A Routing Algorithm for Wireless Mesh Networks

A Routing Algorithm for Wireless Mesh Networks

Problem Formulation

Available channels

C0

C1

C2

C3

7

4

5

3

6

0

1

2

802.11 card

Problem Formulation

Available channels

C0

C1

C2

C3

7

4

5

3

6

0

1

2

R

Problem Formulation

Available channels

C0

C1

C2

C3(2.1, 36)

(2.3, 48) (2.5, 37)

(4, 44)

7

4

5

3

6

0

1

2

(1.9, 15)

(3.7, 14)

(1.9, 35) (2, 27)

(3.7, 14)

(2, 35)

Expected transmission time (ETT): expected time to transmit a packet of fixed size through the link.

Data rate (R)

Problem Formulation

Available channels

C0

C1

C2

C3(2.1, 36)

(2.3, 48) (2.5, 37)

(4, 44)

7

4

5

3

6

0

1

2

(1.9, 15)

(3.7, 14)

(1.9, 35) (2, 27)

(3.7, 14)

(2, 35)

Routing Problem: find the optimal path from a source node to a destination node

Expected transmission time (ETT)

Data rate (R)

Related Works

1- Shortest hop path.

2- Shortest Expected Transmission Count (ETX) path [1].

3- Widest data rate path [2].

4- Shortest Weighted Cumulative Expected Transmission Time (WCETT) path[3].

Shortest Hop Path

(2.1, 36)(2.3, 48) (2.5, 37)

(4, 44)

7

4

5

3

6

0

1

2

(1.9, 15)

(3.7, 14)

(1.9, 35) (2, 27)

(3.7, 14)

(2, 35)

Problems•Does not consider end-to-end delay•May suffer of intra-flow interference

Shortest Expected Transmission Count Path[1]

Problems•Does not consider the data rate of the links•Does not consider end-to-end delay

7

4

5

3

6

0

1

21

4 54

3 43

2

1 1

Number of MAC re-transmissions needed to send a frame from 0 to 7

Widest Data Rate Path [2]

(2.1, 36)(2.3, 48) (2.5, 37)

(4, 44)

7

4

5

3

6

0

1

2

(1.9, 15)

(3.7, 14)

(1.9, 35) (2, 27)

(3.7, 14)

(2, 35)

Problems•May suffer of intra-flow interference•Does not consider end-to-end delay

Expected transmission time (ETT)

Data rate (R)

Weighted Cumulative Expected Transmission Time (WCETT) [3]

Tries to minimize the cumulative ETT and the intra-flow interference

(2.1, 36)(2.3, 48) (2.5, 37)

(4, 44)

7

4

5

3

6

0

1

2

(1.9, 15)

(3.7, 14)

(1.9, 35) (2, 27)

(3.7, 14)

(2, 35)

Weighted Cumulative Expected Transmission Time (WCETT)

(2.1, 36)(2.3, 48) (2.5, 37)

(4, 44)

7

4

5

3

6

0

1

2

(1.9, 15)

(3.7, 14)

(1.9, 35) (2, 27)

(3.7, 14)

(2, 35)

cETT(P1) = 2.1 + 2.3 + 2.5 + 3.7 = 10.6 ms ; MAX{2.1, (2.3+2.5=4.8), 3.7}= 4.8;

WCETT(P1) = (1-B)*10.6 + B*4.8 = 7.7 (B=0.5)

Available channels

C0

C1

C2

C3


(2.1, 36)(2.3, 48) (2.5, 37)

(4, 44)

7

4

5

3

6

0

1

2

(1.9, 15)

(3.7, 14)

(1.9, 35) (2, 27)

(3.7, 14)

(2, 35)

cETT(P1) = 2.1 + 2.3 + 2.5 + 3.7 = 10.6 ms ; MAX{2.1, 4.8, 3.7}= 4.8;WCETT(P1) = (1-B)*10.6 + B*4.8 = 7.7 (B=0.5)

cETT(P2) = 2.1 + 2.3 + 2.5 + 3.7 = 10.6 ms ; MAX{2.1, 8.5}= 8.5;WCETT(P2) = (1-B)*10.6 + B*8.5 = 9.5

Available channels

C0

C1

C2

C3


(2.1, 36)(2.3, 48) (2.5, 37)

(4, 44)

7

4

5

3

6

0

1

2

(1.9, 15)

(3.7, 14)

(1.9, 35) (2, 27)

(3.7, 14)

(2, 35)

cETT(P1) = 2.1 + 2.3 + 2.5 + 3.7 = 10.6 ms ; MAX{2.1, 4.8, 3.7}= 4.8;WCETT(P1) = (1-B)*10.6 + B*4.8 = 7.7 (B=0.5)

cETT(P2) = 2.1 + 2.3 + 2.5 + 3.7 = 10.6 ms ; MAX{2.1, 8.5}= 8.5;WCETT(P2) = (1-B)*10.6 + B*8.5 = 9.5

cETT(P3) = 4 + 1.9 + 2 + 2 = 9.9 ms ; MAX{6, 1.9, 2}= 6;WCETT(P3) = (1-B)*9.9 + B*6 = 7.95

Available channels

C0

C1

C2

C3

ProposalA genetic algorithm [8, 9, 10] that optimizes:

