Introduction to Evacuation Modeling

Contents

• Introduction• Historical development of evacuation studies• Macro Models• Micro Models• Modeling techniques• Case studies

Introduction

Why we need to evacuate?

We understand that absolute prevention of disasters and restricting their spread may be impossible.

Evacuation of people from the hazardous region(s) is per se a way to reduce the ill effects of disasters and evacuation planning is prima facie a critical component in emergency management.

An evacuation model can be a tool to predict the evacuation pattern of people.

The use of evacuation models

• To compute the flow/ evacuation time• To serve as a prediction tool to determine the evacuation

pattern• To identify possible problems in building design• To provide visualization, if equipped, the evacuation

pattern• To perform parametric studies for different evacuation

scenarios by simulation• Etc.

Historical development of evacuation studies

Historical development of evacuation studies

• Research into quantifying and modeling the movement of people has been developed for about half a century.

• One of the earliest methods for calculating evacuation time was proposed by Togawa in 1955

• One of the earliest works focused on movement of people under various conditions was carried out by Fruin 1971

Historical development of evacuation studies (cont’d)

• The early works of evacuation research centered on empirical equations for calculating total evacuation.

• For example, a simplified calculation formula for “time required for escape” by Togawa[1], 1955:

v

k

NB

NT sae

- distance from last doorways to the crowd

NaN

eT

B

sk

v

- evacuation time

- number of people

- breadth of second doorway

- flow capacity

- walking velocity

Example of using Togawa’s equation

sv

k

NB

NT sae 92

2.1

48.34

1.13

208

Consider a cinema

smpersonsN /1.1

personsNa 208

mB 3

mks 48.34smv /2.1

Minimum evacuation time:

Some other calculation methods/ equations – flow capacity approach

• Melinek and Booth [2]• Predtechenskii and Milinskii [3]• Jake Pauls [4]

[2] Melinek SJ and Booth S, "Current Paper CP 95/97," Building Reserach Establishment, Borehamwood 1975.

[3] Predtechenskii V M, Milinskii A I, Planning for foot traffic flow in building, Stroiizdat Publishers, Moscow, 1969 .

[4] Pauls J, Fires and Human Behavior. New York: John Wiley and Sons, 1980.

Example: Multistory Buildings• Consider a 6-story academic building in a school, the

layout plans of all the floors are same:

Classroom40 persons

Stair 1 Stair 2Classroom40 persons

Classroom40 persons

Classroom40 persons

Classroom40 persons

Floor Plan

Assume: total number of population is 1200 persons; total width of stairs is 3m;Height of each floor is 3m

1. According to the Togawa equation:

sv

k

NB

NT sae 256

2.1

725.88

1.13

2/1200

2.2223.03

2/1200

p

2. According to the empirical method by Pauls:

spT 290081.068.0 73.0

Evacuation Time

Population per meter of effective stair width

Evacuation Time

Limitations of the empirical equations

• Provide only the estimation of total movement time

• Accuracy questionable, in particular for large population crowd flow situations

• Neglect the actual evacuation procedures• Not capable of predicting evacuation pattern in a

building

Research on Crowd Movement

J Fruin researched crowds in the early 1970's [5]

His book Pedestrian Planning and Design has been cited in many of the present guidelines for pedestrian planning. This research has become the standard for many subsequent building design and planning operations.

[5] J.J.Fruin, Pedestrian Planning and Design, Revised ed.: Elevator World Educational Services Division, Mobile, AL, 1987.

The LoS (level of service) concept• Fruin describes six levels of service for walkways,

stairways, and queuing.

A-standing and free circulation

C-standing restricted circulation

The Fruin Data v LoS

• Fruin also reports empirical method for calculate speed of movement varying with the level of service.

• Level A provides the highest standard with the least chance of congestion; level F provides the lowest.

• For emergency movement and limited space situations, levels of service C,D, and E are suggested

Walking Speed-Density Relation

The empirical relationships between crowd densities and velocities (extracted from Thompson and Marchant [6])

[6] Thompson PA, Marchant EW. Computer and fluid modelling of evacuation. Safety Science. 1995, 18: 277-289

With the rapid development of computer technologies, evacuation research has concentrated on computer-based models since the 1980s.

