Decision Making for Disaster Protection, Evacuation, and ...ngns/docs/Review_2010... · Decision...
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ONR MURI: Next Generation Network Science
Decision Making for Disaster Protection, Evacuation, and Response
Danielle Bassett, Jean Carlson, Nada Petrovic, Evan Sherwin University of California, Santa Barbara
29 October 2010
David Alderson, Emily Craparo, William Langford, Brian Steckler Naval Postgraduate School
Theory Data Analysis
Numerical Experiments
Lab Experiments
Field Exercises
Real-World Operations
• First principles • Rigorous math • Algorithms • Proofs
• Correct statistics
• Only as good as underlying data
• Simulation • Synthetic,
clean data
• Stylized • Controlled • Clean,
real-world data
• Semi-Controlled
• Messy, real-world data
• Unpredictable • After action
reports in lieu of data
Bassett
Info exchange and collective behavior
Alderson
Disaster response
Craparo
Emergency decision-making
Why study disasters and disaster response?
• Layered view of society, enabled by networks
• At the boundary of network science
– Networks with humans in-the-loop
– Urgent need to take action, with lots of uncertainty
• Immediate relevance (domestic/international)
• Desperate need for theory
– Interesting physical phenomena
– Boundary of physical science and human behavior
– Intersection with public policy
• Opportunities for data collection, modeling
– Ongoing field experiments/exercises/real events
Incident timescales vary by disaster type
minutes hours months
earthquakes
forest fires
tornado
hurricane
flood
minutes
weeks
months
event duration
event warning volcano
tsunami
drought
epidemic
extreme temp
these timescales determine what types of mitigation are possible
famine
days weeks
hours
days
Can shape the evolution of the disaster itself
Build resilience. Recover quickly.
Evacuation
Informed by real-world disaster operations
• Port Au Prince, Haiti – March 21-27 2010 – 2 months after earthquake – An estimated 70% of
buildings were destroyed – Heavy piles of concrete are
will take years to remove
• A large population is living in tent cities with no plumbing or electricity – Concerns about disease
Haitian Community Hospital Waiting Room
NPS research collaboration on Hastily Formed Networks: connecting hospitals
Recent fires in Santa Barbara
Gap fire July 2008
Tea Fire Nov 2008 210 homes
Jesusita Fire May 2009 80 homes 14000 mandatory evacuation
Las Padres National Forest
UCSB
wildfire distributions and policy decisions
• Heavy tailed statistics – Most events => small
– Most losses => few largest events
– High variability=> large events are consistent with statistics
• Need to rethink policy for heavy-tailed distributions
Fires in Los Padres National Forest
Earthquakes
Evacuation
Public Policy
News & Information
Mitigation & Response
Complex Physical Phenomena
Social Networks
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4 Science data sets
+Los Padres Forest
+ HFire Simulation
HOT Cumulative
P(size)
size
Wildfire Simulation via (HFire): Carlson, Doyle, Peterson, et al.
HFire footprints
Data+ HFire
• Dynamics and Feedback • Robust, yet Fragile • Multiscale/Multiresolution
modeling and simulation
Ideal ongoing prototype for development of fundamental themes:
Complex Physical Phenomena
• HFire is a spatially explicit fire simulation based on the Rothermel fire spread equations
• Agreement with real wildfire data, FARSITE (forest service tool) and Modis satellite data for perimeters
Complex Physical Phenomena
Spatial Simplification: HFire Evan Sherwin, Jean Carlson, John Doyle,
Seth Peterson, Nada Petrovic
Simplified version still exhibits key features : • no topography or specific fuels maps • stochastic wind and a random fuel map • statistics match wildfire data and the full HFire. • helps identify key mechanisms for spread • quicker evaluation of long-term decisions
Complex Physical Phenomena
Dynamic Resource Allocation in Wildfire Suppression
Nada Petrovic, Jean Carlson, Dave Alderson
Motivation: Time dynamics are vital for fire response decisions • Fire evolves on the same timescale as
suppression effort • Fire will get worse over time • Response effort can mitigate severity • Limited resources Similar to: disease epidemics, oil spill
Key questions: When to send resources? How much to send?
Mitigation & Response
Fire as Birth and Death Process
Unburned
Burning (j)
Burned
Break region down into discrete units ‘parcels’
Can think of each parcels as geographic region that may be burning
Finite total area of forest => constraint on total number that can burn
β=spread rate per firelet
δ=extinction rate per firelet
Natural Extinction Firelet Death
Fire Spread Firelet Birth
Time until next event (birth or death) is random variable with distribution:
larger j => shorter interval to next event
Time series of simulated fires
Fires tend to die out
Fires tend to spread
β/δ<1
β/δ>1
“Drift”:
Fire Size Distributions depend on relative birth/death rates
• Our model produces power laws in general
• Exponent is characterized by spread/extinction rate
• Special case:
• spread=extinction
• exponent=-1/2 (dashed line) => matches real fire data
Suppression
Unburned
Burning(j)
Burned
Fire Spread
γ=rate at which suppression resources put out firelets
Natural extinction
Suppression
Suppression stabilizes the fire queue
Initial size vs. burn probability
The larger the fire (when you reach it), the more suppression resources that are needed to contain it.
