Boyd, Metcalfe and Amdahl - Air Power Australia · MONASH University Computer Science & Software...

MONASHUniversity

Computer Science & Software EngineeringComputer Science & Software EngineeringComputer Science & Software Engineering

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Computer Science & Software Engineeringhttp://www.csse.monash.edu.au/

Boyd, Metcalfe and Amdahl -ModellingNetworked Warfighting Systems

Carlo Kopp, BE(Hons), MSc, PhDMIEEE, MAIAA, PEngMonash University, Clayton, Australiaemail: [email protected]

c© 2004, Monash University, Australia

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Defining the Problem

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How to Quantify NCW Capability Gains?

• Networked system ‘capability gain’ remains a contentious issue.

• NCW advocates invoke Metcalfe’s Law and point to square law

gains.

• NCW critics argue that the number of engagements effected is the

measure of system capability.

• NCW trials and experiments do indicate measurable capability gains.

• How do these capability gains arise?

• How do we quantify these capability gains?

• How do we maximise these capability gains?

• How do we minimise an opponent’s capability gains?

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NCW - Counter-Air Environment

Target Status and CommandsWedgetail Transmits

Link 16

Link 16

Link 16

TankerLink 16 Relay Platform

Tanker Relays Link 16 Over the Radio HorizonTanker Broadcasts Fuel State and Location

Link 16

Wedgetail AEW&CCombat Air Patrol

Combat Air Patrol

NCW ExampleRAAF Defensive Counter Air

to Combat Air Patrols

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NCW - Strike Environment

Link 16

Link 16

Link 16 Relay Platform

Strike Package

Bypass SAM SitesTo Evade Fighters andWedgetail Threat TracksStrike Package Uses

Link 16

Tanker

RAAF Strike / Offensive Counter Air

Wedgetail AEW&C

Combat Air Patrol

NCW Example

to Combat Air PatrolsTarget Status and CommandsWedgetail Transmits

Tanker Relays Link 16 Over the Radio HorizonTanker Broadcasts Fuel State and Location

Link 16

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NCW - Strike Environment

OK

OVERCAST

KILLBOX INTERDICTIONPERSISTENT BOMBARDMENT/

SV

MUNITIONSAUTONOMOUS

DATALINK/VOX

LOITERING BOMBER

00130

130U.S. AIR FORCE

PERSISTENTSURVEILLANCE

PERSISTENTSURVEILLANCE

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Quantifying Capability Gains

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NCW vs Boyd’s OODA Loop

• Boyd’s Observation-Orientation-Decision-Action loop presents an ab-

straction to represent the event loop in an engagement.

• Vast empirical evidence to support Boyd model - also applicable to

biological ‘predator-prey’ interactions.

• Players in the event loop Observe environment, Orient themselves

to the situation by forming a model, Decide upon a course of action,

and execute that Action.

• Intelligence Surveillance Reconnaissance (ISR) sensors and systems

collect information and a network distributes that information.

• Networking accelerates OODA loops by accelerating the Observation-

Orientation phases and improving situational awareness.

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NCW - A Networked Fabric

A NETWORKED ‘FABRIC’

FRIENDLY AIRSPACE

CONTESTED AIRSPACE

FEBA

FEBA

HOSTILE AIRSPACE

TANKER TANKER

SURVEILLANCE PLATFORM

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The Incompleteness Problem

• Representing capability gains using OO phases of OODA loop puts

focus on information domain gains.

• Real world systems combine information domain and kinetic domain

elements.

• Using only information domain elements neglects constraining sys-

tem behaviours imposed by kinetic domain elements.

• The result can be highly optimistic and unrealistic conclusions about

achievable capability gains.

• Representative modelling of complete system capability gains re-

quires a complete model which can encompass both the OO and

DA phases of the Boyd OODA loop.

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Metcalfe’s Law

• Metcalfe’s Law asserts that the usefulness or utility of a network

increases with the square of the number of nodes in the network.

• Empirically demonstrated on the WWW by correlating gains in sales

revenue against number of nodes connected to the network.

• Metcalfe’s Law is not a predictor of achieved utility, but rather an

indicator of achievable utility.

• ‘Utility’ is seen in terms of connectivity.

• Widely cited as a measure of capability gain in networked warfighting

systems.

• Metcalfe’s Law contains no implicit mechanism to quantify time

domain behaviour in the system.

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Metcalfe’s LawN

um

ber

of

Po

ssib

le C

on

nec

tio

ns

[−]

Number of Network Nodes [−]500 600400300200100 700 800 900 1000

Metcalfe’s Law

0

100000

200000

300000

400000

500000

600000

700000

800000

900000

1e+06Metcalfe’s Law

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Metcalfe’s Law - Time Domain

NK DELAY

SNS/PROC NK DELAY

ISR

ISR

ISR

SNS/PROC NK

OBSERVATION PHASE

FU

NC

TIO

NA

L

USER

TE

MP

OR

AL

INTERPRET/MODEL

ORIENTATION PHASE

DB

NETWORK

COLLATE

MODEL

VALIDATE

SNS/PROC NK DELAY

SNS/PROC NK

SNS/PROC

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Metcalfe’s Law Limitations

• Implicit assumption that gains in connectivity produce gains in time

domain performance.

• Complex time domain dependencies in ISR system and network be-

haviour not accounted for.

• Network saturation and load effects not accounted for.

• Effects of hostile jamming not accounted for.

• Metcalfe’s Law at best a useful predictor of bounds on capability

gain.

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Kinetic Domain - Decision-Action

• Completeness in modelling capability gains requires a kinetic do-

main model which can encompass the Decision-Action phases of the

OODA loop.

• Establish what bounds exist on the number of engagements the sys-

tem can produce within a defined time, with some bounded number

of elements.

