A FORTUNE Article

1
Evacuation Planning Algorithms Qingsong
Lu Advisor Prof. Shashi Shekhar August 9, 2002
2
Outline

• Motivation
• What can GIS do
• Problem statement
• Related works
• A simple example
• Our approach
• Algorithms

3
Motivation

• Why we need evacuation planning?
• Civil defense under emergency and hazard
  situations
• Terrorist attacks (September 11th )
• Toxic agents released in a building, e.g. a
  stadium
• Tornado or hurricane approaching urban districts
• Urban Warfare
• Route planning for soldiers to a target in face
  of obstacles
• Crowd dispersion or evacuation

4
What can GIS do? - ESRI White Paper
GIS plays a significant role in each milestone
of the emergency planning process.
5
What can GIS do? - ESRI White Paper
Preparedness
GIS

• GIS can provide answers to questions
• What evacuation routes should be selected if a
  toxic cloud or plume is accidentally or
  intentionally released from a known plant,
  storage facility, or terrorist device based on
  different wind patterns?
• What are alternative routes?
• How will people be notified?
• Will the road networks handle the traffic?

6
What can GIS do? - A Fortune Article
( Screenshot from www.fortune.com )
7
What can GIS do? - A Fortune Article

• Base Map- Where is source of the plume?
• County map showing land, water, bridges, and
  roads,
• Source Government information system

• Chemical Plume Modeling- Where will plume go?
• Map showing plume dispersion in the next few
  hours,
• Source Plume modeling and prediction tools

• Weather Info- What is the current weather?
• Radar image of current weather,
• Source National Weather Services

• Evacuation Analysis- How to evacuate?
• Map of major highways,
• Source State DOT
• - Issue evacuation instruction to affected people

• Demographic Info- Where are the people?
• Map of population density overlaid on the county
  map
• Source U.S. Census Bureau database

Question not answered How to produce
evacuation plan ?
Evacuation planning
( Images from www.fortune.com )
8
Lessons We Learned
Hurricane Andrew

• Florida and Louisiana, 1992
• No effective evacuation planning
• Traffic congestions on all highways
• Great confusions and chaos

( National Weather Services)
"We packed up Morgan City residents to evacuate
in the a.m. on the day that Andrew hit coastal
Louisiana, but in early afternoon the majority
came back home. The traffic was so bad that they
couldn't get through Lafayette." - Morgan
City, Louisiana Mayor Tim Mott
( http//i49south.com/hurricane.htm )
( www.washingtonpost.com)
9
Lessons We Learned
Black Hawk Down

• Mogadishu, Somalia
• October 3, 1993
• Soldiers trapped by roadblocks
• No alternate evacuation routes
• Rescue team got lost in alleys having no
  planned route to crash site
• 18 Army Rangers and elite Delta Force soldiers
  killed, 73 wounded.

( Mark Bowden, Black Hawk Down A Story of Modern
War )
10
Problem Statement

• Given
• Transportation network (e.g. building floor map,
  city roadmap) with capacity constraints
• Initial number of people to be evacuated and
  their initial location
• Evacuation destinations
• Output
• Scheduling of people to be evacuated and the
  routes to be taken
• Objective
• Minimize total time needed for evacuation
• Minimize computational overhead
• Constraints
• Capacity constraints evacuation plan meets
  capacity of the network

11
Related Works

• Simple network flow algorithms
• Exponential running time
• Implementation EVACNET
• University of Florida and National Fire Research
  Center, 1980s
• Produce optimal plan
• High computational overhead
• Integer programming algorithms
• Hoppe and Tardos (1995)
• The only known polynomial algorithm
• Produce integer optimal solution
• Not practical to implement
• Their algorithm repeatedly minimizes
  submodular functions using the ellipsoid method,
  and is therefore not at all practical. -
  L.Fleisher

12
Related Works

• Heuristic approach
• EXIT89(National Fire Protection Association)
• Only compute shortest distance routes from source
  to staircase for each floor, may not be shortest
  route to destination
• Do not consider capacity constraints
• Only apply to high-rise building evacuation
• Better heuristic algorithms needed