1. End-to-end delay (cumulative ETT)

2. Number of interfering links

3. Data rate along the path

(2.1, 36)(2.3, 48) (2.5, 37)

(4, 44)

7

4

5

3

6

0

1

2

(1.9, 15)

(3.7, 14)

(1.9, 35) (2, 27)

(3.7, 14)

(2, 35)

1- End-to-end delay = 4 + 1.9 + 2 + 2 = 9.9 ms2- Number of interfering links = 03- Data Rate along the path = Min {44, 35, 27, 35} = 27 Mbps

Genetic Algorithm

Coding a solution of the problem (i.e., a path from source node to destination node) as a linear string. Priority-based encoding [4, 5]:

(2.1, 36)(2.3, 48) (2.5, 37)

(4, 44)

7

4

5

3

6

0

1

2

(1.9, 15)

(3.7, 14)

(1.9, 35) (2, 27)

(3.7, 14)

(2, 35)

5 3 0 2 2 7 4 5

0 1 2 3 4 5 6 7Node ID

Priority

0 7 6 5 4

t=0;

Initialize P(t);

do{

Evaluate P(t);

Compute fitness (P);

P(t+1) = Select individuals for crossover;

P(t+1) = Perform crossover of P(t+1);

t = t+1;

} while stop criterion is not reached

Proposed Genetic Algorithm


t=0;

Initialize P(t);

do{

Evaluate P(t);




t = t+1;


P ...

1 3 4

3 2 2

5 4 3

4 3 1

5 4 3

Initialize P


P ...

1 3 4

3 2 2

5 4 3

4 3 1

5 4 3

t=0;

Initialize P(t);

do{

Evaluate P(t);




t = t+1;


Compute the objective functions of each solution

Evaluate P


P ...

1 3 4

3 2 2

5 4 3

4 3 1

5 4 3

t=0;

Initialize P(t);

do{

Evaluate P(t);




t = t+1;


Based on the objective functions, compute fitness

Compute Fitness

The fitness of a solution is a measure that quantifies how good the solution is.


P ...

1 3 4

3 2 2

5 4 3

4 3 1

5 4 3

t=0;

Initialize P(t);

do{

Evaluate P(t);




t = t+1;


Selection according to fitness

.2 2 3

1 3 4

3 1 3

..

P(t+1)


t=0;

Initialize P(t);

do{

Evaluate P(t);




t = t+1;


Perform crossover

.2 2 3

1 3 4

3 1 3

.. .1 3 3

2 2 4

3 1 5

..Crossover

P(t+1)

P(t+1)

Multi-objective Problems

A problem with two objective functions.

End-to-end delay

# of interfering links



End-to-end delay




End-to-end delay




End-to-end delay




End-to-end delay



Non-dominated (optimal) solutionsEnd-to-end delay



Fitness computation – SPEA [6]End-to-end delay





3




3

5




3

5

5




3

5

52




3

5

52

3 + 5 + |P|




3

5

52

18

5+5+10




3

5

52

18

20

5+10




3

5

52

18

20

15

5+5+3+10




3

5

52

18

20

15

23

5+5+2+10




3

5

52

18

20

15

23

22

3+5+5+2+10




3

5

52

18

20

15

23

22

25

Work in Progress

•Some preliminary ‘runs’ in random networks to test the algorithm.

•The distributed protocol is being developed in CNET[7].

References1. D. De Couto, D. Aguayo, J. Bicket, R. Morris. High-throughput path metric for multi-

hop wireless routing, in 9th International Conference on Mobile Computing and Networking (Mobicom 2003), September 2003, San Diego, California - USA.

2. L. Iannone, K. Kabassanow, S. Fdida, Evaluation of cross-layer rate-aware routing in a wireless mesh network test bed, Eurasip journal on wireless communications and networking, vol 2007, Article Id 86510, 2007.

3. R. Draves, J. Padhye, B. Zill, Routing in multi-radio, multi-hop wireless mesh networks, in: 10th International Conference on Mobile Computing and Networking (Mobicom 2004), September 2004, Philadelphia, PA – USA.

4. M. Gen, R. Cheng, D. Wang, Genetic algorithms for solving shortest path problems, Proc. IEEE International Conference on Evolutionary Computation, pp. 401-406, 1997.

5. M. Gen, L. Lin, Multiobjective hybrid genetic algorithm for bicriteria network design problem, 8th Asia Pacific Symposium on Intelligent and Evolutionary Systems, December 2004, Australia.

6. E. Zitzler, L. Thiele, Multiobjective evolutionary algorithms: a comparative case study and the strength pareto approach. IEEE Trans. on Evolutionary Computation 3, 1999, pp. 257-271.

7. http://www.csse.uwa.edu.au/cnet3

8. C. Coello, D. Van Veldhuizen, G. Lamont, Evolutionary Algorithms for Solving Multi-Objective Problems, Kluwer Academic Publishers; ISBN: 0306467623, May 2002.

9. http://www.waseda.jp/sem-genlab/prof_gen.html

10. http://www.lania.mx/~ccoello/EMOO/


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Multi-objective Optimization

Weighted Mapping Cross-over

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A Routing Algorithm for Wireless Mesh Networks