Evacuation Simulations using Cellular Automata

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Evacuation Simulations using Cellular AutomataPablo Cristian Tissera, Marcela Printista, Marcelo Luis ErrecaldeLab. de Investigacion y Desarrollo en Inteligencia Computacional (LIDIC)Universidad Nacional de San Luis - Ej. de los Andes 950 - (D5700HHW) San Luis, Argentina

Presented by Mohamed Fazeen

Ruwan Nawarathna

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Presentation Outline

Introduction Cellular Automata Formulation of Cellular Automata

and Some Examples Introduction to the Evacuation

Simulation Model Description Experiments Conclusions & Future Work

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Introduction to Cellular Automata (CA)

CA is a result of, The joint work of John Von

Neumann and Stanislaw Ulam. A study related to machines with auto-

replication capabilities.

Later popularized due the work proposed by Jhon H. Conway, “the game of life” in 1970.

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What is CA?

The CA are mathematical systems with discrete values in space, time and state.

Have, Auto-replication Universal computation capabilities▪ The property of being able to perform

different tasks with the same underlying construction just by being programmed in a different way

Auto-organization effects ▪ Can generate extreme ordered behaviors from a total

disorder.

Brain’s Brain CA

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ExampleGosper's Glider Gun creating "gliders" in the cellular automaton Conway's Game of Life.

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Formulation of CA – Basic Elements

Let,A – D dimensional array of cells with each

element of the array has associated a finite state (Cellular Space)

Q – A finite set of states (Ex: true, false , 0, 1 etc.)

ci – An arbitrary cell of A, (ith cell)

∑ – Input alphabet (input states)

δ – The transition function is given by,

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Formulation of CA - Neighborhood Let,

is the set of cells considered as neighborhood of an arbitrary cell excluding ci.

is the number of adjacent cells.

Then,

Thus,is the specification of which cells are included in a neighborhood

Ex: Moore's Neighborhood

Because, ∑ is given by all possible combination of the cell states of the adjacent (neighboring) cells.

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Formulation of CA – Transition Function The transition function of states

is a mapping such that If is the state of the cell ci at the time t And, are

the states of the adjacent cells to ci,

Then,

denotes the state of ci in the time t + 1.

i.e. state at t+1 of ci is determined by

considering the state of the ci and the

neighboring cells

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Formulation of CA – Transition Rules

The δ function is usually represented in tabular form with rules:

There are many ways of specifying rules. (Ex: Brian's Brain, Wireworld, Rule 90, Rule 184)

It is possible to specify probabilistic transition rules, where an arbitrary probability p can be associated to a transition rule.

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Formulation of CA - Definition

The Cellular Automation is defined as 4-

tuples

Implies that CA consist of A D-Dimensional cell arrayA set of finite states A transition function A neighborhood

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Example – Elementary CA (ECA)

Refers to a class of CA , studied by Stephen Wolfram.

Definition ECA, A - one-dimensional array Q - set of states with elements {0, 1} . : Neighborhood δ - Transition function (set of rules)

defined as follows (next slide),

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Example – Elementary CA (ECA) – Transition function

If a cell at time t is inactive (0), is activated at time t+1 if some of the adjacent cells (left or right) are active (1).

An active cell at time t, is turned inactive at time t+1 if its adjacent cells are both actives or both inactives.

In other case a cell preserve its previous state.Called Rule 90

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Example – Elementary CA (ECA) – Evolution of ECA

When above rules are evolved and arranged in consecutive lines, this will generate the following “Sierpinski Triangle”.

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John Conway’s “Game of Life” Consists of a collection of cells based on a few

mathematical rules Can live, Die, or Multiply, depending on the initial conditions.

Cells form various patterns throughout the game.

Transition Rules,

For a space that is 'populated':Each cell with one or no neighbors dies, as if by loneliness.Each cell with four or more neighbors dies, as if by

overpopulation.Each cell with two or three neighbors survives.

For a space that is 'empty' or 'unpopulated'Each cell with three neighbors becomes populated.

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Applications of CA

Computer Science Cryptography Fractal Generation Computer Graphics Image processing Genetic Algorithm Calibration Design of massively parallel hardware

Simulations of biology, chemistry, physics. ferromagnetism according to Ising mode forest fire propagation nonlinear chemical reaction-diffusion systems turbulent flow biological pigmentation patterns breaking of materials growth of plants and animals

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Summary of CA

Dynamic system that represent a grid of locally connected finite automata. Finite Automata: describes a class of models of computation

that are characterized by having a finite number of states.

Each Automation, produces an output from several inputs modifies its state in this process by means of a transition

function.

The state of a cell of a CA in a particular generation only depends on, The states of its neighboring cells and The state, the cell had in its previous generation.

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In this work CA is used in order to specify and implement a simulation model called EVAC that allows to investigate behavioral dynamics for pedestrians in an emergency evacuation.

