1. Sync and Swarm Behavior for Sensor Networks
Joint IEEE Communications Society and AEROSPACE Chapter Presentation
Sync and Swarm Behavior for Sensor Networks
Stephen F. Bush
GE Global Research

2. Stephen F. Bush (www.research.ge.com/~bushsf)
Outline
Overview
Synchronization as coordinated behavior …
Relating code size and “self-locating” capability (bushmetric)
Characteristics of swarm behavior
Pulse-Coupled Oscillation
A simple example of swarm behavior
Boolean Network
A means of studying swarm behavior
Conclusion
Swarm behavior only beginning to be harnessed for coordinated behavior
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3. Stephen F. Bush (www.research.ge.com/~bushsf)
Metric Motivation
A measure of the ability of code to maintain itself in “optimal” location in a changing network topology
no code redundancy allowed within the network and code must contain its own algorithm for determining where to move.
Hill climbing, but the hills are continuously changing…
Who cares? …constrained (sensor) network in which many more network programs and services are installed than will fit on all nodes simultaneously
Benefit for small code size (a la Kolmogorov Complexity) to move faster within network– unless larger code size is somehow “smarter”
Bush, Stephen F., “A Simple Metric for Ad Hoc Network Adaptation,” to appear in IEEE Journal on Selected Areas in Communications: AUTONOMIC COMMUNICATION SYSTEMS
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4. Stephen F. Bush (www.research.ge.com/~bushsf)
Bushmetric
Diameter is longest shortest path within network graph
Diameter rate of change:
Code hop rate:
Metric:
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5. Stephen F. Bush (www.research.ge.com/~bushsf)
Impact of Beta
Code moves as fast or faster than network changes:
Code slower than network:
Code moves at same rate as network changes:
On next slide, code continuously polls neighbors’ distance to clients and moves to minimize expected value and variance to reach clients
Many possible algorithms: one that balances code size with code “intelligence” wins
Smart but large code: not good, small but poor movement choices: also not good
Smallest code that describes future state of the network related to Kolmogorov Complexity
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6. Stephen F. Bush (www.research.ge.com/~bushsf)
Bushmetric Landscape
Bushmetric quantifies the relation among: link rates, code size, and the dynamic nature of the network
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7. Anticipating Network Topological Behavior…
…With Smallest Code Size!
Beta Is a Fundamental Metric Relating Code Size and Network Graph Prediction
Defined for One Service Floating Through Network
Can ‘N’ Smaller, Simpler Migrating Code ‘Packets’ Do Better?
Shift focus to large numbers of simple interacting ‘agents’
E.g. Impacts Network Coding
Bush, Stephen F. and Smith, Nathan,“The Limits of Motion Prediction Support for Ad hoc Wireless Network Performance,” The 2005 International Conference on Wireless Networks (ICWN-05) Monte Carlo Resort, Las Vegas, Nevada, USA, June 27-30, 2005.
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8. Overview of Swarm Characteristics
No central control
No explicit model
Ability to sense environment (comm. Media)
Ability to change environment (comm. Media)
Inter-connectivity dominates system behavior
“any attempt to design distributed problem-solving devices inspired by the collective behavior of social insect colonies or other animal societies” (Bonabeau, 1999)
Stephen F. Bush (

