Development of a Safest Routing Algorithm for Evacuation

Simulation in Case of Fire

Denis Shikhalev

, Renat Khabibulin

and Armel Ulrich Kemloh Wagoum

The State Fire Academy of EMERCOM of Russia, 129366, B. Galushkina 4, Moscow, Russia

Jülich Supercomputing centre, Forschungszentrum Jülich GmbH, 52428 Jülich, Germany

Keywords: Pedestrians Dynamics, Criticality, Evacuation System, Re-routing.

Abstract: Route choice of pedestrians during an emergency evacuation can be influenced by many factors. In this

contribution we elaborate three criteria to consider during an evacuation with a fire hazard. The criteria are

combined in an objective function which is minimized during the simulation. The function defines the safe-

ness of a route. In addition an algorithm is presented which evaluates and redirects the pedestrians to the

safest path during the simulation. The algorithm shows a positive impact on the evacuation time and overall

on the safety during an evacuation simulation. A long term goal of the presented algorithm could be the in-

tegration in an evacuation system that gives instructions or recommendations during the evacuation process

using dynamic indicators.

1 INTRODUCTION

Remembering the location of emergency exits cer-

tainly plays an important role during an emergency

evacuation. Some empirical studies have shown that

in some cases almost 80% of adult visitors were not

able to recall the finding of at least one of an emer-

gency exit. The survey was conducted in a shopping

mall in the city of Fiume Veneto in Italy by inter-

viewing people (Carattin, 2011). It is also known

that the availability of safe escape routes during an

evacuation constitutes one of the most critical as-

pects of a building’s safety in case of fire (Kobes,

Helsloot et al, 2010). Moreover the analysis of some

existing escapes route systems from different coun-

tries (Shikhalev and Khabibulin, 2013) shows that

only one third of the systems were able to determine

the direction of the escape route using a scientifical-

ly well founded method. This way, there is a prob-

lem of calculating the safest escape route for people

in case of fire. This problem is related on one hand

to the difficulty in finding the best escape route

(from the point of view of people’s safety) to outside

and on the other hand to the limited functionality of

escape route system.

Considering these factors some thought should

be given on decisions support systems that are able

to determine the safest route during an emergency

evacuation. In this paper we propose an escape route

assessment algorithm. Based on actual input data

(the numbers of pedestrians, the value of fire haz-

ards), the algorithm computes the safest route for

people out of the danger zone. The algorithm can be

integrated into escape route systems. This work is

structured as follow: the second section presents

some related works in the area of computing safe

routes during evacuations. The newly introduced

criteria are presented in the third section. This is

followed by a case study and analysis. Some con-

cluding remarks are given in the last section.

2 RELATED WORKS

The problem of calculating the safest escape route

has been considered from various points of view (Pu

and Zlatanova, 2005; Jalali and Noroozi, 2009; Fil-

ippoupolitis, Gorbil et al, 2011). The main similarity

between those approaches is the fact that they oper-

ate on a graph-based structure. Generally, the Dijks-

tra or the Floyd-Warshall’s algorithms are used to

compute the paths (Evans and Minieka, 1992). The

choice of the algorithm depends on the features of

the problem to be solved (for example, in some

cases the weight of edges is negative and this cannot

directly be handled by the Dijkstra algorithm). The

685

Shikhalev D., Khabibulin R. and Ulrich Kemloh Wagoum A..

Development of a Safest Routing Algorithm for Evacuation Simulation in Case of Fire.

DOI: 10.5220/0004919706850690

In Proceedings of the 6th International Conference on Agents and Artiﬁcial Intelligence (ICAART-2014), pages 685-690

ISBN: 978-989-758-015-4

 2014 SCITEPRESS (Science and Technology Publications, Lda.)

main differences in the approaches are the definition

of the weights of the edges in the constructed evacu-

ation graph. (Filippoupolitis, Gorbil et al, 2011)

expresses the weight of the edges as the effective

length which gives indications about the threat level

of a part of the escape route. This metric consists of

two variables. The first variable is the physical

length of the escape route section. The second varia-

ble is the intensity of the hazards. The presented

results of their simulation show a reduction in the

percentage of fatally injured evacuees. (Jalali and

Noroozi, 2009) defined a certain elapsed time used

as the weight of the edges in their model. They in-

vestigated the evacuation of an underground mine

and calculated the elapse time as a function of the

length of a mine escape route coupled with a passage

simplicity factor. Other authors focused on the

quickest path taking into account different factors

like queue size at exits (Kemloh Wagoum et al.,

2012; Kretz, 2009). These approaches however did

not include a direct threat source, a fire for instance.

