Object Identifier No:IISM00620100001

1. Each particle in GP has an autonomous self-

driving force, to embody its own autonomy and the

personality of network entity.

2. The dynamic state of every particle in GP is a piecewise

linear function of its stimulus, to guarantee a stable

equilibrium state.

3. The stimulus of a particle in GP is related to its own

objective, utility and intention, and to realize the multiple

objective optimizations.

4. There is variety of interactive forces among particles,

including unilateral forces, to embody various

social interactions in networks.

The bandwidth allocation policy of a network link depends on

the payment policy of a network path. It changes dynamically

according to the situation of the demands and supplies of

bandwidths and influences the kinematics and dynamics of the

link particles and path particles in their force-fields. The link

particles move in resource force-field FR and the path particles

that require bandwidth assignment move in demand force-field

FD as shown in figure1. Normally a network path pays less

amount under the condition that its bandwidth requirement is

satisfied. It is embodied in the proposed model by the

corresponding path particle. Similarly to maximize the price

benefit a link tries to assign its own bandwidth to the path that

pays maximal price.

III. MODEL FOR BANDWIDTH ALLOCATION

3.1 EVOLUTION OF GP:

The mathematical model based on GP [1] for dynamic

bandwidth allocation that involves m links, n paths and p

channels is defined with following notations:

ri : The maximum bandwidth of link Ai.

d j

: The bandwidth that channel T j requires.

q j : The maximum payoff that channel T

j can

afford for its d j.

Ai : The ith physical link in the network.

Tk : The kth path of the jth channel T j.

a ik : The bandwidth that link Ai allots to path Tk.

P ik : The price per unit bandwidth that path Tk tries to

Pay link Ai.

Bandwidth Allocation in ATM Networks Using

Novel Particle Approach M. Dhivya, M. Sundarambal and L. Nithissh Anand

A

ISBN-978-1-4507-2041-0 © by CiiT 2010 Published by Coimbatore Institute of Information Technology 1

mailto:[email protected]


3.1.1Total Utility:

u k(t) is the distance from the current position of the path

particle T k to the upper boundary of the demand force-field FD

at time t, and let JD(t) be the total utility of all the path

particles in FD. uk(t) and JD(t) are defined respectively as stated

below;

m

u k(t) =δ 1 exp[- ∑ a ik(t) / p ik(t) ] (1) i=1

p n

J D (t) = α1 ∑ ∑ u k(t) (2) j=1 k=1

u i (t) is the distance from the current position of the link

particle Ai to the upper boundary of the resource Force-field

FR at time t, and let JR(t) be the total utility of all the link

particles in FR. ui(t) and JR(t)are defined respectively as stated

below;

p n

u i(t) =δ 2 exp [- ∑ ∑ p ik(t) / a ik(t) ] (3) j=1 k=1

m

J R (t) = α2 ∑ u i(t) (4)

i=1

δ 1, δ 2 >1,and 0< α1, α2 <1.

3.1.2 Potential Energy:

At time t, the potential energy functions, PD(t) and PR(t),

that are caused by the upward gravitational forces of the force-

fields, FD and FR, are defined respectively as stated below;

p n

PD(t) = ε 2 ln[- ∑ ∑ exp [( u k(t))

2 / 2 ε

2] - ε

2 ln(n) (5)

j=1 k=1

m

PR(t) = ε 2 ln ∑ exp [( ui (t))

2 / 2 ε

2] - ε

2 ln(m) (6)

i=1

At time t, the potential energy functions, QD(t) and QR(t),

that are caused by the interactive forces among the particles

in FD and FR are defined respectively as stated below;

p n

Q D (t)= β1 ∑ [∑ a ik(t) – d j(t)]

2 + E D(t)

j=1 k=1

p n m

+ ρ∑ [ ∑ ∑ a ik(t) p ik(t) – q j(t)]

2 (7)

j=1 k=1 i=1

m n p

Q R (t) = β2 ∑ [∑ ∑ a ik(t) – r j(t)]

2 + ER(t) (8)

i=1 k=1 j=1

0< ε<1, 0< β1 β2, ρ<1;

ED(t) and ER(t) are the potential energy functions that involve

other kinds of the interactive forces among the particles in

FD and FR, respectively.

3.1.3 Stability:

Dynamic equations for path particle T k and link particle Ai

are defined respectively as stated below;

du k (t)/dt =φ1(t)+φ2(t) (9)

φ1(t) = - u k(t) + γ1 v1 (t) (9a)

φ2(t) =-[ε1 +ε2 dJ D(t)/d u k(t) + ε3dPD(t)/du k(t)

+ ε4 dQD(t)/d u k(t)] *

m

∑ [d u k(t) / dp ik(t)]2 (9b)

i=1

(OR)

du i (t)/dt = ψ1(t)+ ψ 2(t) (10)

ψ 1(t) = - u i(t) + γ2 v2(t) (10 a)

ψ 2(t) = -[ λ 1 + λ 2 dJ R(t)/d u i(t)+ λ 3 dPR(t)/d ui (t)

+ λ 4 dQR(t)/d u k(t) ] *

n p ∑ ∑ [d u i (t) / da ik(t)]

2 (10 b)

k=1 j=1

v1(t) and v2(t) is a piecewise linear function.

