Joint IEEE Communications Society
and AEROSPACE Chapter
Presentation
Sync and Swarm Behavior for
Sensor Networks
Stephen F. Bush
[email protected]
GE Global Research
http://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
(www.research.ge.com/~bushsf)
Metric Motivation
Outline
•
• Overview
– Synchronization as coordinated behavior …
– Relating code size and “self-locating” capability
(bushmetric)
– Characteristics of swarm behavior
– no code redundancy allowed within the
network and code must contain its own
algorithm for determining where to
move.
• 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
(www.research.ge.com/~bushsf)
Bush, Stephen F., “A Simple Metric for Ad Hoc Network
Adaptation,” to appear in IEEE Journal on Selected Areas
in Communications: AUTONOMIC COMMUNICATION
SYSTEMS
A measure of the ability of code to
maintain itself in “optimal” location in a
changing network topology
•
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”
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:
max u ,v d (u, v, t 2 )  max u ,v d (u, v, t1 )
t
h2  h1
t
h2  h1
 
max u ,v d (u, v, t 2 )  max u ,v d (u, v, t1 )


E h
dt
d / dt  

 max u ,v d (u , v) 
Stephen F. Bush
(www.research.ge.com/~bushsf)
Impact of Beta
•
•
•
•
Code moves as fast or faster than network changes:   1
Code slower than network:   1
Code moves at same rate as network changes:   1
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
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
Stephen F. Bush
(www.research.ge.com/~bushsf)
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.
Stephen F. Bush
(www.research.ge.com/~bushsf)
Overview of Swarm
Characteristics
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
(www.research.ge.com/~bushsf)
• 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
(www.research.ge.com/~bushsf)
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
Stephen F. Bush
(www.research.ge.com/~bushsf)
Well-Known Swarm
Telecommunication Examples
• ANT Routing
Techniques
Outline
• Overview
– Scout packets
reinforce “pheromone”
along best routes
– 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
• Pulse-Coupled
Oscillation
• Conclusion
– Swarm behavior only beginning to be harnessed for
coordinated behavior
Stephen F. Bush
(www.research.ge.com/~bushsf)
Stephen F. Bush
(www.research.ge.com/~bushsf)
– Localized oscillation
converges to global
synchrony
Connectionless Networking For
Energy Efficiency
Wireless Networks Are
Inherently Broadcast
Legacy Networking Utilizes
Point-to-point Packet
Communication
Pulse Coupled Oscillators (PCO)
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Local exchanges only
Wake Up Every for 5 mS Every 15
Seconds to Re-sync to GPS Master
clocks
5 mS
14.995 S
Stephen F. Bush
(www.research.ge.com/~bushsf)
14.995 S
Sync Energy Impact Overview
Size (bits)
Central Timestamp/Position
Broadcast
NTP
Rate (pkts/s)
PCO
Ref Broadcast
Distance (m)
Stephen F. Bush
(www.research.ge.com/~bushsf)
Sync Regimes
Transmission Energy
Intensive
Reception Energy Dominates
Pathloss Exponent: 3
Pathloss Exponent: 2
Power reduction versus node density using
nearest-neighbor range
Use More Frequent Lower-Energy Transmissions in Receiver Dominated Regime to Reduce
Receiver Energy
Stephen F. Bush
(www.research.ge.com/~bushsf)
Emergent Case: Peskin’s Model
Leaky Integrate and Fire
xi (t )
T
dxi
 S 0  xi   (t )
dt
i (t )  0,1
initial rate of accumulation
S0
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
[0, xth ]
i
leakage
coupling
strength
 (t )
GE version based upon extremely
short packet pulses
Avoids noise/jamming issues
 (t ) 
Converges to global reference time
***Could encode more information required for setup
Stephen F. Bush
(www.research.ge.com/~bushsf)
# packets
Emergent Power Savings
R(2, 3, or 4)
r2
R
Power: ~
R 2,3,or 4
r2
r
r
r<<R
Power: ~
Stephen F. Bush
(www.research.ge.com/~bushsf)
r2
r
2
r

