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

0

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

2

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.