EMIS 8392 1

Lecture 16 - Chapter 8Lecture 16 - Chapter 8

Designing Mesh Designing Mesh NetworksNetworks

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Example #1Example #1

• InputsInputs– 4 Sites A, B, C, D4 Sites A, B, C, D– Traffic MatrixTraffic Matrix– Equip = 64K bpsEquip = 64K bps– TrunksTrunks– Utilization Utilization < < 50%50%

A BB CC DD

AA -- 3232 3232 --

BB 3232 -- -- 3232

CC 3232 -- -- 3232

DD -- 3232 3232 --

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Feasible Design #1 (Tree)

A

D

B

C

DemanDemandd

RoutinRoutingg

ValuValuee

A-B A-D-B 32

A-C A-D-C 32

B-A B-D-A 32

B-D B-D 32

C-A C-D-A 32

C-D C-D 32

D-B D-B 32

D-C D-C 32

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Link Loading (Utilization < 50%)

Link Loading

Trunks

A-D 64 bps 2

D-A 64 2

B-D 64 2

D-A 64 2

C-D 64 2

D-C 64 2

A

D

B

C

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Feasible Design #2 (Mesh)

Demand

Routing

Value

A-B A-B 32

A-C A-C 32

B-A B-A 32

B-D B-D 32

C-A C-A 32

C-D C-D 32

D-B D-B 32

D-C D-C 32

A

D

B

C

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Link Load (K bps)

Trunks

A-B 32 1

B-A 32 1

A-C 32 1

C-A 32 1

B-D 32 1

D-B 32 1

C-D 32 1

D-C 32 1

A

D

B

C

4 64Kbps trunks

Utilization = 50%

Final Design

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Optimization Models

Multicommodity Problem – let the commodity be represented by the origin nodes

Commodity A: From A to other nodes

Commodity B: From B to other nodes

Commodity C: From C to other nodes

Commodity D: From D to other nodes

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The 4 Commodities

A

D

B

C

A

D

B

C

A

D

B

C

A

D

B

C

{64}

{64}{64}

{64}

{-32}

{-32}

{-32}

{-32}

{-32}

{-32}

{-32}

{-32}

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Examine a Potential Solution

A

D

B

C

A

D

B

C

A

D

B

C

A

D

B

C

64 Kbps 32 Kbps

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A

D

B

C

How much equipment is required for this solution?

Total 64 K Trunks = 9

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AMPL Models

Node-Arc Model

Arc-Path Model

---------------------------------- NodeArc1L16.txt, dataNA1L16.txt, outNA1L16.txt

ArcPath1L16.txt, dataAP1L16.txt, outAP1L16.txt

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Solution – Both Models

A B C D

A 32 32

B 32 32

C 32 32

D 32 32

A

D

B

C

4 64K trunks

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New Traffic Matrix

A B C D

A 5 29

B 79 13 80

C 52 7 41

D 52 88 22

34

172

100

162

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See

NodeArc2L16.txt, dataNA2L16.txt, outNA2L16.txt

ArcPath2L16.txt, dataAP2L16.txt, outAP2L16.txt

Model and Data Files

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Solution Node-Arc Model

A

D

B

C

A

D

B

C

A

D

B

C

A

D

B

C34

27

552

725 8712

60

916

32

52

5

83

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Uses 11 Trunks

A

D

B

C

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Arc-Path Solution (same 11 Trunks)

A-C: 5 Path 4 A-C

A-D: 29 Path 25 A-D

B-A: 79 Path 7 B-A with 64

Path 8 B-C-A with 3

Path 9 B-D-A with 12

TOTAL 79