1

Min Power Routing in Wireless Networks

Hai Jiang and Zhijun Huang

March 22, 2001

CS215 Project Report:

2

Outline

• Introduction

• Previous Work

• Problem Formulation

• Modified Bellman-Ford Algorithm

• Simulation Results

• Conclusion

3

Introduction

• Why Min Power in Wireless Network?

1. Limited Energy : Battery Operated Network

2. Interference Reduction and Spectrum Reuse

• How to minimize power consumption?

1. Physical Level:

Low-power CPU/Display

High-capacity Battery

=> Little Room for further reduction

2. Higher Level: Power-aware protocols

MAC Layer

Network Layer *

…

4

Previous Work

• Singh and Raghavendra (98)

1/Eremain : reflect node’s reluctance to forward packets

Non-localized Dijkstra’s Algorithm: Shortest Weighted Path

• Rodoplu and Meng (98)

Power consumption: u(d)= d4 2 108 Non-localized Bellman-Ford Algorithm: Shortest Path

• Gomez etc (99)

Power cost function: Pi * f(Bi)

• Heizelman and Chandrakasan (00)

Radio Model: Etx (k, d) = Eelec * k + Eamp * k * d2

Hierarchical Clustering

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Existing Problem

• Network with minhop algorithm

Critical Node, N6, expends power faster

=> die first

Problem: how to balance power consumption?

• How to consider hop-count constraint?

1

0

2

34

5 6

0

6

Radio Model

• Transceiver/Receiver Circuity

Eelec = 50nJ/bit

• Transmit Amplifier

Eamp = 100pJ/bit/m2

• Transmit

Etx (k, d) = Eelec * k + Eamp * k * d2

• Receive

Erx (k) = Eelec * k

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Problem Formulation• Each Node : Remaining Energy Ei

Each Edge : Transmission Energy Pi

• Object:

For each path, Min

such that, Ei > Emin and Hop-count < M

=>

Min , such that Hop-count < M

i Ei

Pi

i EEi

Pi

min

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Modified Bellman-Ford Algorithm

B ellm an-Ford

1. In itia lize(G ,s)2 . fo r i = 1 to V [G ] -13 . do fo r each edge (u , v) in E [G ]4 . do if d [v] > d [u ] + w ( u , v )5 . then d [v] = d [u ] + w ( u ,v )6 . P [v] = u7 . re tu rn T R U E

B ellm an-Ford w / m ax hop constra in t

1 . In itia lize(G ,s)2 . fo r i = 1 to V [G ] -13 . do fo r each edge (u , v) in E [G ]4 . do fo r each entry k in node v5 . if d [v,k] > d [u , k-1 ] + w( u , v )6 . then d [v,k] = d [u , k-1 ] + w( u ,v )7 . P [v] = u8. re turn TR U E

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Modified Bellman-Ford Algorithmhop # from

sourcepow ercos t

pa ren tnode

0

1

2

3

. .

.

. .

.

. .

.

M -4

M -1

M -2

M -3

in fin ity 4

in fin ity

in fin ity

in fin ity

in fin ity

in fin ity

in fin ity

in fin ity

0

1

2 1

3

M -4

M -3

M -2

M -1

hop # fromsource

pow ercos t

pa ren tnode

0

1

2

3

. .

.

. .

.

. .

.

M -4

M -1

M -2

M -3

in fin ity

in fin ity

in fin ity

in fin ity 1

in fin ity

in fin ity

in fin ity

in fin ity

0

1 0

2

3

M -4

M -3

M -2

M -1

node 1 node 2

W 12 =3

node 0src

W 01 =1

W 12 =3

node 3

node 4

node 5

2

4

67

3

8

10

4

3

5

10

hop # fromsource

pow ercos t

pa ren tnode

0

1

2

3

. .

.

. .

.

. .

.

M -4

M -1

M -2

M -3

in fin ity 4

in fin ity

in fin ity

in fin ity

in fin ity

in fin ity

in fin ity

in fin ity

0

1

2 1

3

M -4

M -3

M -2

M -1

hop # fromsource

pow ercos t

pa ren tnode

0

1

2

3

. .

.

. .

.

. .

.

M -4

M -1

M -2

M -3

in fin ity

in fin ity

in fin ity

in fin ity 1

in fin ity

in fin ity

in fin ity

in fin ity

0

1 0

2

3

M -4

M -3

M -2

M -1

node 1 node 2

W 12 =3

W 12 =3

w 21 = 4

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Simulation Settings

• Method

Simulator : written in C;

Algorithms: Min-hop

Min-power w/ Hop Constraint

Min-power w/o Hop Constraint

• Parameters

RadioRange : 100 m

Network Size : 600 m x 600 m

Node Number : 100 - 200

Max Hop : 5, 10, 20, No Constraint

Time Steps : 2000 rounds

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Min-power prolongs network lifetime!

Number of Alive Nodes (Total 100 Nodes)

60

65

70

75

80

85

90

95

100

0 500 1000 1500

Time Step (Rounds)

Aliv

e N

od

es minhop

power_5h

power_10h

power_20h

power

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Number of Alive Nodes (Total 200 Nodes)

100

120

140

160

180

200

0 500 1000 1500

Time Step (round)

Aliv

e N

od

es power_5h

power_10h

power_20h

power

minhop

Network Density increase => Min-power is more effective

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Critical nodes in Minhop die fast => Minhop is the worst !

Successful Connections every 20 rounds (total 100 nodes)

0

50

100

150

200

20 420 820 1220 1620

Time Step (rounds)

#Con

nect

ions

power_5h

power_10h

power_20h

power

minhop

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Network Density increase => Min-power is more effective

Successful Connections every 20 rounds (total 200 nodes)

0

50

100

150

200

20 420 820 1220 1620

Time Step (rounds)

#Con

nect

ions

power_5h

power_10h

power_20h

power

minhop

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Original Network

Minhop: 200_Node Network(Time = 0)

0

100

200

300

400

500

600

0 100 200 300 400 500 600

X

Y

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Minhop v.s. Minpower at Time = 1000

Minpower: 200-Node Network (Time = 1000)200 Alive Nodes

0

100

200

300

400

500

600

0 100 200 300 400 500 600

XY

Minhop: 200-Node Network(Time=1000)148 Alive Nodes

0

100

200

300

400

500

600

0 100 200 300 400 500 600

X

Y

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Minhop v.s. Minpower at Time = 2000

Minpower: 200-node Network (Time = 2000)146 Alive Nodes

0

100

200

300

400

500

600

700

0 100 200 300 400 500 600 700

X

Minhop: 200-Node Network (Time = 2000)131 Alive Nodes

0

100

200

300

400

500

600

700

0 100 200 300 400 500 600 700

X

y

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Minhop and Minpower w/o constraint : Consume Similar Energy

Total Energy Consumed (Total 100 Nodes)

0

5000

10000

15000

20000

25000

30000

35000

40000

0 500 1000 1500

Time Steps (round)

En

erg

y (m

J)power_5h

power_10h

power_20h

power

minhop

20

More node died in Minhop => Minhop Consume Less Energy at later time

Total Energy Consumed (total 200 nodes)

0

1000020000

3000040000

5000060000

7000080000

90000

0 500 1000 1500

Time Steps (round)

En

erg

y (m

J)power_5h

power_10h

power_20h

power

minhop

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Conclusion

• Develop min power routing algorithm with hop constraint

• Network lifetime prolongs in this algorithm

• Energy savings are greater in Densor networks

• Next improvement: try to do simulation in GlomoSim