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MONASHUniversity
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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
SERIAL WORKLOADCOMPONENT
SERIAL WORKLOADCOMPONENT
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
(c) 2003, Carlo Kopp
~215 NMI (R−37/R−172)
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Minimising Opposing Connectivity
(c) 2003, Carlo Kopp
(c) 2003, Carlo Kopp
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 $