Conceptual issues in scaling sensor networks

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Conceptual issues in scaling sensor networks

• Massimo Franceschetti,
• UC Berkeley

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State of the art on scaling
Cory Sharp Shawn Schaffert Shankar Sastry group
PEG 100 sensor nodes, 1 evader, 2 pursuers
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Can we dramatically scale this?

• Practical problems
• Conceptual problems

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Theory
Practice

• Connectivity
• Routing
• Storage
• Failures
• Packet loss
• Malicious behavior
• Remote operation

• Percolation theory
• Random graphs
• Distributed computing
• Distributed control
• Channel physics
• Distributed sampling
• Network information theory
• Network coding

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Some conceptual issues

• LARGE SCALE CONNECTIVITY
• ROUTING
• CAPACITY
• CONTROL

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Single hop model
Random connection model
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Multi-hop connectivity model
There is a phase transition at a critical node
density value
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How does the critical density change
with the shape of the connection function?
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General Tendency

• When the selection mechanism with which
• nodes are connected to each other is
• sufficiently spread out, then few links
• (in the limit one on average) will suffice to
• obtain global connectivity.

Balister, Bollobas, Walters (2003) Franceschetti,
Booth, Cook, Bruck, Meester (2003) D. Dubhashi,
O. Haggstrom, A. Panconesi (2003) R. Meester, M.
Penrose, A. Sarkar (1997) M. Penrose (1993)
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General Tendency

• In contrast, when connections do not spread
• out, few links are not enough for
• connectivity.

Xue and P. R. Kumar (2003) O. Haggstrom and R.
Meester (1996)
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Spread out connections (1)
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Theorem
Franceschetti, Booth, Cook, Bruck, Meester (2003)
For all connection functions
it is easier to reach connectivity in this model
of unreliable network
longer links are trading off for the
unreliability of the connection
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Spread out connections (2)
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Two different spreading strategies
Mixture of short and long links
Links are made all longer
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Theorem
Balister, Bollobas, Walters (2003) Franceschetti,
Booth, Cook, Bruck, Meester (2003)
Consider annuli shapes A(r) of inner radius r,
unit area, and critical density
For all , there exists a
finite , such that A(r) percolates,
for all
It is possible to decrease the connectivity
threshold by taking a sufficiently large shift !
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What have we learned
CNL
CNLaverage number of connections per node needed
for connectivity
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What about routing?

• Navigation in the small world
• Need links at ALL scale lengths !

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Intuition scale invariance
Z
r2
r1
Model of neighbors density
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Intuition scale invariance
Z
r2
r1
Model of neighbors density
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Intuition scale invariance
Z
r2
r1
Model of neighbors density
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Intuition scale invariance
Z
r2
r1
Slow close to destination
Slow far from destination
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Theorem
Franceschetti Meester (2003)
T
e
d
S
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Bottom line
T
e
d
S
Build routing trees that are scale invariant to
route with few hops at all distance scales
Want to balance the number of short and long
links Need to exploit the hairy edge (D.
Culler)
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Summary

• Towards a system theory of large scale networks
• Conceptual issues at different levels
• Design for complexity strategy
• Close the gap between theory and practice