r2
r
r2
r
Energy Savings Example
Power to sync:
Power to sync:
 d nearest
d max
2
2
~ 123.56
~ 304.72
Original CSIM Simulation Node Locations
Minimum Broadcast Power ~ 304.72 * timestamp message size ~128 bits
PCO Power ~ 123.56 * No message required ~1 bit
Each node can oscillate 315.67 times and use less energy than a single broadcast;
Sync actually takes << 50 oscillations (transmit energy savings is 6:1)
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
(www.research.ge.com/~bushsf)
Non-Mobile Case – Total Power
and Efficiency
Total power consumed by the network to maintain
synchronization is significantly less using emergent
synchronization
Synchronization efficiency is the proportion
of nodes (n) synchronized (s) normalized by
power (p). The emergent synchronization
technique is consistently more power
efficient
Stephen F. Bush
(www.research.ge.com/~bushsf)
s
np
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
Stephen F. Bush
(www.research.ge.com/~bushsf)
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
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
(www.research.ge.com/~bushsf)
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
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…
Stephen F. Bush
(www.research.ge.com/~bushsf)
Properties of Boolean Networks
Outline
• Swarm Properties
• 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
(www.research.ge.com/~bushsf)
– Simple Nodes
• More Interesting
Behavior With
Larger Numbers
– Inter-connectivity
Has Significant
Impact
– Positive and
Negative
Reinforcement
• 1s and 0s
– Self-organization
Stephen F. Bush
(www.research.ge.com/~bushsf)
• Attractor
Formation
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
Stephen F. Bush
(www.research.ge.com/~bushsf)
An Example Boolean Network
K=2
N=3
A^B
p = 0.5
A|B
A^B
Input 1 Input 2 Output
0
0
0
0
1
0
1
0
0
1
1
1
A|B
Input 1 Input 2 Output
A^B
Stephen F. Bush
(www.research.ge.com/~bushsf)
0
0
0
0
1
1
1
0
1
1
1
1
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…
Stephen F. Bush
(www.research.ge.com/~bushsf)
Setting the Truth Values
A^B
Input 1 Input 2 Output
0
0
0
0
1
0
1
0
0
1
1
1
A|B
Input 1 Input 2 Output
0
0
0
0
1
1
1
0
1
1
1
1
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
Stephen F. Bush
(www.research.ge.com/~bushsf)
State Diagram
The induced Boolean Network for initial
topology is shown above.
The state transition graph is shown above;
attractors are points and cycles from which
there is no escape.
Stephen F. Bush
(www.research.ge.com/~bushsf)
Attractors
basin
= system state pattern
length 2
cycle
Stephen F. Bush
(www.research.ge.com/~bushsf)
Running the Network
7
Cycle
Number
Size
of basin
Lowest
leading to starting state
cycle
4
7
toValue[] converts binary state to decimal+1
Stephen F. Bush
(www.research.ge.com/~bushsf)
Boolean Network Properties
• K=1
– 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
Stephen F. Bush
(www.research.ge.com/~bushsf)
A Slightly More Complex
Random Boolean Network
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
(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
(www.research.ge.com/~bushsf)
An Example Derrida Plot
“Edge of Chaos”
1
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…
0
D(T)
Stephen F. Bush
(www.research.ge.com/~bushsf)
1
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
Stephen F. Bush
(www.research.ge.com/~bushsf)
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
Stephen F. Bush
(www.research.ge.com/~bushsf)
Perturbation Analysis
cycle
cycle
Ergodic Cycles
Division of Each Element by Row Total Yields Markov Chain
Power-law Avalanche of Changes Observed Given Random Perturbations
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
(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
(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
[email protected])
Stephen F. Bush
(www.research.ge.com/~bushsf)