sandia national laboratories nisac’s core partners are sandia national laboratories and los alamos...

SandiaNationalLaboratories

NISAC’s core partners are Sandia National Laboratories and Los Alamos National Laboratory. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy under contract DE-AC04-94AL85000. Los Alamos National Laboratory

is operated by the University of California for the United States Department of Energy under contract W-7405 ENG-36.

Simulation and Analysis of Cascading Simulation and Analysis of Cascading Failure in Critical InfrastructureFailure in Critical Infrastructure

Robert Glass1, Walt Beyeler1, Kimmo Soramäki2, Morten Bech3 and Jeffrey Arnold3

1Sandia National Laboratories2European Central Bank

3Federal Reserve Bank of New York



log(Size)

log(

Fre

quen

cy)

“Big” events are notrare in many such systems

Earthquakes: Guthenburg-Richter

Wars, Epidemics, Cities

Power Blackouts Telecom outages“heavy tail”

region

Extinctions, Forest fires

Traffic jams, Stock crashes

First Stylized Fact: Multi-component Systems First Stylized Fact: Multi-component Systems often have power-laws & “heavy tails”often have power-laws & “heavy tails”



Dissipation

Temperature

Cor

rela

tion

Tc

External Drive

What keeps a non-equilibrium system at a phase boundary?

Equilibrium systems:

Power Law - Critical behavior – Phase transitionsPower Law - Critical behavior – Phase transitions

e.g., Magnets & the Curie point



Drive

1987 Bak, Tang, Wiesenfeld’s “Sand-pile” or 1987 Bak, Tang, Wiesenfeld’s “Sand-pile” or “Cascade” Model“Cascade” Model

Cascade fromLocal Rules

RelaxationLattice

“Self-Organized Criticality”power-laws

fractals in space and time



Illustrations of natural and constructed network systems from Strogatz [2001].

Food WebFood Web

New York state’sNew York state’sPower GridPower Grid

MolecularMolecularInteractionInteraction

Second Stylized Fact: Networks are UbiquitousSecond Stylized Fact: Networks are Ubiquitous



tolerant to random failure

Properties:vulnerable to

informed attack…

Hierarchical with “King-pin” nodes

Special properties of the “Scale-free” networkSpecial properties of the “Scale-free” network

Power-law degree distribution



NetworkNodesLinks

OtherNetworks

Drive

Dissipation

ActorsAdapt& Rewire

PolyNetBuilt in Repast

Tailored Interaction Rules

Our Conceptual Approach: Rules ON Networks Our Conceptual Approach: Rules ON Networks for Bottoms up Simulation of Infrastructuresfor Bottoms up Simulation of Infrastructures



Stylized Physical Infrastructure Applications:High Voltage Electric Power Grids

Payment and Banking Systems

Epidemics

Self-organized Terrorist/Extremist groups

Stylized Social Applications:

Social/Report Network Evolution

Where we are headed:Combined Physical-Human “Infrastructure” Systems

Information Networks

Crisis and recovery from WMD & Bio attacks

Physical + SCADA + Market + Policy Forcing

Development & ApplicationsDevelopment & Applications

Abstract Studies



BTW sand-pile on varied topologyBTW sand-pile on varied topology

Fish-netor Donut

Scale-free

BTW Sand-pile

0

20000

40000

60000

80000

100000

120000

1 59 117 175 233 291 349 407 465 523 581 639 697 755 813 871 929 987

time steps

Cas

cad

e S

ize

(no

des

)

Square Lattice "Fish-net" Scale-free

time

size

BTW Sand-pile

-6

-4

-2

0

2

4

6

0 1 2 3 4 5 6

log(size)lo

g(f

req

uen

cy)

Square Lattice "Fish-net" Scale-Free

Roll-off points Roll-off points

Linear (Scale-Free) Linear (Square Lattice "Fish-net")

log(size)log(

freq

)Random sinksSand-pile rules and drive10,000 nodes



Cascading BlackoutsCascading Blackouts

Fish-netor Donut

Scale-free

Sources, sinks, relay stations, 400 nodes

Power-Grid: Scale-Free

0

50

100

150

200

250

300

350

0 1000 2000 3000 4000 5000 6000 7000

time stepssi

ze (

no

des

)

timesi

ze

Scale-free

Power-Grid: Square Lattice "Fish-net"

0

50

100

150

200

250

300

350

400

450

0 50000 100000 150000 200000

time steps

size

(n

od

es)

time

size

Fish-net

DC circuit analogy, load, safety factorsRandom transactions between sources and sinks



Trading Day

0Openingbalance

adapts tocontrol risk

0

Pay

Training Period

Cascading PeriodB

alan

ce

Time

Bal

ance

0

Bal

ance

Time

Cascading Liquidity Loss within Payment SystemsCascading Liquidity Loss within Payment Systems

banks

payments



Cascading Liquidity in Scale-free NetworkCascading Liquidity in Scale-free Network

Fedwire

0

100

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0 100000 200000 300000 400000 500000 600000 700000 800000 900000 1000000

Time

Nu

mb

er o

f F

ailu

res

Realization 1, No Predictability Realization 1, 50% Predictability

Patterned Transactions

time

bank

de

faul

ts

Random removal vs Attack of the Highest Degree node

Fedwire

0

5000

10000

15000

20000

25000

30000

35000

0 200000 400000 600000 800000 1000000 1200000

Time

Ava

ilab

le L

iqu

idit

yRealization 6 Realization 7 Realization 4, Directed Realization 6, Directed

time

liqu

idit

y


SandiaNationalLaboratories 13

Everyone

me

Nuclear Family

me

Classes (There are 6 of these)

me

Extended Family

me

Teen Extra

me

Cascading Infectious DiseasesCascading Infectious Diseases

KidsTeensAdultsSeniors

Agent classes

•Infectivity•Mortality•Immunity•Etc.

Class Specific Parameters

Teen Laura Glass’s Groups

Links&

Frequency

Parameters can change whenSymptomatic



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time (days)

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time (days)

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14

Without Immunity

With Immunity & Mortality

Behavioral Changes when Symptomatic

Agent differentiation

Influenza Epidemic in Structured Village of 10,000:Influenza Epidemic in Structured Village of 10,000:Increasing RealismIncreasing Realism

Structure: Heterogeneous Network + Like with Like



Flu Epidemic Mitigation: Vaccination Strategies Flu Epidemic Mitigation: Vaccination Strategies

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0 20 40 60 80 100 120

time (days)

nu

mb

er

infe

cte

d

Kids & Teens!

Current policy

Seniors only (yellow)

<60% required

Network Structure + Physics of Transmission ProcessAllows Effective Mitigation Design



General Remarks:General Remarks:

Developmental directions

Generalization/Abstraction

Detailed applications withDomain experts

Concepts from Complexity Science are valuable and allow a simulation approach for critical infrastructures that is flexible and has wide

ranging applications

Focus on POLICY

Tools/Insight for Rapid deploymentEncapsulation/Integration-NABLE-BOF simulator

sandia national laboratories nisac’s core partners are sandia national laboratories and los alamos...

Documents

constructed network

equilibrium systems

wiesenfelds sandpile

heterogeneous network

simulation approach

multicomponent systems

scalefree networktolerant

phase boundary