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Sync and Swarm Behavior for Sensor Networks Stephen F. Bush bushsf@research.ge.com GE Global Research http://www.research.ge.com/~bushsf Joint IEEE Communications Society and AEROSPACE Chapter Presentation

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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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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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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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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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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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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.

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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)

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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

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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

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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 ((( ))) Local exchanges only Pulse Coupled Oscillators (PCO) 5 mS 14.995 S Wake Up Every for 5 mS Every 15 Seconds to Re-sync to GPS Master clocks

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Stephen F. Bush (www.research.ge.com/~bushsf) Sync Energy Impact Overview Size (bits) Rate (pkts/s) Distance (m) Ref Broadcast NTP Central Timestamp/Position Broadcast PCO

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Stephen F. Bush (www.research.ge.com/~bushsf) Receiver Energy Dominates Transmitter Energy Dominates Reception Energy Dominates Transmission 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

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Stephen F. Bush (www.research.ge.com/~bushsf) Emergent Case: Peskins Model is time after previous firing initial rate of accumulation leakage Leaky 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

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Stephen F. Bush (www.research.ge.com/~bushsf) Emergent Power Savings R (2, 3, or 4) R r2r2 r r2r2 r r2r2 r r2r2 r r2r2 r r<

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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) Power to sync: ~ 123.56 Power to sync: ~ 304.72

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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)

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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

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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

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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

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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

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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

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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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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

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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

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Stephen F. Bush (www.research.ge.com/~bushsf) An Example Boolean Network A^B A|B A^B p = 0.5 A^B Input 1Input 2Output 000 010 100 111 A|B Input 1Input 2Output 000 011 101 111 K = 2 N = 3

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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…

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Stephen F. Bush (www.research.ge.com/~bushsf) Setting the Truth Values A^B Input 1Input 2Output 000 010 100 111 A|B Input 1Input 2Output 000 011 101 111

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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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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.

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Stephen F. Bush (www.research.ge.com/~bushsf) Attractors = system state pattern cycle basin length 2

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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

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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

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Stephen F. Bush (www.research.ge.com/~bushsf) A Slightly More Complex Random Boolean Network

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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

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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 D t+1 Plotted As a Function of D t 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

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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…

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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 N 1/2 A System of 100,000 Nodes (2 100,000 States) Flows Into Incredibly Small Attractor –Just 318 States Long

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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

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Stephen F. Bush (www.research.ge.com/~bushsf) Perturbation Analysis 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

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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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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

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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 bushsf@research.ge.com)

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