Fairness in a Static Wireless Network Marc GILG 1 Pascal LORENZ 1 - - PowerPoint PPT Presentation

Generalities The star network Algorithm Simulations Conclusion

Fairness in a Static Wireless Network

Marc GILG1 Pascal LORENZ1 Abderrahim MAKHLOUF2

1University of Haute-Alsace 2University of Pierre and Marie Curie

ResCom 2008

Generalities The star network Algorithm Simulations Conclusion

Outline

1

Generalities Network model Fairness

2

The star network Definition Fairness in a star network

3

Algorithm

4

Simulations The 8 star network A no-star network

5

Conclusion

Generalities The star network Algorithm Simulations Conclusion Network model

Ad-hoc networks Ad-hoc networks An Ad-Hoc network is made of wireless nodes which establish channel communications between themselves. A node can be in two states : transmission or reception. The limitation of radio communication implies that the communications of channel are limited in distance and that they act in half duplex mode.

Generalities The star network Algorithm Simulations Conclusion Network model

Network model Network Model the network is packet-switched the nodes are in half-duplex mode

• nly nodes in some distance are receiving the packet

the time is divided in time slots packets are sent in a time slot

Generalities The star network Algorithm Simulations Conclusion Fairness

Fairness Definition The fairness index of a shared resource xi is given by f(xi) = n

i=1 xi

2 n n

i=1 x2 i

(1) A network is fair if f(x) = 1.

Generalities The star network Algorithm Simulations Conclusion Fairness

Fairness Definition The fairness index of a shared resource xi is given by f(xi) = n

i=1 xi

2 n n

i=1 x2 i

(1) A network is fair if f(x) = 1. Remark for Ad-Hoc networks A node with a high degree of connectivity in transmission will interfere with a high number of nodes. One of the consequences of this is that each node will not have the same transmission and reception rate. The fairness of an Ad-Hoc network is not obvious.

Generalities The star network Algorithm Simulations Conclusion Definition

Definition of a star network Definition The star network SNn is composed of n + 1 nodes {X0, X1, . . . , Xn} where {X1, . . . , Xn} are neighbors of the node X0, and there is no connexion between Xi, Xj for i, j > 0.

Generalities The star network Algorithm Simulations Conclusion Definition

Definition of a star network Definition The star network SNn is composed of n + 1 nodes {X0, X1, . . . , Xn} where {X1, . . . , Xn} are neighbors of the node X0, and there is no connexion between Xi, Xj for i, j > 0. 4-star network graph X0 X1 X2 X3 X4

Generalities The star network Algorithm Simulations Conclusion Fairness in a star network

Reception rate in a star network. Notations The following notations will be used : Let xi be the reception rate of node Xi Let Si

j be the transmission rate of node Xj which is a

neighbor of node Xi

Generalities The star network Algorithm Simulations Conclusion Fairness in a star network

Reception rate in a star network. Notations The following notations will be used : Let xi be the reception rate of node Xi Let Si

j be the transmission rate of node Xj which is a

neighbor of node Xi Reception rate We have xi = S0 for 1 ≤ i ≤ n We have x0 = n

i=1 S0 i

Generalities The star network Algorithm Simulations Conclusion Fairness in a star network

Fairness in a star network Lemma For a star network SNn, the fairness for the reception rates hold

• nly and only if :

S0 −

n

• i=1

S0

i = 0

(2)

Generalities The star network Algorithm Simulations Conclusion

Algorithm Algorithm

1

computes the sum of the neighbors transmission rates Ai

2

compares the sum Ai to the node Yi transmission rate Si.

3

if Si − Ai > s then reduce Si, if Sj becomes negative, then set it to 0.

4

if Si − Ai < s then increase Si if it is possible.

5

if Sj = 0 for a long time, then increase it.

6

go to step 1

Generalities The star network Algorithm Simulations Conclusion The 8 star network

Fairness of a SN8 star network

0.41 0.415 0.42 0.425 0.43 0.435 50 100 150 200 250 300 350 400 450 500 Fairness index Time Slots ’ex.txt’

Generalities The star network Algorithm Simulations Conclusion The 8 star network

Rate difference to fairness

• 16
• 14
• 12
• 10
• 8
• 6
• 4
• 2

50 100 150 200 250 300 350 400 450 500 Diffrence rate to fairness Time Slots ’ex-1.txt’

Generalities The star network Algorithm Simulations Conclusion The 8 star network

Fairness of a SN8 star network with modified access algorithm

0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.5 0.51 50 100 150 200 250 300 350 400 450 500 550 Fairness index Time Slots ’ex.txt’

Generalities The star network Algorithm Simulations Conclusion The 8 star network

Rate difference to fairness

• 2.5
• 2
• 1.5
• 1
• 0.5

0.5 1 1.5 2 50 100 150 200 250 300 350 400 450 500 550 Diffrence rate to fairness Time Slots ’ex-1.txt’

Generalities The star network Algorithm Simulations Conclusion A no-star network

Network topology X0 X2 X6 X3 X1 X5 X4

Generalities The star network Algorithm Simulations Conclusion A no-star network

Fairness of a no-star network

0.66 0.68 0.7 0.72 0.74 0.76 0.78 0.8 20 40 60 80 100 120 140 160 Fairness index Time Slots ’ex.txt’

Generalities The star network Algorithm Simulations Conclusion A no-star network

Rate difference to fairness

15 20 25 30 35 40 45 50 55 60 65 20 40 60 80 100 120 140 160 Diffrence rate to fairness Time Slots ’ex-1.txt’

Generalities The star network Algorithm Simulations Conclusion A no-star network

Fairness of a no star network with modified access algorithm

0.64 0.66 0.68 0.7 0.72 0.74 0.76 0.78 0.8 20 40 60 80 100 120 140 160 Fairness index Time Slots ’ex.txt’

Generalities The star network Algorithm Simulations Conclusion A no-star network

Rate difference to fairness

37.5 38 38.5 39 39.5 40 40.5 20 40 60 80 100 120 140 160 Diffrence rate to fairness Time Slots ’ex-1.txt’

Generalities The star network Algorithm Simulations Conclusion

Conclusion Conclusion We study the fairness of a Ad-Hoc network A N-star network was introduced. An expression of transmission rates was established to solve the fairness problem. An algorithm was given to get the fairness in a star network. Simulations was done for star networks and no star networks.

Generalities The star network Algorithm Simulations Conclusion

Conclusion Conclusion We study the fairness of a Ad-Hoc network A N-star network was introduced. An expression of transmission rates was established to solve the fairness problem. An algorithm was given to get the fairness in a star network. Simulations was done for star networks and no star networks. Further works In some further work, we propose to study multiple star network to approach a general Ad-Hoc network.