Types of computer-based evacuation models:

Evacuation Models

Macro models Micro models

Continuous DiscreteCoarse Network Models

Static Network Dynamic Network

Macro Models/ Coarse network models

Macro Models/ Coarse Network Models

• Regard the movement of crowd as fluid flow• Not paying attention to individual parameters• Always are coarse network flow models• Examples: EVACNET [7], EXITT [8], Exit89 [9]

[7] Kisko, T.M. and Francis, R.L., 1985. “EVACNET+: A computer program to determine optimal building evacuation plans”, Fire Safety J., 9:211-220

[8] EXITT/ Hazard Model, Building and Fire Research Laboratory, National Institute of Standard and Technology, Gaithersburg, M.D

[9] Fahy, RF, "Exit89 - An evacuation model for high-rise buidlings - recent enhancements and example applications", Proccedings of International Conference on Fire Research and Engineering, Orlando, NIST & SFPE, 332-340, 1993

Macro Modeling ProceduresResolve the geometry of building

into a network structure consisting of nodes and arcs

Define the capacity of the nodes and the flow capacity of the arcs

Define the routing plan

At each time step, move people from node to node iteratively

Network representation in a coarse network model (macro model)

1V

2V

3V 5V

4V

6V

Nodes: components of the building

Arcs: viable passageways between the defined nodes

Capacity of node: the upper limit on the number of people that can be contained in the building component

Flow capacity of arc: the upper limit on the number of people that can traverse

Node

Arc

Example of network representation of a building

Example:EVACNET4*

• Developed by Thomas Kisko; enhanced version of EVACNET+ developed by Francis and Kisko in 1984

• A user-friendly interactive computer program that models building evacuations.

• Accepts a network description of a building and information

• Produces results that describe an optimal evacuation of the building (minimized the time)

*Free downloaded from “http://www.ise.ufl.edu/kisko/files/evacnet/#links”

Network Representation in EVACNET4

Destination

Work place

Hall

Lobby

Stairwell

Initial content Capacity

Capacity and travel time

Pros and Cons of Macro Models

• Provide results of evacuation times• Easy to supply input data• Less computational demand• Easy to developed as optimization models

Pros:

Cons:

• Ignore the population’s individuality• Not providing detailed calculation results of individual

movement• Exact evacuation pattern cannot be visualized

Micro Models

Micro Models

• Treat each occupant as an active agent• Track exact locations of each individual• Some consider personal behavior• Examples: SIMULEX [10], EXODUS [11], SGEM[12], etc

[10] Thompson PA, Marchant EW. A computer model for the evacuation of large building populations. Fire Safety Journal. 1995, 24: 131-148

[11] Galea ER, Galparsoro JMP. EXODUS: An Evacuation Model for Mass Transport Vehicles. Fire Safety Journal. 1994, 22: 341-366

[12] Lo SM, Fang Z, Lin P, Zhi GS. An Evacuation Model: the SGEM Package. Fire Safety Journal. 2004, 39:169-190

Micro Models (cont’d)

• Discrete: The space are divided into grids; the coordinates of people are discrete; (EXODUS,SIMULEX)

• Continuous: the coordinates of people are continuous. (SGEM, Social force model)

With respect to representation of space, there are two modeling methods:

Example: Simulex

Visualization of simulation output in Simulex

Pros and Cons of Micro Models

• Providing detailed calculation results of individual movement

• Individual behavior can be added to the model

Pros:

Cons:

• Difficult to supply input data• Hugh computational demand

Evacuation model can also be classified in accordance with their

modeling techniques ……….

Modeling Techniques

Modeling Techniques

Optimization Models

Simulation Models

Static Network Flow

Dynamic Network Flow

Random Walker Model

Cellular Automaton Model

Social Force Model

Magnetic Force Model

Agent-based Model

Optimization Models

• Produces results that describe an optimal evacuation of the building

• Assumes that people are evacuated as quickly as possible

A Static Network Flow ApproachStatic flow (Ford and Fulkerson, 1962) theory has been widely adopted

to optimize the evacuation planning, and the most classic is the minimum cost flow problem.

