1. Introduction to Evacuation Modeling

2. Contents Introduction Historical development of evacuation studies
Macro Models
Micro Models
Modeling techniques
Case studies

3. Introduction

4. Why we need to evacuate?

5. 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.

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

7. 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.

8. Historical development of evacuation studies

9. 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

10. 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:
- evacuation time
- number of people
- breadth of second doorway
- flow capacity
- walking velocity
- distance from last doorways to the crowd

11. Example of using Togawa’s equation
Consider a cinema
Minimum evacuation time:

12. 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,
[4] Pauls J, Fires and Human Behavior. New York: John Wiley
and Sons, 1980.

13. Example: Multistory Buildings
Consider a 6-story academic building in a school, the layout plans of all the floors are same:
Floor Plan
Assume: total number of population is 1200 persons; total width of stairs is 3m;Height of each floor is 3m

14. 1. According to the Togawa equation:
Evacuation Time
2. According to the empirical method by Pauls:
Population per meter of effective stair width
Evacuation Time

15. 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

16. 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.

17. The LoS (level of service) concept
Fruin describes six levels of service for walkways, stairways, and queuing.
A-standing and free circulation
B-standing and partially restricted circulation
C-standing restricted circulation
D-circulation is severely restricted
E-circulation within the queue is not possible
F-no movement is possible within the queue

18. The Fruin Data v LoS

19. 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

20. 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:

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

22. Types of computer-based evacuation models:
Macro models
Micro models
Coarse Network Models
Continuous
Discrete
Static Network
Dynamic Network

23. Macro Models/ Coarse network models

24. 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., “EVACNET+: A computer program to determine optimal building evacuation plans”, Fire Safety J., 9:
[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, , 1993

25. Macro Modeling Procedures
Resolve 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

26. Network representation in a coarse network model (macro model)
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

27. Example of network representation of a building

28. 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 “

29. Network Representation in EVACNET4
Hall
Stairwell
Capacity and travel time
Initial content
Capacity
Lobby
Work place
Destination

30. 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
Cons:
Ignore the population’s individuality
Not providing detailed calculation results of individual movement
Exact evacuation pattern cannot be visualized

31. Micro Models

32. 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:
[11] Galea ER, Galparsoro JMP. EXODUS: An Evacuation Model for Mass Transport Vehicles. Fire Safety Journal. 1994, 22:
[12] Lo SM, Fang Z, Lin P, Zhi GS. An Evacuation Model: the SGEM Package. Fire Safety Journal. 2004, 39:

33. Micro Models (cont’d)
With respect to representation of space, there are two modeling methods:
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)

34. Example: Simulex
Visualization of simulation output in Simulex

35. Pros and Cons of Micro Models
Providing detailed calculation results of individual movement
Individual behavior can be added to the model
Cons:
Difficult to supply input data
Hugh computational demand

36. Evacuation model can also be classified in accordance with their modeling techniques ……….

37. Modeling Techniques

38. Modeling Techniques Optimization Models Simulation Models
Static Network Flow
Optimization Models
Dynamic Network Flow
Random Walker Model
Cellular Automaton Model
Simulation Models
Social Force Model
Magnetic Force Model
Agent-based Model

39. Optimization Models
Produces results that describe an optimal evacuation of the building
Assumes that people are evacuated as quickly as possible

40. A Static Network Flow Approach
Static 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.
Send the occupants from the source nodes to destinations via the network
Virtual source
Virtual sink
Source Nodes
Destinations
Objective: minimize the total time required for evacuation

41. 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

42. 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.

43. 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).

44. A Dynamic Quickest Flow Model
......
Source nodes: regions at risk; departure time is
time-dependent
Safety Destinations
Network: parameters are time-varying
Destroyed by disaster
Optimization objective:
Min.
Each arc has a time-varying post capacity and travel time:
Flow on arc(i,j):
Dynamic capacity:
s.t.
Initial flow:
Each node has a time-varying capacity:
: time-varying maximum capacity;
: time-varying travel time ;
: flow on arc (i,j);
: supply at source at t;
: flow waiting time at vertex i;
: dynamic node capacity;
:next time.

45. 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

46. 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:
- 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

47. “Social Forces” exerted to a person
Repulsive effect of others
Move in desired direction
Destination
Attracted by others (friends)

48. Social Force Model (cont’d)
The simulation results are capable of describing several observed collective phenomena :lane formation, oscillation at bottleneck, and clogging

49. Example of Social Force Model

50. 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

51. 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

52. Basic rules Computing probabilities statistically
1. Moving forward and backward
Given mean speed and its deviation p0 p1
p-1 or

53. Basic rules (Cont’d) 2. Moving transversally
Given mean speed and its deviation
3. Filling the transition matrix
q-1 q0 q1

54. Experimental results of CA Model
Evacuation of a large room
Discrete floor field
Only allowed to move in 4 directions

55. 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

56. Relationship between crowd flow velocity and crowd density
By using the above mentioned approach, a relationship between the crowd flow density and crowd flow velocity has been generated (3,000 runs)
Relationship between crowd flow velocity and crowd density 5
y = x2 – 0.59x
Detailed information given in: Lo SM, Fang Z, Zhi GS. An Evacuation Model: the SGEM Package. Fire Safety Journal. 2004, 39:

57. A flow equation can be expressed as:

58. 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

59. 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

60. Drift Point Vs. Evacuation Time
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.

61. Door Width Vs. Evacuation Time
When the number of people is less than 40, there is no significant difference in two curves.

62. Example: Simulex, Exodus, SGEM, ……. etc
Simulation Models
Example: Simulex, Exodus, SGEM, ……. etc

63. Using the SGEM for illustration
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):
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:

64. 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.

65. A grid of cells in zone

66. Simulation Outputs

67. Thank You!