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Sync and Swarm Behavior for Sensor Networks
Stephen F. Bush
GE Global Research
http://www.research.ge.com/~bushsf
Joint IEEE Communications Society and AEROSPACE Chapter
Presentation
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)
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”
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
Bush, Stephen F., “A Simple Metric for Ad Hoc Network Adaptation,” to appear in IEEE Journal on Selected Areas in Communications: AUTONOMIC COMMUNICATION SYSTEMS
Stephen F. Bush (www.research.ge.com/~bushsf)
Bushmetric
t
tvudtvud vuvu
),,(max),,(max 1,2,
t
hh
12
),,(max),,(max 1,2,
12
tvudtvud
hh
vuvu
dt
vud
hEdtd
vu
),(max/
,
Diameter is longest shortest path within network graph
Diameter rate of change:
Code hop rate:
Metric:
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
11
1
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
• 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)
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)
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– Scout packets
reinforce “pheromone” along best routes
• Pulse-Coupled Oscillation– Localized oscillation
converges to global synchrony
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)
Connectionless Networking For Energy Efficiency
Wireless Networks Are Inherently Broadcast
Legacy Networking Utilizes Point-to-point Packet
Communication
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Local exchanges only
Pulse Coupled Oscillators (PCO)
5 mS
14.995 S 14.995 S
Wake Up Every for 5 mS Every 15 Seconds to Re-sync to GPS Master
clocks
Stephen F. Bush (www.research.ge.com/~bushsf)
Sync Energy Impact Overview
Size (bits)
Rate (pkts/s)
Distance (m)
Ref Broadcast
NTP
Central Timestamp/PositionBroadcast
PCO
Stephen F. Bush (www.research.ge.com/~bushsf)
Rec
eive
r En
ergy
D
omin
ates
Transm
itter
Energy
Dominates
Reception Energy DominatesTransmission Energy
Intensive
Sync Regimes
Use More Frequent Lower-Energy Transmissions in Receiver Dominated Regime to Reduce Receiver Energy
Pathloss Exponent: 2
Pathloss Exponent: 3
Power reduction versus node density using nearest-neighbor range
Stephen F. Bush (www.research.ge.com/~bushsf)
],0[ thx
i
T
)(t
)(txi
0S
Emergent Case: Peskin’s Model
1,0)( ti is time after previous firing
)(0 txSdt
dxi
i
initial rate of accumulation
leakageLeaky Integrate and Fire coupling
strength
Converges to global reference time ***Could encode more information required for setup
• 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
)(t
Stephen F. Bush (www.research.ge.com/~bushsf)
Emergent Power Savings
R(2, 3, or 4)
R
r2
r
r2
r
r2
r
r2
r
r2
r
r<<RPower: ~ 4,3,2 orR Power: ~ 2r
Stephen F. Bush (www.research.ge.com/~bushsf)
Energy Savings Example
PCO Power ~ 123.56 * No message required ~1 bit
Minimum Broadcast Power ~ 304.72 * timestamp message size ~128 bits
Original CSIM Simulation Node Locations
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)
2nearestdPower to sync: ~ 123.56
Power to sync: ~ 304.722
maxd
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
np
s
Stephen F. Bush (www.research.ge.com/~bushsf)
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
The expected rate of node movement is the same for both emergent and broadcast
simulations
Synchronization power efficiency with node mobility. Efficiency decreases slightly for emergent and broadcast
techniques
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
There is sudden rise in the proportion of nodes out of synchronization tolerance in
the broadcast technique with node mobility
Clock variance shows a sudden increase with node mobility for the broadcast
technique while having no perceptible effect on the emergent technique
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
• 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
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)
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
A^B
A|B
A^B
p = 0.5
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
K = 2N = 3
Stephen F. Bush (www.research.ge.com/~bushsf)
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 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.
Stephen F. Bush (www.research.ge.com/~bushsf)
Attractors= system state pattern
cycle
basin
length 2
Stephen F. Bush (www.research.ge.com/~bushsf)
Running the Network
toValue[] converts binary state to decimal+1
7
4
7
Size of basin
leading to cycle
Lowest starting state
Cycle Number
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
D(T)
D(T+1)
D(T+1)=D(T)
K=3 K=2
K=4
0 1
1
Order
Chaos
“Edge of Chaos”
Returns to state seen in the past…
Returns to new state…
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
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 Analysiscy
cle
cycle
Large Values Along Diagonal
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-configuringDifficult to Detect (Predict)
Final ResultLarger 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])