13
A Simple Example Building Layout
Two-story building - Two Staircases - Two exits
on first floor
14
A Simple Example Node and Edge Definition
Nodes
Edges
15
A Simple Example

• Each node has
• Node capacity
• ( max. number of people the node can hold)
• Initial occupancy
• ( number of people at the node )
• Each edge has
• Edge capacity
• ( max. number of people can travel through this
  edge simultaneously )
• Travel time
• ( how long it takes to travel through this edge)

Max. cap 50
Init. Occup 10
Max cap 50
Init. Occup 5
Capacity6
Travel time3
Max. cap 65
Init. Occup 15
16
Node-Edge Graph Model
Node
N1, 50 (10)
Node ID, Max Capacity (Initial Occupancy)
(7,1)
N3, 30
N5, 6
N4, 8
(3,3)
(3,3)
Edge
(Max Capacity, Travel time)
(7,1)
(3,4)
(5,4)
Exit
N2, 50 (5)
N6, 10
N7, 8
Node ID
Second Floor
N9, 25
First Floor
(2,5)
(5,5)
(6,4)
(14,4)
(6,4)
EXIT 1
N11, 8
(8,1)
(3,3)
N10, 30
(6,3)
N8, 65 (15)
N13
(3,1)
(6,4)
N12, 18
(3,3)
N14
EXIT 2
17
Evacuation Plan Table 1
Number of people move though each edge starting
from each time interval
- Global based, assignment of flow to edges, -
Does not show routes
18
Evacuation Plan Table 2

• Individual based, divide flow into groups
• Show routes

19
Our Approach

• Model node occupancy and edge capacity as a time
  series instead of a fixed number.
• Representation
• For given node Ni
• Occup( Ni , t ) occupancy of node Ni at time
  point t
• For given edge Ni-Nj
• Cap( Ni-Nj ,t ) available capacity of edge
  Ni-Nj at time
  point t

20
Heuristic Algorithm 1

• 1. For each source node, find the shortest-time
  route from this source to any exits,
• (pick one if there is a tie)
• 2. Sort source nodes by its shortest route time,
  increasing order
• (if there is a tie, place the one with
  larger cut capacity first)
• 3. For each route, in the order of step 2
• For each time interval on this route,
  subtract the flow from the available edge
  capacity and update node occupancy
• flow used capacity of edge Ni-Nj at time t
  by this route
• flow min occup( Ni , t ) , cap( Ni-Nj , t
  )
• cap( Ni-Nj, t t traveltime(Ni-Nj) reduced
  by flow
• occup( Ni, t1 ) occup( Ni , t ) - flow
• occup ( Nj, ttraveltime(Ni-Nj) ) increased by
  flow
• 4. Make plan table from results of step 3 total
  flow amount for each edge for each time interval

21
Result Evacuation Plan
Number of people move though each edge starting
from each time interval
N8-N10 N10-N13 N1-N3 N3-N4 N4-N6 N6-N10 N2-N3 N3-N5 N5-N7 N7-N11 N11-N14
0 6 7 5
1 6 3 3 3
2 3 3 2
3 6 3
4 6 1 3 3
5 3 3 2
6 3
7 1
8 3 2
9 3 2
10 3 1
11 1
12
13 3 2
14 3 2
15 3 1
16 1
- 17 time units to evacuate, may use much more
time when routes are not disjoint - Nodes closer
to destination has higher priority.
22
Heuristic Algorithm 2

• While any non-destination node occupancy gt 0
• Find shortest time path SP from any source S to
  any destination node.
• Cap(SP) smallest edge capacity on SP
• flow min Occup(S), Cap(SP)
• Capacity of edges for each time interval on SP
  reduced by flow
• Occupancy of each outgoing nodes on SP reduced
  by flow
• Occupancy of each incoming nodes on SP
  increased by flow
• Need to generalize shortest path algorithm to
  work with time series edge capacity and
  traveltime
• More fairness for nodes farther to the
  destination
• Implementation in progress

23

• Questions or Comments ?
• Thank you.