γ1, γ2 >1; 0< λ 1, λ 2, λ 3 ,λ 4, ε1, ε2, ε3 ,ε4,<1

dp ik(t)/dt = - ε1[ d u k(t) / dp ik(t)] - ε2[dJ D(t)/dp ik(t)]

-ε3[dPD(t)/dp ik(t)] - ε4[dQD (t)/dp ik(t)]

(11)

da ik(t)/dt = - λ 1[ d u i(t) / da ik(t) - λ 2[dJ R(t)/da ik(t)]

-λ 3[dPR(t)/ da ik(t)] - λ 4[dQR (t)/da ik(t)]

(12)

3.2 GP ALGORITHM:

Based on the above mathematical model the algorithm is

written as given below.

Input:

Maximum bandwidth ri , required bandwidth d

j ,

Maximum payoff q j

Output:

1. Initialization:

Figure1: GPAA to optimize bandwidth allocation-

a) Demand force- field FD for path particles. b) Resource force-field FR for link particles.



At time t=0;

Initiate bandwidth a ik(t) and price p ik(t)

2. calculate utility, potential energy functions as per the

Equations (1) to (8).

3. If

du k (t)/dt =0;

(Or) du i (t)/dt =0;

hold for every particle ,finish with success;

Else goto step 4.

4. Calculate du k(t)/dt and update u k(t)

calculate dui (t)/dt and update ui(t)

calculate da ik(t)/dt ,

a ik(t) = a ik(t -1) + da ik(t)/dt

calculate dp ik(t)/dt,

p ik(t) = p ik(t -1)+ dp ik(t)/dt

goto step 2.

A network with 7 nodes and 11 edges as exhibited in

Figure 2: is considered with the set of node pairs:

V ={(v1,v7),(v2,v6),(v4,v6),(v1,v3),(v1,v5)}

Figure 2: A network with 7 nodes and 11 edges

The communication bandwidth bij requested between given

set of (v=vi,vj) network node pairs are:

B ={15,25,21,20,17}

The virtual path sets are:

T18 ={(e8,e9),(e1,e2,e3),(e1,e11,e9),(e1,e2,e12,e9)}

T27 = {(e2, e3,e4),(e11,e10,e5),(e11,e9,e4),

(e2, e12,e10,e5), (e2,e12,e9,e4)}

T47 ={(e10,e5),(e9,e4)}

T16 ={(e7,e6),(e8,e10),(e1,e11,e10)}

T26 ={(e11,e10),(e2,e12,e10)}

And the set of links with maximum allowable bandwidths are

{e1=10 ;e2=8; e3=3; e4=18; e5=19; e6=8; e7=12; e8=15;

e9=4; e10=6;e11=15;e12=20}

The minimal price, bandwidth requested, maximal price,

maximum bandwidths of link are given as input, to the GPA

algorithm. The QOS index required by every virtual path

connection (VPC) is generated randomly within 0.5 to 1.5.

IV. MAX-MIN FAIRNESS ALGORITHM

The Max-Min fairness is computed via an iterative

procedure. The algorithm classifies every virtual session as

either completely utilized or not[3].

The allocated rate for session P is denoted by rp and the

allocated flow on network is[4];

Fa= ∑ δp(a) r p

pεP

δp(a)=1 if a is on path P and 0 otherwise.

r p>=0, for all p ε Pk

Fa<=Ca, for all a ε A.

Ca is capacity of arc a and r is vector of allocated rates.

4.1 MMF ALGORITHM :

Initial Conditions:

K=1,where k is the iterative index.

Capacity Fa =0; rate r p=0; P1=P; A

1=A;

1. nk

=number of paths ; p ε Pk

with δp(a)=1

2. rate vector r- k = min(Ca-Fa(k-1))/n

k

3. r p = r p(k-1)+ r- k for p ε Pk

Else

r p = r p(k-1)

4. Fa = ∑ δp(a) r p

pεP

5. A(k+1) = {a|Ca-Fa > 0}

6. P(k+1) = {p| δp(a)=0,for all ¢ A(k+1)}

7. k = k+1

8. If P k is empty, then stop; else goto 1.

The above algorithm terminates and finds the max-min

fairness vector r, if it exists, within k steps.

Initially all sessions are unsaturated, and their status change

from unsaturation to saturation. A session is allocated a rate r p

equal to minimum of the link bandwidth on its path. Initially

bandwidth allocated to the link is one third of the minimum

bandwidth of link on its session P. The algorithm checks the

saturation condition and updates the bandwidth till the session

is saturated. The algorithm terminates if all the sessions are

saturated.

For the network in figure 2: the bandwidth requested,

minimal price (rp) and the allowable bandwidth of link (Ca)

are given as input to MMF algorithm.