Eg: forced evacuation of a large number of people due to the threat of the fire, within a building with a specific number of exits.

Due to real world experimental research has ethical, financial and logical limitations, simulations are desired.

The simulation allows to specify, different scenes with a large number of people and environmental

features making easier to study the complex behaviors that arise when the

people interact.

Evacuation Simulations using Cellular Automata

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To analyze the strengths and limitations of CA for modeling this type of domains.

To present a simulation tool that allows to design, construct, execute, visualize and analyze different configurations of a building to be evacuated.

To evaluate the performance of a forced evacuation under different fire conditions.

To identify relevant aspects that should be considered in the design of new buildings.

Objective of This Work

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A finite two-dimensional array with closed boundaries.

Each cell of the cellular space represents a 40 x 40 cm square. This is the space usually occupied by a person in a crowd

with maximal density

So, one grid of 10 x 10 m will contain 25 x 25 cells

Model Description – Cellular Space (A)

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Cells can be one of the states of the set,

Model Description – States (Q)

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The neighborhood considered in the model is Moore's Neighborhood that includes the eight cells surrounding the central cell.

Individual has all possible movement directions.

Model Description - Neighborhood (N)

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Before the simulation starts, the diverse information related to, outer walls, inner obstacles, individuals,

combustible locations, cells with fire, and arrangement of the exits are defined.

In EVAC (a simulation system built by the authors), this task can be realized by means of its graphical interface.

Model Description – Initial Configuration

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Rules about the building: a cell in state W or O (outer wall or obstacle) will not change its state throughout the simulation.

Model Description – Transitional Rules (δ) – Rule 1

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Rules about smoke propagation: A cell with smoke (in one of the following states: S,

SF, PS or PSF.) in time t, also will have smoke in time t+1.

If at time t ▪ central cell → no smoke,▪ some adjacent cells → have smoke, Then the central cell also will have smoke at time t+1 with a

probability proportional to the number of adjacent cells with smoke.

Ex: the central cell will have smoke in the next time step with probability ½

Model Description – Transitional Rules (δ) – Rule 2

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Rules about fire propagation: these rules are analogous to the rules

for smoke propagation as explained above.

However, they incorporate an additional constraint: a non-zero combustion level of the cell is required.

Model Description – Transitional Rules (δ) – Rule 3

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Rules about the people motion:

A cell without a person at time t, will have a person at time t+1 if;

1. At least one adjacent cell contains an individual2. .

In other cases, the cell does not change its state.

Model Description – Transitional Rules (δ) – Rule 4

The distance from the current cell to an exit

The distance from the cell occupied by the individual to the exit

<

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Two important aspects considered in people motion simulation.1. Estimation of distances from the cells

to an exit ▪ Cellular space was represented in a

weighted graph▪ Dijkstra's algorithm was used to calculate

the shortest path.

Model Description – Transitional Rules (δ) – Rule 4 Cont…

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Two important aspects considered, Cont…2. Handling of collisions between individuals.▪ To avoid collision the current cell will in charge of

selecting an individual among the neighbors.

▪ Following rules use in selectiona) Shorter to the exit will not be considered as a

candidate.b) If more than one candidate, a person with minor

number of damage points will be selected.c) Still the conflict persists, a candidate selected

randomly.

Model Description – Transitional Rules (δ) – Rule 4 Cont…

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The experiments were carried out with EVAC, an integrated simulation system based on cellular automata.

The idea of the experiment is to verify their CA model for simple evacuation scenarios.

The experiment conceptually divided in to three groups

Each group correspond to environmental configuration show in each row in the following figure

Experiments

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Experimental Results

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Experimental Results Cont…

Exit Size (m)

Evacu

ati

on

Tim

e (

s)

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In this work CA were used for developing and implementing a simulation model of emergency evacuations due to the fire threat.

A software named EVAC was developed for the above purpose.

These studies were intended to detect which modifications that would improve the evacuation processes in designing new buildings.

The authors claimed that CA are a very suitable tools for modeling this class of problems.

Conclusion

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Authors mentioned that they are developing a hybrid model where the dynamics of fire and smoke propagation are modeled by means of CA.

In the future authors are planning to add structural dynamic changes that could occur during the evacuation process. for instance, the creation of a new exit as

consequence of shattering window.

Future Work

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P. C. Tissera, M. Printista, M. L. Errecalde, “Evacuation Simulations using Cellular Automata,” Journal of Computer Science & Technology, Vol. 7, No. 1, pp. 14-20, 2007.

Finite automata by M. V. Lawson, Department of Mathematics, School of Mathematical and Computer Sciences, Heriot-Watt University.

http://en.wikipedia.org/wiki/Cellular_automaton

http://www.bitstorm.org/gameoflife/

http://en.wikipedia.org/wiki/Brian's_Brain

References