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 bushsf@research.ge.com GE Global Research http://www.research.ge.com/~bushsf

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)

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

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

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

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)

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)

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 14.995 S Stephen F. Bush (www.research.ge.com/~bushsf)

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

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

Emergent Power Savings R(2, 3, or 4) R r2 r Power: ~ Power: ~ r<<R Stephen F. Bush (www.research.ge.com/~bushsf)

Energy Savings Example Power to sync: ~ 123.56 Power to sync: ~ 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)

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 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 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 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)

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)

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)

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 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 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 1 A|B Input 1 Input 2 Output 1 Stephen F. Bush (www.research.ge.com/~bushsf)

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)

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

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

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

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

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)

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 1 “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) Stephen F. Bush (www.research.ge.com/~bushsf)

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 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 (www.research.ge.com/~bushsf)

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)

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)

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