1. Xiaobing Wu, Guihai Chen and Sajal K. Das
Avoiding Energy Holes in Wireless Sensor Network with Nonuniform Node Distribution
Xiaobing Wu, Guihai Chen and Sajal K. Das
Parallel and Distributed Systems 2008

2. Outline
Introduction
Energy Hole Problem
Analysis of the Nonuniform Node Distribution Strategy
Impossibility of Balanced Energy Depletion
Possibility of Subbalanced Energy Depletion
Novel Nonuniform Node Distribution Strategy and q-switch Routing
Simulation

3. Energy Hole Problem in Sensor Network
Unbalanced energy utilization
Some nodes deplete their power more quickly
Sink
Sink
Sink
Energy hole
Energy hole
Energy hole

4. Related Work
Approaches that have been proposed to mitigate the energy hole problem
Sink mobility
Multiple sinks
Hierarchical deployment
Clustering
Non-uniform initial energy budgets
Non-uniform node distribution
The objective of this paper

5. Contributions of this paper
Prove that balanced energy utilization is impossible for many-to-one traffic pattern.
Prove that subbalanced energy utilization is possible
Propose a nonuniform node deployment strategy
Propose a q-switch routing

6. Assumptions and Network Model
Assume that all the nodes are deployed in a circular area with a radius R
The width of each corona
is 1 unit length
Maximum transmission range
Nodes belonging to a corona
will forward data
generated by both themselves
and nodes from coronas

7. Assumptions and Network Model
Assume that each sensor node generates and sends L bits of data per unit time
Regular reporting
The initial energy of each sensor is 
Sending 1 bit costs e1 units of energy
Receiving 1 bit costs e2 units of energy

8. Energy Consumption Ni : the number of nodes in Ci
Ei: the energy consumed per time unit
by nodes in Ci

9. Balanced v.s. Subbalanced

10. Impossibility of Balanced Energy Depletion
Proof
If balanced energy depletion is achieved, then
Average energy consumption per node

11. Impossibility of Balanced Energy Depletion

12. Subbalanced Energy Depletion
Proof: If the network achieves the subbalanced energy depletion
Average energy consumption per node

13. Subbalanced Energy Depletion

14. Subbalanced Energy Depletion
the number of nodes in coronas increases in geometric progression with a common ratio of q

15. Nonuniform Node Distribution -- Subbalanced Energy Depletion
q=3 16 8 48
144

16. Nonuniform Node Distribution -- Subbalanced Energy Depletion
Proof

17. Nonuniform Node Distribution -- Subbalanced Energy Depletion

18. Nonuniform Node Distribution Strategy
The number of nodes in Ci
Subbalanced Energy Depletion

19. Nonuniform Node Distribution Strategy

20. q-Switch Routing

21. Simulation

28. Conclusion
This paper explored the theoretical aspects of the nonuniform node distribution strategy in WSNs.
Although it is impossible to achieve balanced energy depletion, subbalanced energy depletion in the network is possible.