Virtual source

Virtual sink

Source Nodes Destinations

Objective: minimize the total time required for evacuation

Send the occupants from the source nodes to destinations via the network

A Dynamic Network Flow Approach

• Based on the static networks• Expand the network over a time horizon T

Static Networks Dynamic Networks

The network structure and properties

are unchangeable

The network parameters such as travel time,

arc capacity and node capacity

are time-varying

Dynamic Network Vs. Static Network

Under a fire, the capacity of a passageway may decreased or totally blocked due to the development of smoke

Dynamic network models are more suitable for evacuation optimization with the time-varying features.

Problem Studied

• Evacuation problem modeled as quickest flow problem in dynamic networks.

• Definitions: Dynamic flow network (G,u,t,S,T) is a directed graph G =

(V,E) with edge capacity uxy > 0 and transit time txy > 0 for every edge xy and set of sources (rooms) and set of sinks (final exit points).

A Dynamic Quickest Flow Model

... ...

... ...

...... ... ...

... ...

......

Source nodes: regions at risk; departure time istime-dependent

Safety Destinations

Network: parameters are time-varying

)()(),( 0

txt ijEji

ij

T

t

Destroyed by disasterOptimization objective:

Min.

Each arc has a time-varying post capacity and travel time: )(tij

Flow on arc(i,j):Dynamic capacity:

)(txij

T

tij

T

t

tstx00

)()(

)()()( tytxtx ijiij

)()( tutx ijij

)()( tCtx iij

s.t.

Initial flow: )(tS )(tuij

Each node has a time-varying capacity: )(tCi

)(tuij

: time-varying maximum capacity;)(tuij)(tij : time-varying travel time ;

)(txij : flow on arc (i,j);)(tS : supply at source at t;

: flow waiting time at vertex i;)(tCi: dynamic node capacity; )(tyi

t :next time.

Magnetic Force Model

• The underlying theory (Okazaki 1979; Okazaki and Matsushita 1993) was developed on the basis of magnetic theory.

• Assumes that each entity (person or obstacle) has a positive pole, while the target location has a negative pole

• Each person is driven by two forces: magnetic force and force to avoid the collision

• Not much development reported

Social Force Model

• Proposed by Dirk Helbing et al. in 1992• Regarding the persons as objects• The movement of people follows Newton’s second law:

321

)(FFF

dt

tdvm i

mv t

1F 2F

3F

- mass

- velocity

- time

- force toward desired direction

- repulsion force from others

- attractive effects

An additional fluctuation item can be added to the equation to account for the behavioral reaction of the evacuee

Destination

“Social Forces” exerted to a person

Move in desired direction

Repulsive effect of others

Attracted by others (friends)

1F

Social Force Model (cont’d)

The simulation results are capable of describing several observed collective phenomena :lane formation, oscillation at bottleneck, and clogging

Example of Social Force Model

Cellular Automata Model• Cellular Automata were invented by mathematicians Neuman and

Ulam (Wolfram 1986). • A simple CA model know as N-S model was introduced to model

vehicular motion (Nagel and Schreckenberg, 1992)• The space is divided into discrete cells, and each cell can have one

of a finite number of states.(e.g. 0-void or 1-occupied. )

Cellular Automata Grid

Cellular Automata Model(cont’d)Simple rules are defined to determine what the state of each cell will change to

The preferred walking direction can be presented via a 3×3 matrix and each element denotes the probability of next step

Basic rules• Computing probabilities statistically

1. Moving forward and backward• Given mean speed and its deviation ),( v

or

v

h

l

p0 p1p-1

Basic rules (Cont’d)2. Moving transversally

• Given mean speed and its deviation

3. Filling the transition matrix

),( to q-1

q0

q1

Experimental results of CA Model• Evacuation of a large room

– Discrete floor field– Only allowed to move in 4 directions

Random Walker Model• Presented by Tajima et al in 1993• The pedestrians move from cell to cell on a square

lattice in three directions: forward, upward, download• The directions are assigned with different transition

probabilities

Relationship between crowd flow velocity and crowd density

0

0. 2

0. 4

0. 6

0. 8

1

1. 2

1. 4

1. 6

1. 8

0 1 2 3 4 5 6 7

Density (Person/square metre)