9. Overview of Swarm Characteristics
Many aspects of collective activities result from self-organization
“Something is self-organizing if, left to itself, it tends to become more organized.” –Cosma Shalizi
“Self-Organization in social insects is a set of dynamical mechanisms whereby structures appear at the global level of a system from interactions among its lower-level components” –Swarm Intelligence
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10. Well-Known Swarm Telecommunication Examples
ANT Routing Techniques
Scout packets reinforce “pheromone” along best routes
Pulse-Coupled Oscillation
Localized oscillation converges to global synchrony
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11. Connectionless Networking For Energy Efficiency
Wireless Networks Are Inherently Broadcast
Legacy Networking Utilizes Point-to-point Packet Communication
Pulse Coupled Oscillators (PCO)
((( )))
((( )))
Local exchanges only
Wake Up Every for 5 mS Every 15 Seconds to Re-sync to GPS Master clocks
5 mS S
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12. Sync Energy Impact Overview
Size (bits)
Central Timestamp/Position
Broadcast
NTP
Rate (pkts/s)
PCO
Ref Broadcast
Distance (m)
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13. Sync Regimes
Receiver Energy Dominates
Transmitter Energy Dominates
Reception Energy Dominates
Transmission Energy Intensive
Pathloss Exponent: 2
Pathloss Exponent: 3
Power reduction versus node density using nearest-neighbor range
Use More Frequent Lower-Energy Transmissions in Receiver Dominated Regime to Reduce Receiver Energy
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14. Emergent Case: Peskin’s Model
initial rate of accumulation
leakage
Leaky Integrate and Fire
coupling
strength
is time after previous firing
K-nearest Neighbor Transmission Distance
Tradeoff Transmission Energy for Convergence Time
Robust
No Single Point of Failure
Node Mobility Has Low Impact on Performance
Avoids noise/jamming issues
GE version based upon extremely short packet pulses
# packets
Converges to global reference time
***Could encode more information required for setup
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15. Emergent Power Savings
R(2, 3, or 4) R r2 r
Power: ~
Power: ~
r<<R
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16. Energy Savings Example
Power to sync: ~
Power to sync: ~
Original CSIM Simulation Node Locations
Minimum Broadcast Power ~ * timestamp message size ~128 bits
PCO Power ~ * No message required ~1 bit
Each node can oscillate times and use less energy than a single broadcast;
Sync actually takes << 50 oscillations (transmit energy savings is 6:1)
Stephen F. Bush (

17. Stephen F. Bush (www.research.ge.com/~bushsf)
Simulation Specs
Nodes: 612 randomly placed
PCO packet size: 16 bits
Non-PCO packet size: 180 bits
Transmission Rate: 4 Mbs
Clock drift: 10-8
Non-PCO Algorithm: Time Ref Broadcast (assumes center-most master node)
Movement: Brownian motion
Channel: Hata-Okumura
Receiver power: 50 mW
Transmitter power: Min required to reach k-nearest neighbors where k=1
Sync Interval: 50 ms (so we could see impact quickly)
Stephen F. Bush (

18. Non-Mobile Case – Total Power and Efficiency
Synchronization efficiency is the proportion of nodes (n) synchronized (s) normalized by power (p). The emergent synchronization technique is consistently more power efficient
Total power consumed by the network to maintain synchronization is significantly less using emergent synchronization
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19. Node Density – Mobile Case
Change in node density caused by node movement. Both simulations show similar decreases in density. Nodes spread out from an initial concentration in this simulation
Pulse phase shows no perceptible change with node mobility
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20. Efficiency and Rate of Node Movement – Mobile Case
Synchronization power efficiency with node mobility. Efficiency decreases slightly for emergent and broadcast techniques
The expected rate of node movement is the same for both emergent and broadcast simulations
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21. Stephen F. Bush (www.research.ge.com/~bushsf)
Jitter – Mobile Case
Clock jitter is significantly increased for the broadcast technique while the emergent technique is unaffected by node mobility
Stephen F. Bush (

22. Variance, Proportion Out-of-sync – Mobile Case
Clock variance shows a sudden increase with node mobility for the broadcast technique while having no perceptible effect on the emergent technique
There is sudden rise in the proportion of nodes out of synchronization tolerance in the broadcast technique with node mobility
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23. Stephen F. Bush (www.research.ge.com/~bushsf)
PCO Recap/BN Intro
PCO leads to common sync
What about inducing more complex patterns?
Boolean Networks…
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24. Properties of Boolean Networks
Swarm Properties
Simple Nodes
More Interesting Behavior With Larger Numbers
Inter-connectivity Has Significant Impact
Positive and Negative Reinforcement
1s and 0s
Self-organization
Attractor Formation
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25. Properties of Boolean Networks
BN Properties
N Simple Nodes
Boolean Functions
K Interconnections
Small K
Yields Localized Interconnections
Larger K
Yields a More Globally Inter-connected System
p Probability of ‘1’ Result From Boolean Function
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26. An Example Boolean Network
A^B
Input 1
Input 2
Output 1
K = 2
N = 3
A^B
p = 0.5
A|B
A|B
Input 1
Input 2
Output 1
A^B
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27. Analyzing a Random Boolean Network Using Mathematica
A^B
A|B
A^B
Pre-determining the state transitions is not, in general, a solvable problem…
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28. Setting the Truth Values
A^B
Input 1
Input 2
Output 1
A|B
Input 1
Input 2
Output 1
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29. Stephen F. Bush (www.research.ge.com/~bushsf)
Attractors
Imagine Any Given Spatial Positioning of Nodes
On/Off States Form Patterns Over Time
The Network May Appear Chaotic, However:
Only Finite Number of Possible States
Thus, There Must Be Repeating States, Either:
Frozen
Cycles
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30. State Diagram
The state transition graph is shown above; attractors are points and cycles from which there is no escape.
The induced Boolean Network for initial topology is shown above.
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31. Stephen F. Bush (www.research.ge.com/~bushsf)
Attractors
basin
= system state pattern
length 2
cycle
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32. of basin leading to cycle
Running the Network
Size
of basin leading to cycle
Cycle
Number
Lowest
starting state 7 4 7
toValue[] converts binary state to decimal+1
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33. Boolean Network Properties
Very Short State Cycles, Often of Length One and you Reach One Quickly
K=N and P=0.5
Long State Cycles (for Large N), Small Number of Such Attractors, Around N/e
Little Homeostasis, Massively Chaotic
K=4 or 5 and p=0.5
Similar to K=N, Massively Chaotic Again
K=2 and P=0.5
Well Behaved, Number of Cycles Around, These Are Both 317 for N=100,000
Increasing p From 0.5 Towards 1.0
Has an Effect similar to Decreasing K
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34. A Slightly More Complex Random Boolean Network
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35. Stephen F. Bush (www.research.ge.com/~bushsf)
Derrida Plot
Discrete Analog of a Lyapunov Exponent
Lyapunov exponent
Designed to measure sensitivity to initial conditions
Averaged rate of convergence of two neighboring trajectories
Stephen F. Bush (

