LABORATOIRE DE RECHERCHE EN

I NFORMAT I QUE

Energy and Routing Optimization in Wireless Sensor Networks

Joseph Rahmé Advisors:Aline C.Viana and Khaldoun Al Agha

hipercom.lri.fr

Introduction

Energy is a scarce resource in sensor networks.It is thus important to opti-

mize energy consumption in order to extend the life of the sensor network.

We introduce a model that quantiﬁes per-state energy consumption (Recep-

tion,Sleep,Transmission and Overhearing),and approximates the remaining

energy of a node.

Our cost functions use the information about the remaining energy to calcu-

late energy-efﬁcient routes.

The Energy Model

We use our model,represented by the following formulas,to quantify the

energy consumed for each node state:

(k) = I

k

[

k

+

2

2

(

2

6

ln(

e

2

k

e

2

k

1

) +

1

2e

2

2

k

+

1

3e

3

2

k

)]

r

(k) = I

k

[

k

+

2

2

(ln(

e

2

(L

k

)

e

2

k

e

2

(L

k

)

1

)

1

2

(

1

e

2

2

L

1

e

2

(L

k

)

)

1

3

(

1

e

3

2

L

1

e

3

2

(L

k

)

)]

Where

(k);

r

(k) are the energy consumed per state with and without recovery,re-

spectively.I

k

represents the current value during state duration

k

L is the total duration of a node state including idle time, is the rate at

which the active charges are replenished at the battery’s electrode surface

Our Cost Functions

Our approach consists of four cost functions,and takes the following criteria

into account:

First Cost Function

Goal:minimize the end-to-end energy needed to route a packet between a

source and a destination

E

1

(k;i) = E

TX

+

X

n

1

2N

1

(k)

E

RX

+

X

n

2

2N

2

(k)

E

I

(1)

,where

• N

1

(k) is the set of 1-hop neighbors of node k;

• N

2

(k) is the set of 2-hop neighbors of node k;

• E

TX

,E

RX

and E

I

are the energy consumed for a transmission,recep-

tion and overhearing respectively.

Second Cost Function

Goal:Find a route in which intermediate nodes,between a source and a

destination,possess high remaining energy:

E

2

(k;i) = minf(E

r

(k) E

TX

);

min

n

1

2N

1

(k)

(E

r

(n

1

) E

RX

)

min

n

2

2N

2

(k)

(E

r

(n

2

) E

I

)g

(2)

,where

• E

r

(k) is the remaining energy of node k;

• E

r

(n

1

),E

r

(n

2

) are the remaining energy of the 1-hop and 2-hop neigh-

bors affected by the transmission of node k

Third Cost Function

Goal:Find a path with intermediate nodes that have high remaining energy

E

3

(k;i) = min f

E

r

(k)

E

TX

;min

n

1

2N

1

(k)

E

r

(n

1

)

E

RX

;min

n

2

2N

2

(k)

E

r

(n

2

)

E

I

g

(3)

Fourth Cost Function

Goal:Optimize the ﬁrst cost function by considering the remaining energy of

the neighbors

E

4

(k;i) = c

f

E

1

(k;i)

E

r

(i)

;8i 2 N

1

(k) (4)

Results

Illustration of the First and Fourth Cost Functions

Conclusion and Future Work

Simulation results demonstrate that the fourth cost function signiﬁ-

cantly increases the network’s lifetime.This is expected since it con-

siders both the remaining energy and the end-to-end energy consumed.

We next plan to implement the fourth cost functions as a routing metric,

using the OLSR routing protocol,in order to make the routing protocol

energy efﬁcient.

1

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