Wal

king

Vel

ocity

(m/s

)Green GuideTogaw aGas lattice modelPredtechenskiiFruinAnsoHankinEquation 1

Eq 1: y = 0.0412x2 - 0.59x + 1.867

5

y = 0.0412x2 – 0.59x + 1.867

Detailed information given in: Lo SM, Fang Z, Zhi GS. An Evacuation Model: the SGEM Package. Fire Safety Journal. 2004, 39: 169-190

By using the above mentioned approach, a relationship between the crowd flow density and crowd flow velocity has been generated (3,000 runs)

2.41.0

2.475.0867.159.00412.0

75.04.1

u 2i

A flow equation can be expressed as:

Study on Required Number of Exits in a Room: Application of Random Walker Model

• A random walker model is developed to calculate the evacuation time for a room

• The rule of calculating walking probabilities (D is the drift point):

(a) Pt,x = D + (1 – D) / 3; Pt,y = (1 – D) / 3; Pt,-y = (1 – D) / 3(b) Pt,x = 0; Pt,y = 1 / 2; Pt,-y = 1 / 2(c) Pt,x = D + (1 – D) / 2; Pt,y = 0; Pt,-y = (1 – D) / 2(d) Pt,x = D + (1 – D) / 2; Pt,y = (1 – D) / 2; Pt,-y = 0(e) Pt,x = 1; Pt,y = 0; Pt,-y = 0(f) Pt,x = 0; Pt,y = 0; Pt,-y = 1(g) Pt,x = 0; Pt,y = 1; Pt,-y = 0(h) Pt,x = 0; Pt,y = 0; Pt,-y = 0

• The size of the room is 10m×10m;each grid is 0.5m×0.5m

• If the width of exit is 1.2m, then evacuation time =117s

0s 50s 100s

Drift Point Vs. Evacuation TimeThe Effect of Drift Point on the Evacuation Time

0

10

20

30

40

50

60

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Drift Point

Eva

cuat

ion

Tim

e (s

)

Number of People is50

Number of People is100

Number of People is150

Evacuation time drops significantly when drift point is increased to 0.6. Before or after this critical point the evacuation time varies slightly. The nature of this curve may lie in a phase transition process with the increase of drift point. The crowd is transformed from passive state to active state.

Door Width Vs. Evacuation Time

The Effect of Door Width on the Evacuation Time

02468

1012141618

5 10 15 20 25 30 35 40 45 50 55 60 65 70

Number of People

Ev

ac

ua

tio

n T

ime

(s

)

1 Exit

2 Exits

When the number of people is less than 40, there is no significant difference in two curves.

Simulation ModelsExample: Simulex, Exodus,

SGEM, ……. etc

Case Studies

Using the SGEM for illustration

References:

Lo SM, Fang Z. A Spatial-Grid Evacuation Model for Buildings. Journal of Fire Science. 2000, 18(5): 376-394

Zhi GS, Lo SM, Fang Z. A Graph Based Algorithm for Extracting Units and Loops from Architectural Floor Plans for a Building Evacuation Model. Computer-Aided Design. 2003, 35: 1-14

Lo SM, Fang Z, Zhi GS. An Evacuation Model: the SGEM Package. Fire Safety Journal. 2004, 39:

169-190

Features in SGEM

• A microscopic simulation model• Able to capture the geometrical information from AutoCAD

architectural plans (general building plans)• AutoCAD-based Graphical User Interface• Animated Output• Mixed discrete/continuous modeling technique• Able to add behavioral rules to individuals• Route selection process on the basis of game theory included• Able to simulate over 100,000 evacuees’ movement (depends on

computer’s capacity)• Etc.

A grid of cells in zone

Simulation Outputs

Thank You!