Sync and Swarm Behavior for Sensor Networks

1
Sync and Swarm Behavior for Sensor Networks
Joint IEEE Communications Society and AEROSPACE
Chapter Presentation

• Stephen F. Bush
• bushsf_at_research.ge.com
• GE Global Research
• http//www.research.ge.com/bushsf

2
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

3
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
4
Bushmetric
Diameter is longest shortest path within network
graph
Diameter rate of change
Code hop rate
Metric
5
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

6
Bushmetric Landscape
Bushmetric quantifies the relation among link
rates, code size, and the dynamic nature of the
network
7
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.
8
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)

9
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

10
Well-Known Swarm Telecommunication Examples

• ANT Routing Techniques
• Scout packets reinforce pheromone along best
  routes
• Pulse-Coupled Oscillation
• Localized oscillation converges to global
  synchrony

11
Connectionless Networking For Energy Efficiency
Wireless Networks Are Inherently Broadcast
Legacy Networking Utilizes Point-to-point Packet
Communication
Pulse Coupled Oscillators (PCO)
Wake Up Every for 5 mS Every 15 Seconds to
Re-sync to GPS Master clocks
12
Sync Energy Impact Overview
Size (bits)
Central Timestamp/Position Broadcast
NTP
Rate (pkts/s)
PCO
Ref Broadcast
Distance (m)
13
Sync Regimes
Use More Frequent Lower-Energy Transmissions in
Receiver Dominated Regime to Reduce Receiver
Energy
14
Emergent Case Peskins Model

• K-nearest Neighbor Transmission Distance
• Tradeoff Transmission Energy for Convergence
  Time
• Robust
• No Single Point of Failure
• Node Mobility Has Low Impact on Performance

Converges to global reference time Could
encode more information required for setup
15
Emergent Power Savings
rltltR
16
Energy Savings Example
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 ltlt 50 oscillations (transmit energy savings
is 61)
17
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 k1
• Sync Interval 50 ms (so we could see impact
  quickly)

18
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
19
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
20
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
21
Jitter Mobile Case
Clock jitter is significantly increased for the
broadcast technique while the emergent technique
is unaffected by node mobility
22
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
23
PCO Recap/BN Intro

• PCO leads to common sync
• What about inducing more complex patterns?
• Boolean Networks

24
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

25
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

26
An Example Boolean Network
K 2
N 3
AB
p 0.5
AB
AB
27
Analyzing a Random Boolean Network Using
Mathematica
AB
AB
AB
Pre-determining the state transitions is not, in
general, a solvable problem
28
Setting the Truth Values
29
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

30
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.
31
Attractors
basin
length 2
cycle
32
Running the Network
Size of basin leading to cycle
Lowest starting state
Cycle Number
7
4
7
toValue converts binary state to decimal1
33
Boolean Network Properties

• K1
• Very Short State Cycles, Often of Length One and
  you Reach One Quickly
• KN and P0.5
• Long State Cycles (for Large N), Small Number of
  Such Attractors, Around N/e
• Little Homeostasis, Massively Chaotic
• K4 or 5 and p0.5
• Similar to KN, Massively Chaotic Again
• K2 and P0.5
• Well Behaved, Number of Cycles Around, These Are
  Both 317 for N100,000
• Increasing p From 0.5 Towards 1.0
• Has an Effect similar to Decreasing K

34
A Slightly More Complex Random Boolean Network
35
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

36
Derrida Plot

• Consider a Normalized Hamming Distance (D)
  Between Two Initial States (N nodes)
• D(s1,s2)/N
• Dt1 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

37
An Example Derrida Plot
1
Edge of Chaos
D(T1)D(T)
Returns to new state
Chaos
D(T1)
K4
K2
K3
Order
Returns to state seen in the past
0
1
D(T)
38
Derrida Plot Trends

• K2 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

39
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

40
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
41
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

42
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 gt Boolean Network
43
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_at_research.ge.com)