• Decision processes involve delays since decision-makers often depen-

dent on inputs from superiors and subordinates, introducing queue-

ing behaviours into the system.

• Executing Actions involves sequences of events such as positioning

a platform for an engagement, also introducing queueing behaviours

into the system.

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Kinetic Domain Constraint ExampleQueue for

Runway, TakeoffTransit to

Target AreaQueue for

Aerial RefuellingTransit to

Station

Transit fromStation

Queue forAerial Refuelling

Transit from

Aw

ait

Tar

get

ing

Dir

ecti

ves

Orb

it S

tati

on

Target AreaQueue for

Approach, Land

SERIAL WORKLOADCOMPONENT

PARALLELWORKLOADCOMPONENT



PARALLEL

COMPONENTWORKLOAD

StrikeTargets

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Kinetic Domain - Decision-Action

• In practical terms the system at the Decision-Action level involves

complex mixes of sequential / serial / queueing behaviours, and

some parallel behaviours.

• How do we best model a complex mix of serial and parallel func-

tions?

• Answer: exploit Amdahl’s Law used in supercomput-

ing.

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Amdahl’s Law

• Amdahl’s Law asserts that a large system of ‘processors’ working

in parallel to solve a single problem can never achieve aggregate

performance equal to the sum of the achievable performance of each

and every individual processor in that system. The idealised ‘linear

speedup’ in problem solving cannot be achieved for any real world

problem, or:

Speedup = (s + p ) / (s + p / N ) = 1 / (s + p / N )

- where s and p are the serial and parallel time fractions.

• In Amdahl’s Law, the nature of the workload imposes constraints

on behaviour, regardless of the number of elements in the system

performing work. In networked warfighting systems, we thus treat

entities performing work as processors in a complex serial / parallel

system, executing tasks.

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Amdahl’s Law

1.31% Serial Fraction1.7% Serial Fraction

15

25

30

35

40

45

50Linear (Ideal) Speedup

4540353025Number of CPUs [−]

20151050

Sp

eed

up

[−]

Amdahl’s Law

0

5

10

20

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Boyd vs Metcalf vs Amdahl

D AO OOBSERVATION ORIENTATION DECISION ACTION

Amdahl’s LawMetcalfe’s Law

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Decision Action Capability Gains• Capability of the system in the Decision-Action phases reduces with

the increasing number of ‘serial chains’ within the system.

• Capability of the system in the Decision-Action phases increases with

the increasing level of parallelism in the system.

• Complex sequential decision processes thus impair capability regard-

less of networking capability.

• Maximising the number of platforms, maximising concurrent engage-

ments per platform and maximising platform persistence in proximity

to targets maximises parallelism and thus capability.

• Empirical experience supports conclusions derived from Amdahl’s

Law.

• Metcalfe and Amdahl models are complementary, not exclusive.

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Maximising Capability Gains

O ADO ACTIONOBSERVATION

‘MAXIMISE CONNECTIVITY’‘MINIMISE SERIAL CHAINS’‘MAXIMISE SENSOR CAPABILITY’

DECISIONORIENTATION

‘MAXIMISE PARALLELISM’

23

A22−23

23

A22−23

23

A22−23

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Minimising an Opponent’s Gains

• Given two mutually opposed networked systems, maximising own

capability requires:

1. Maximising number of ISR elements

2. Maximising connectivity (and link capacity)

3. Maximising parallelism

4. Minimising serialism

• Minimising the opponent’s capability requires:

1. Reducing the opponent’s number of ISR elements

2. Minimising the opponent’s connectivity (and link capacity)

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Minimising Opposing ISR Capability

RADARACTIVE

LR AAM LAUNCH

BOOSTER JETTISON (R−172)

MIDCOURSE INERTIAL GUIDANCE

R−37

Kh−31 Mod.1

Kh−31 Mod.2

(c) 2003, Carlo Kopp

HOMING

Counter AWACS/AEW&C Role (2 x Kh−31, R−37 or R−172)

R−172

TERMINAL


~215 NMI (R−37/R−172)

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Minimising Opposing Connectivity



L−BAND HIGH POWER JAMMING

Distance to Datalink Transmitter Distance to Jammer

Su−30/32 Electronic Attack Role (2−5 x High Power Jammer Pods)

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Minimising Opposing Connectivity

L−BAND HIGH POWER JAMMING

(c) 1

998,

200

4 C

arlo

Kop

p

Tanker Orbit

Jamm

er Fo

otp

rint

Datalink Relay

Datalin

k Ch

ann

el

Distance to Datalink TransmitterDistance to Jammer

Hostile Support Jammer

Wedgetail Orbit

Datalink Channel

Datal

ink

Chann

el

Inbound Hostiles

ISR Data Source

Defensive Fighter CAP

THE DATALINK AND ISR JAMMING PROBLEM

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Conclusions

• Amdahl’s Law provides a valuable abstraction for modelling the im-

pact of the Decision-Action phases of the OODA loop on system

capability gains.

• Amdahl’s Law complements Metcalfe’s Law by providing for a com-

plete abstraction to model OODA loop behaviour.

• Amdahl’s Law presents a model which relates achievable numbers

of engagements to time.

• Metcalfe’s Law, conversely, presents capability gains indirectly, as it

measures utility in terms of connectivity.

• Fusion of Boyd, Metcalfe and Amdahl provides an intellectual frame-

work for understanding capability gains in networked warfighting sys-

tems.

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End Presentation

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Revision Information

This document is currently at revision level:

$Id: CSE-3141-2004.tex,v 1.1 2004/02/06 12:34:52 carlo

Exp carlo $

Boyd, Metcalfe and Amdahl - Air Power Australia · MONASH University Computer Science & Software...

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