Wireless Sensor Networks:
Minimum-energy communication
Mario Čagalj
supervised by prof. Jean-Pierre Hubaux (EPFL-DSC-ICA)
and prof. Christian Enz (EPFL-DE-LEG, CSEM)
mario.cagalj@epfl.ch
Wireless Sensor Networks
 Large number of heterogeneous sensor devices

Ad Hoc Network
 Sophisticated sensor devices

communication, processing, memory capabilities
Wireless Sensor Networks: Minimum-energy communication
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Project Goals
 Devise a set communication mechanisms s.t.
they
Minimize energy consumption
 Maximize network nodes’ lifetimes
 Distribute energy load evenly throughout a network
 Are scalable (distributed)

Wireless Sensor Networks: Minimum-energy communication
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4
Minimum-energy unicast
Wireless Sensor Networks: Minimum-energy communication
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Unicast communication model
 Link-based model
each link weighed
 how to chose a weight?
B

 Power-Aware Metric [Chang00]

1
C
1
1
A
1
E
1
D
Maximize nodes’ lifetimes
include remaining battery energy (Ei)

B
x   x2
c  (e  r ) 1  E i 
ij ij 0  E 
i

e  energy spent in transmitting
ij
r  energy spent in receiving
0
cBC
C
cAB
A
Wireless Sensor Networks: Minimum-energy communication
cCD
cAE
E
cED
D
6
Unicast problem description
 Definitions
undirected graph G = (N, L)
 links are weighed by costs
 the path A-B-C-D is a minimum cost path
from node A to node D, which is the onehop neighbour of the sink node
 minimum costs at node A are total costs
aggregated along minimum cost paths

D
C
 Minimum cost topology
Minimum Energy Networks [Rodoplu99]
 optimal spanning tree rooted at one-hop
neighbors of the sink node
 each node considers only its closest
neighbors - minimum neighborhood

Wireless Sensor Networks: Minimum-energy communication
B
A
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Building minimum cost topology
 Minimum neighborhood
notation: N i - minimum neighborhood of node i  N
 P1: minimum number of nodes enough to ensure connectivity
 P2: no node  N falls into the relay space of any other node  N
i
i

 Finding a minimum neighborhood
nodes maintain a matrix of mutual link costs among neighboring
nodes (cost matrix)
 the cost matrix defines a subgraph H on the network graph G

1

 c21
c
 31
 c41
c
 51
c12
c13
c14
1
c23
c24
c32
1
c34
c42
c43
1
c52
c53
c54
c15 

c25 
c35 

c45 
1 
C
A
Wireless Sensor Networks: Minimum-energy communication
B
Finding minimum neighborhood
8
 We apply shortest path algorithm to find optimal
spanning tree rooted at the given node
subgraph H
 Theorem 1: The nodes that immediately follow the root
node constitute the minimum neighborhood of the root
node
 Theorem 2: The minimum cost routes are contained in
the minimum neighborhood
 Each node considers just its min. neighborhood
Wireless Sensor Networks: Minimum-energy communication
Distributed algorithm
 Each node maintains forwarding table

E.g. [originator ¦ next hop ¦ cost ¦ distance]
 Phase 1:
 find minimum neighborhood
 Phase 2:
 each node sends its minimum cost to it neighbors
 upon receiving min. cost update forwarding table
 Eventually the minimum cost topology is built
Wireless Sensor Networks: Minimum-energy communication
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An example of data routing

Different routing policies

different packet priorities

Properties

energy efficiency

nuglets [Butt01]

scalability

packets flow toward nodes with

increased fault-tolerance
lower costs
Wireless Sensor Networks: Minimum-energy communication
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Minimum-energy broadcast
Wireless Sensor Networks: Minimum-energy communication
Broadcast communication model
b
Eab
Eac
a


c

Omnidirectional antennas
By transmitting at the power level max{Eab,Eac} node a
can reach both node b and node c by a single
transmission
Wireless Multicast Advantage (WMA) [Wieselthier et al.]
Trade-off between the spent energy and
the number of newly reached nodes
Power-aware metric



Ebc


12
include remaining battery energy (Ei)
embed WMA (ej/Nj)
b
Every node j is assigned a broadcast cost c j
X2
 
X1 E j
e j  
Ej 

b
cj 
X3
U ( j)
N j  node j ' s neighbourh ood
Oij  overlappin g set of nodes i and j
U j  node j ' s uncovered set
Wireless Sensor Networks: Minimum-energy communication
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Broadcast cover problem (BCP)
 Set cover problem
 F  {S ,..., S m}, S j  N
1
 Covering C  F s.t. N   j : S
Example:
j
C
S
S1
j
S3
j
C1={S1, S2, S3}
 cost (S j ) associated with S j  C
 cost (C )   j : S
S2
S4
cost (S )
C
j
S5
C2={S3, S4, S5}
C1 , cost (C1 )  cost (C2 )
C2 , cost (C1 )  cost (C2 )
C*= 
 Find cover C *  arg min {cost (Ci )}
 BCP
C
i
Greedy algorithm:
Sj Nj
at each iteration add the set Sj that minimizes
ratio cost(Sj)/(#newly covered nodes)
 cost ( S j )  e j
 cost (C )  broadcast cover cost
 Find cover that minimizes broadcast cover cost
 The set of forwarding nodes belong to a tree rooted at originator
Wireless Sensor Networks: Minimum-energy communication
X2
 Ej 

e Xj 1 
E 
 j
c bj 
X3
U ( j)
Distributed algorithm for BCP
 Phase 1:
 learn neighborhoods (overlapping sets)
 Phase 2: (upon receiving a bcast msg)
1: if neighbors covered HALT
2: recalculate the broadcast cost
3: wait for a random time before re-broadcast
4: if receive duplicate msg in the mean time goto 1:
 Random time calculation
 cib 
 random number distributed uniformly between 0 and  b   
 c0 
Wireless Sensor Networks: Minimum-energy communication
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Simulations
 GloMoSim [UCLA]

scalable simulation environment for wireless and wired networks
average node degree ~ 6
average node degree ~ 12
Wireless Sensor Networks: Minimum-energy communication
Simulation results (1/2)
Wireless Sensor Networks: Minimum-energy communication
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Simulation results (2/2)
Wireless Sensor Networks: Minimum-energy communication
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Conclusion and future work
 Power-Aware Metrics

trade-off between residual battery capacity and transmission
power are necessary
 Scalability

each node executes a simple localized algorithm
 Unicast communication

link based model
 Broadcast communication


node based model
Can we do better by exploiting WMA properly?
Wireless Sensor Networks: Minimum-energy communication
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19
Minimum-energy broadcast
b
Pab
a


c
if (Pac – Pab < Pbc) then transmit at Pac
As the number of destination increases the complexity of this formulation increases rapidly.
Requirement for distributed algorithm.
- forwarding nodes
What are good criteria for selecting forwarding nodes?





Pac

Propagation model: Pab  kdab
,   [2..6]
Omnidirectional antennas
Wireless Multicast Advantage (WMA) [Wieselthier et al.]
Minimum-energy broadcast:
Challenges:


Pbc




Broadcast Incremental Power (BIP) [Wieselthier et al.]
Add a node at minimum additional cost
Centralized
Cost (BIP) <= Cost (MST)


2
8
4
9
1
10
5
Improvements?

4
2
1
Take MST as a reference
Branch exchange heuristic…
… to embed WMA in MST
2
6
8
5
5
4
7
3
Wireless Sensor Networks: Minimum-energy communication
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