V. PERFORMANCE ANALYSIS

The Generalized particle approach (GPAA) and Max-Min

fairness algorithm is implemented with MATLAB 7.0.1.

The solution obtained is given below.

12

2

1 8 4

5

3 6 7

10

8

8 19

18 6

14 4

20

15 3



TABLE 1: BANDWIDTH ALLOCATION

Path

path set

Bandwidth allocation

GPAA MMF

T18

e8,e9 8.2500 4

e1,e2,e3

3.7125 3

e1,e11,e9 1.6706 4

e1,e2,e12,e9 1.3669 4

T27

e2,e3,e4

13.7500

3

e11,e9,e4

6.1875

4

e11,e10,e5 2.7844 6

e2,e12,e9,e4 1.2530 4

e2,e12,e10,e5 1.0252 6

T47

e9,e4 11.5500 4

e10,e5 9.4500 6

T26 e11,e10 9.3500 6

e2,e12,e10 7.6500 6

T16

e7,e6 11.0000 8

e8,e10 4.9500 6

e1,e11,e10 4.0500 6

In Table1: the performance comparisons of bandwidth

allocation for paths are given. Every path set in a path is

analyzed separately using both algorithms.. The amount of

bandwidth allocated is tabulated respectively. The requested

bandwidth is distributed among the path sets according to the

respective algorithms.

In figure 3: and 4: the bandwidth allocation for path 1 and

path2 are given. For path1 the bandwidth allocation using

Max-Min fairness algorithm gives fair allocation. For path 2

the bandwidth allocation using Max-Min fairness algorithm

doesn’t meet the requirement. The GPAA exhibits much better

performance than the MMF in terms of bandwidth allocation

for path2.

In figure 5: the success rates of both the algorithms are

compared. The success rate is computed as the difference

between requested bandwidth and allocated bandwidth. The

success rate of GPAA is better compared to Max-Min fairness

algorithm. For path 2 and 3 the success rate is very less in

Max-Min fairness algorithm.

Figure 3: Illustrates bandwidth allocation for path1, where fairness is

obtained in MMF and priority analysis is seen in GPAA.

1 2 3 4 50

2

4

6

8

10

12

14

path set no

bandw

idth

allocation (

Mbps)

bandwidth allocation for path 2

MMF

GPAA

Figure 4: Illustrates bandwidth allocation for path 2; where in GPAA

the need is met and in MMA the allocation is not satisfied.

1 2 3 4 50.4

0.5

0.6

0.7

0.8

0.9

1

path no

success r

ate

(%)

path no VS success rate

MMF

GPAA

Figure5: the comparison of GPAA and MMF algorithm with success

rate. In figure 6: the price allocation for every path set of path 3 is

analyzed. For shortest path the price allocated is low.



1 2 3 4 50.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

path set no

price b

oundary

PRICE ALLOCATION FOR PATH 2

Figure 6: The satisfactory degree of path 2 through GPAA.

Taking 100 no of particles of size 10*10; price distribution

and utility distribution are computed as shown in figure 7: and

8: respectively.

0

5

10

0

5

100.5

1

1.5

resource no

Price distribution of 10 * 10 particles

user no

pric

e di

strib

utio

n

Figure 7: The particles distribution within the price boundary.

0

5

10

0

5

101

2

3

utility

dis

trib

ution

Utility distribution of 10 *10 particles

resource nouser no

Figure 8: The total utility value for 10*10 particles

In figure 8: the utility distribution of all the particles at the

final stage of GPAA execution is illustrated.

The routing optimality can be determined with the shortest

path and the feasible bandwidth allocated for that.

In Table 2: The performance comparisons of shortest path,

success rate, net bandwidth allotted are given. It illustrates that

the algorithm GPAA exhibit better performance than the

MMF algorithm in terms of bandwidth allocation and success

rate, whereas they have approximately same shortest paths.

TABLE 2: OPTIMAL ANALYSIS OF PARAMETERS

Path

Requested

Bandwidth

Network

Bandwidth

Utilization

Success rate Shortest path

GPAA MMF GPAA MMF GPAA MMF

T18 15 15 15 100% 100% e8,

e9

e8,

e9

T27 25 25 23 100% 92%

e2,

e3,

e4

e11,

e9,

e4

T47

21

21

10

100%

47%%

e9,

e4

e10,

e5

T2 6

17

17

12

100%

70%

e11,

e10

e11,

e10

T16

20

20

20

100%

100%

e7,

e6

e7,

e6

VI. CONCLUSION

In this paper a generalized particle approach algorithm is

used to estimate the bandwidth allocation in ATM networks.

The performance evaluation using GPAA is compared with

MMF algorithm and found better in terms of success rate,

network bandwidth utilization, price allocation and quality of

service. In future, congestion factor, breakdown factor,

fairness factor can be incorporated in GPA model to optimize

the bandwidth allocation.

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Bandwidth allocation in ATM Networks using Novel Particle approach / Performance Analysis of ATM networks using modified particle approach

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