Simulation and Analysis of Cascading Failure in Critical Infrastructure

Transcription

1 Simulation and Analysis of Cascading Failure in Critical Infrastructure Robert Glass 1, Walt Beyeler 1, Kimmo Soramäki 2, Morten Bech 3 and Jeffrey Arnold European Central Bank 3 Federal Reserve Bank of New York NISAC s core partners are and Los Alamos Laboratory. is a multiprogram laboratory operated by Corporation, a Lockheed Martin Company, for the United States Department of Energy under contract DE-AC4-94AL85. Los Alamos Laboratory is operated by the University of California for the United States Department of Energy under contract W-745 ENG-36.

2 First Stylized Fact: Multi-component Systems often have power-laws & heavy tails Big events are not rare in many such systems log(frequency) Earthquakes: Guthenburg-Richter Extinctions, Forest fires Wars, Epidemics, Cities heavy tail region Traffic jams, Stock crashes Power Blackouts Telecom outages log(size)

3 Power Law - Critical behavior Phase transitions Dissipation Equilibrium systems: e.g., Magnets & the Curie point Correlation What keeps a non-equilibrium system at a phase boundary? External Drive T c Temperature

4 1987 Bak,, Tang, Wiesenfeld s Sand-pile or Cascade Model Lattice Drive Relaxation Cascade from Local Rules Self-Organized Criticality power-laws fractals in space and time

5 Second Stylized Fact: Networks are Ubiquitous Food Web Molecular Interaction New York state s Power Grid Illustrations of natural and constructed network systems from Strogatz [21].

6 Special properties of the Scale-free network Power-law degree distribution Hierarchical with King-pin nodes Properties: vulnerable to informed attack tolerant to random failure

7 Our Conceptual Approach: Rules ON Networks for Bottoms up Simulation of Infrastructures PolyNet Built in Repast Adapt & Rewire Actors Other Networks Network Nodes Links Tailored Interaction Rules Drive Dissipation

8 Development & Applications Abstract Studies Stylized Physical Infrastructure Applications: High Voltage Electric Power Grids Payment and Banking Systems Information Networks Physical + SCADA + Market + Policy Forcing Stylized Social Applications: Epidemics Social/Report Network Evolution Self-organized Terrorist/Extremist groups Crisis and recovery from WMD & Bio attacks Where we are headed: Combined Physical-Human Infrastructure Systems

9 BTW sand-pile on varied topology BTW Sand-pile Fish-net or Donut Cascade Size (nodes) size time time steps Square Lattice "Fish-net" Scale-free BTW Sand-pile Scale-free Random sinks Sand-pile rules and drive 1, nodes log(freq) log(frequency) log(size) Square Lattice "Fish-net" Scale-Free Roll-off points Roll-off points Linear (Scale-Free) Linear (Square Lattice "Fish-net")

10 Cascading Blackouts Fish-net or Donut size (nodes) size Fish-net Power-Grid: Square Lattice "Fish-net" steps time Scale-free size (nodes) 5 Sources, sinks, relay stations, 4 nodes DC circuit analogy, load, safety factors Random transactions between sources and sinks Power-Grid: Scale-Free Scale-free steps time

11 Cascading Liquidity Loss within Payment Systems banks payments Pay Balance Balance Trading Day Time Opening balance adapts to control risk Training Period Cascading Period Balance Time

12 Cascading Liquidity in Scale-free Network Patterned Transactions bank defaults Number of Failures Fedwire Time Realization 1, No Predictability Realization 1, 5% Predictability time liquidity Random removal vs Attack of the Highest Degree node Available Liquidity Fedwire Time Realization 6 Realization 7 Realization 4, Directed Realization 6, Directed time

13 Cascading Infectious Diseases Agent classes Teen Laura Glass s Groups Kids Teens Adults Seniors Links & Frequency me me Class Specific Parameters Infectivity Mortality Immunity Etc. me Nuclear Family Extended Family me Teen Extra me Classes (There are 6 of these) Parameters can change when Symptomatic Everyone 13

14 Influenza Epidemic in Structured Village of 1,: Increasing Realism 35 Number Infected Without Immunity Agent differentiation With Immunity & Mortality Behavioral Changes when Symptomatic time (days) Structure: Heterogeneous Network + Like with Like 14

15 Flu Epidemic Mitigation: Vaccination Strategies 3 number infected Seniors only (yellow) Current policy Kids & Teens! <6% required time (days) Network Structure + Physics of Transmission Process Allows Effective Mitigation Design

16 General Remarks: 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 Developmental directions Encapsulation/Integration -NABLE -BOF simulator Detailed applications with Domain experts Generalization/Abstraction Tools/Insight for Rapid deployment