Vulnerability of Complex Infrastructure Systems
Torbjörn Thedéen
Safety Research, KTH
•HAZARDS
• Nature-Acts of God: Earthquakes, Extreme floods, Thunder storms ...
• Failures of material ...• Human lapses• Organizational errors• Hackers• Terrorism• War
D a t a N e t w o r k
P o w e r N e tF i n a n c e N e t
T r a n s p o r t N e t w o r k
I N F R A S T R U C T U R E S
… … .
Info Stairs
Many dataClassical statistical analysis
Few dataLogical modelReliability methodsPRASubjective
Probabilities
Bayesian methods
Precursors, Incidents
•Research Areas
• Terrorist Groups• Motivation• Religious, political,
social, economic studiesConditional
• Power+possibilities
• Conditional Vulnerability
• Consequences given ´attacks´:
• Dams, transportation, power grids...
Vulnerability USA October 07
Vulnerability of Road Transportation Systems
(Erik Jenelius KTH)
Conditional Vulnerability
• Road systems modelled as a connected graph
• Conditioned of one link is out, the consequences are estimated:
• The increased total traffic time• The unsatisfied demand• The most ´important´ or one link at random
is taken out
Example
• Northern Sweden
• The average traffic is known
• The traffic for a disturbed net can be calculated
Unsatisfied veh/total00 - 0.00050.0005 - 0.00170.0017 - 0.00360.0036 - 0.00840.0084 - 0.024
0 200 400 Kilometers
Figur 6
Vehicles/day0 - 15931594 - 48114812 - 1053310534 - 1958619587 - 35742
0 200 400 Kilometers
Figur 2
Vehicle min/veh0 - 0.020.02 - 0.080.08 - 0.190.19 - 0.450.45 - 1.22
0 200 400 Kilometers
Figur 5
Vulnerability of Power Net
Power Generation
Power Transmission
Power Distribution and Consumption
Power Generation
Dam Safety and Security
Safety analysis OK, but security antagonistic threats??
Nuclear Power Plants. PRA safety OK,
Defense passive?
Power Nets - Vulnerability
• (Statistical Analysis of Collapses) Too few!
• Vulnerability analysis of empirical graph model – partly classisfied!
• Vulnerability analysis of idealized graph model (coupled branching processes)
•
Power law of large consequences, power grid
Power Net – Graph Model
Power stations
Transformers
400 kV
110 kV
220 V Consumers
…………
Powergeneration
Consumers
Branching Process
Limiting result
• One link is removed at random. The proportion of unserved consumers has in the limit a distribution with a right tail of power type exponent – 1.
Vulnerability and Terrorism
Terrorism
Motivation Terrorist groups
Basis Common goal
Cause fear, chaos and deaths!
TERRORISM AND DEFENSE
Enemy infrastructure
Criticalinfrastructure
?Partly known Known
Fighting Terrorism
• Knowledge or qualified guesses about probable terrorist groups, their goals and actions constitutes:
• Basis for our defence of infrastructures ...
• Basis for our actions against terrorist groups
Fight Between Two Networks
• Our critical infrastructures: power, transportation, data, finance, water ...
• KNOWN TO THE ENEMY!
• Enemy infrastructure: terrorist groups
• ALMOST UNKNOWN TO US!
Terrorist Network
Known links and nodesUnknown links and nodes
Sampling Procedures
• Random sampling of nodes/links
• In time or in time periods
• Markov sampling
• Markov sampling with side conditions
Estimates – random sampling
• Link distribution
• Shortest path
• Sampling in many time periods – (N, p):
• ML estimates of p and N (Size of the terrorist population)