Next steps: characterizing optimal policy decisions (and prepositioning)
Evacuation
Public Policy
News & Information
Mitigation & Response
Complex Physical Phenomena
Social Networks
VITAL Report: Rick Church and Ryan Sexton UCSB, April 2002
Evacuation
VITAL Report: Rick Church and Ryan Sexton UCSB, April 2002
Critical intersections
Exit (sink) locations
Legend
766 houses
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A Space-Time Flow Optimization Model for Neighborhood Evacuation
LTJG William P. Langford, USN M.S. Thesis, Operations Research Department
Naval Postgraduate School
March 2010
Goal: Develop a network flow optimization model that can be used to inform decision makers in the event of a short or no-notice evacuation.
Approach: Build a spatial network representation of a neighborhood and extend it into Space-Time.
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t t+1 t+2 Source node
Transshipment node
Sink node
Legend
Staying still
Movement between locations
Time-space network
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Spatial network
Building the space-time network
A Space-Time Flow Optimization Model for Neighborhood Evacuation
Simple network flow model captures first order behavior of the more time-intensive micro-scale traffic simulation.
• Our model’s ability to solve large problems quickly makes it a useful tool for disaster-preparation planning – Best case evacuation and clearing times – Impact of individual behavior on the group – Evacuation policy: critical intersections (traffic control)
Mission Canyon specifics • Staggering vs. simultaneous evacuation has little effect on
total clearing time: bottlenecks near canyon exit • Many intersections are critical because of
– the number of houses isolated if blocked, or – the large increase in clearing time if blocked.
Evacuation
Public Policy
News & Information
Mitigation & Response
Complex Physical Phenomena
Social Networks
Evacuation
News & Information
1. the way that agents exchange and update information,
2. the way that individual agents make decisions based on this information, and
3. the collective behavior that results from these decisions.
Our Interest in Evacuation Behavior
Evacuation
News & Information
Making Emergency Decisions with Uncertain Information
Emily Craparo, Jean Carlson,
Dave Alderson
Individual Decision Modeling
Many uncertainties exist:
• Time disaster will occur
• Intensity of disaster
• Consequences of being present during disaster
• Consequences of evacuating at time t
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Outcomes (deaths, property damage) depend on the
• severity of the disaster
• effectiveness of the response
– mitigation
– evacuation
Individual Decision Modeling
• A simple two-intensity model
– Disaster either occurs or not
• Evacuation has immediate cost
• Staying in a disaster is worse
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R
f+rt
0
f evacuate
stay
disaster no disaster
t1 t2 t3 t5 t4
stay stay stay stay
evac. evac. evac. evac. evac.
….
• The decision-maker (DM) has two options:
– Evacuate the area
– Stay and gather more information
Dynamic Programming Model
• Consider a disaster scheduled to occur (or not) at fixed time T.
• DP model primitives
– State space: probability that disaster will occur: 0<p<1.
– Actions and Costs:
– Transition probabilities:
• Evacuation is an absorbing state
• If DM chooses to stay:
R
f+rt
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f evacuate
stay
disaster no disaster
p (1+p)/2
p/2
w/ prob. p
w/ prob. 1-p
Dynamic Programming Model • General Bellman equation:
• For us, at time t<T:
• At time t=T:
• For the two-intensity problem, intensity PDF is described by p. 30
1( ) min ( , ) ( )t a t tJ s E c s a J s
(intensity PDF, ) min (intensity PDF, ) , (intensity PDF, 1)eJ t E c t E J t
Cost-to-go: no evacuation Cost to evacuate
(intensity PDF, ) min (intensity PDF, ) , (intensity PDF, )e sJ T E c T E c T
Cost of being present when disaster occurs
Cost to evacuate
Two-Intensity “Scheduled” Disaster at T=5: Computational Results
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Cost to stay as a function of intensity – only incurred at time t=T.
Cost to evacuate as a function of lead time, intensity.
Value function: J(i1, i2, t)
Policy: 0=stay, 1=evacuate.
i2 count
i1 c
ou
nt
i2 count
i1 c
ou
nt
(as with J)
Optimal policy is a threshold policy at each time step.
Two-Intensity “Scheduled” Disaster at T=5: Computational Results
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Now, waiting is not penalized in the first few time periods.
Optimal policy is a “waiting period” followed by a threshold policy.
Two-Intensity “Scheduled” Disaster at T=5: Computational Results
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Now, evacuating late is no better than staying (and again, waiting is not penalized initially).
Optimal policy is a “waiting period,” then a threshold policy, then a “riding out the storm” period.
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Analytical Results
• Under certain conditions,
• the optimal policy is defined by a receding series of thresholds on p.
• If conditions do not hold, optimal policy is a more complicated threshold function.
( ( ))i
i
fp
f R r
Threshold at t=T-1
Threshold at t=T-2
R r1
r2
f
10
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R rr
0 1
0 1 0
( )( )
( ) ( )
R r R rf
r r R r
Summary
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• DP model results confirm intuition on optimal policies
• Threshold policy as start for descriptive modeling
• Ongoing work:
• Decision problem variations
• p evolves differently (e.g., historical data)
• Expanded action set – e.g., prepare to evacuate
• Application to other domains
• e.g., small vessel engagement
• Are DMs really rational? Behavioral experiments.