36. Stephen F. Bush (www.research.ge.com/~bushsf)
Derrida Plot
Consider a Normalized Hamming Distance (D) Between Two Initial States (N nodes)
D(s1,s2)/N
Dt+1 Plotted As a Function of Dt
Ordered Regime Is Below Diagonal, i.e. States Do Not Diverge
Phase Transition occurs ON the Diagonal Line
Chaotic Conditions Above the Diagonal Line
States Diverging
Stephen F. Bush (

37. An Example Derrida Plot1
“Edge of Chaos”
Returns to new state…
D(T+1)=D(T)
Chaos
D(T+1)
K=4
K=2
K=3
Order
Returns to state seen in the past… 1
D(T)
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38. Stephen F. Bush (www.research.ge.com/~bushsf)
Derrida Plot Trends
K=2 and Random Choice of 16 Boolean Functions
States Lie on the Phase Transition
State Cycles in Such Networks Have Median Length of N1/2
A System of 100,000 Nodes (2100,000 States) Flows Into Incredibly Small Attractor
Just 318 States Long
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39. Perturbation Analysis
Single State Changes Leading From One Attractor to Another
Consider a C x C Matrix of Cycles Perturbed As a Function of the New Cycle to Which They Change
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40. Perturbation Analysis
cycle
cycle
Ergodic Cycles
Large Values Along Diagonal
Division of Each Element by Row Total Yields Markov Chain
Power-law Avalanche of Changes Observed Given Random Perturbations
Stephen F. Bush (

41. Stephen F. Bush (www.research.ge.com/~bushsf)
Outline
Overview
Synchronization as coordinated behavior …
Relating code size and “self-locating” capability (bushmetric)
Characteristics of swarm behavior
Pulse-Coupled Oscillation
A simple example of swarm behavior
Boolean Network
A means of studying swarm behavior
Conclusion
Swarm behavior only beginning to be harnessed for coordinated behavior
Stephen F. Bush (

42. Stephen F. Bush (www.research.ge.com/~bushsf)
Example Usage
Self-configuring
Difficult to Detect (Predict) Final Result
Larger Load Yields Greater Attractor Complexity and More Cluster Heads
Larger Concentrations of Nodes Tend to Yield More Complex Attractors and Thus More Cluster Heads
Robust: Always Results in a Feasible Partitioning
Sensor Network => Boolean Network
Stephen F. Bush (

43. Stephen F. Bush (www.research.ge.com/~bushsf)
Recap…
Beta metric (code size, movement, position)
Pulse coupled oscillation (example collective behavior)
Boolean Networks
a Mechanism for Engineering Adaptive “Edge of Chaos” Wireless Network Protocols
Engineering Useful Boolean Networks
Boolean Networks That Satisfy K-SAT Problems
Building A Boolean Network to Mimic A Known System
(Discussed in More Detail in a Proposed Tutorial by
Stephen F. Bush (