sync and swarm behavior for sensor networks stephen f. bush [email protected] ge global...

Sync and Swarm Behavior for Sensor Networks

Stephen F. Bush

[email protected]

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


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”


Outline







Bush, Stephen F., “A Simple Metric for Ad Hoc Network Adaptation,” to appear in IEEE Journal on Selected Areas in Communications: AUTONOMIC COMMUNICATION SYSTEMS


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:


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


Bushmetric Landscape

Bushmetric quantifies the relation among: link rates, code size, and the dynamic nature of the network


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.


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)


Outline








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


Well-Known Swarm Telecommunication Examples

• ANT Routing Techniques– Scout packets

reinforce “pheromone” along best routes

• Pulse-Coupled Oscillation– Localized oscillation

converges to global synchrony


Outline








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


Sync Energy Impact Overview

Size (bits)

Rate (pkts/s)

Distance (m)

Ref Broadcast

NTP

Central Timestamp/PositionBroadcast

PCO


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


],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


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


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


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)


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


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


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


Jitter – Mobile Case

Clock jitter is significantly increased for the broadcast technique while the emergent technique is unaffected by node mobility


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


PCO Recap/BN Intro

• PCO leads to common sync

• What about inducing more complex patterns?

• Boolean Networks…


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


Outline








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


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


0 0 0

0 1 1

1 0 1

1 1 1

K = 2N = 3


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…


Setting the Truth Values

A^B


0 0 0

0 1 0

1 0 0

1 1 1

A|B


0 0 0

0 1 1

1 0 1

1 1 1


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


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.


Attractors= system state pattern

cycle

basin

length 2


Running the Network

toValue[] converts binary state to decimal+1

7

4

7

Size of basin

leading to cycle

Lowest starting state

Cycle Number


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


A Slightly More Complex Random Boolean Network


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


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


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…


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


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


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


Outline








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


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])

sync and swarm behavior for sensor networks stephen f. bush [email protected] ge global...

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