The first steps to address this shortcoming is al-

ready taken by some simulation tools, for instance

FDS+Evac (K., Simo Hostikka, S. et al., 2007)

which combines a pedestrian evacuation model with

a fire spreading model. While the presented ap-

proaches are very promising, we think that other

factors need to be considered while calculating al-

ternative routes during evacuation under imminent

danger.

3 THE SAFEST PATH

CRITERION

While assessing the safety of a route during an evac-

uation under imminent danger, a fire hazard for

instance, the focus has to be on the building as a

whole and on some of its sections in particular

(Predtechenskii and Milinskii, 1978). A section can

be the portion between two crossings of escape

routes for example. So the very first step is to identi-

fy the different segments of the evacuation routes

network. There are two different sources of hazards.

The primary source is the imminent danger (e.g.

fire) and the second sources is the process of the

evacuation itself, where jamming at bottlenecks may

cause severe injuries or even be fatal, and excessive

speed may cause tripping related injuries even with-

out jamming. Also the physical length of the escape

route should be considered. Thereby, at least three

parameters (fire, evacuation, length) should be taken

into account to objectively assess people’s safety

during evacuation.

3.1 Obstruction

The first criterion gives information about the usage

of the current section. The obstruction criterion is

determined by the ratio of the people’s density on a

section of the escape route network to the maximum

people’s density that does not cause adverse effects

to humans. Usually, the density is expressed as the

ratio between the number of people and the area of

the escape route section. The value of the obstruc-

tion is given in Equation 1. D

cur

is the current density

on the considered section of the escape route. D

max

the maximal density on a section of the escape route.

The value for D

max

can be retrieved from different

empirical studies (Kholsgevnikov et al, 2008; Ger-

man Fire Protection Association, 2012; Huang et al,

2013).











(1)

3.2 Timeliness

The second factor is directly linked to the fire haz-

ard. During a fire in shopping mall people can be

damage by fire hazards (high temperature, a large

amount of smoke, low visibility, toxic products of

combustion etc.) due to long pre-evacuation time for

instance. A criterion of timeliness leads away from

routes where fire hazards will be reached. The time-

liness is defined in Equation 2. X

cur

is the current

value of one of the fire hazards on section of an

escape route. X

is the critical value of one of the

fire hazards on the section of the escape route. K

a safety coefficient. The values of X

cur

are obtained

from fire detectors. X

is obtained from various

empirical studies (Gann, R., Babrauskas et al., 1994;

Raj, 2008).











∙



(2)

3.3 Length

The third criterion is the relative physical length of

the current section. It is defined in Equation 3. l

cur

the current length of the section and l

max

is the max-

imal length of a section found in the complete net-

work of the investigated structure.











(3)

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686

3.4 Multi-objective Optimization

Due to the aforementioned criticality criteria should

be taken into account together to solve an optimiza-

tion problem which is characterized by the following

features:

- the impact factor of the different criteria is not

known and their real influence on the assessment

of the escape routes is uncertain;

- it is hard to find good compromise when each

criterion has its own minimal value;

- best values of each criterion are located as closer

to zero as possible.

Based on these features we built the following opti-

mization strategy: firstly we calculate a node in 3 -

dimensional space which is obtained by the criteria.

Secondly, we find the distance between the obtained

node and zero because we have the constraint that all

values of each criterion should be minimal. So the

distance is a complex criterion which is named as

the safest path criterion.

The first task is solved by getting value of the

criteria from different sources described in the pre-

vious section. The second task is to find the shortest

distance between two nodes in an n-dimensional

space. The Euclidean distance is applied to this pur-

pose (Marler and Arora, 2004; Deza and Deza,

2013). This is explained in Equation 4. q

and p

are

the nodes in the n-dimensional space.

,



















(4)

Applying equation (4) for our task we combine the

criteria (1), (2), (3) in one φ - safest path criterion

(Figure 1). The process of combining is presented in

Figure 1.

Figure 1: The process of combining.

The problem can then be formulated as:

Calculate the safest escape route for person N

,…,N

from the starting positions m

, m

,…,m

the safety areas s

, s

,…,s

. The constraint is that the

value of each criterion (1), (2), (3) should be mini-

mal. As an optimization criterion we use the safest

path criterion φ:





∙







∙







∙







(5)

at:

→ min, i=1,…,n ;

→ min, i=1,…,n .

where:

α, β, γ – the weight coefficient at a

, b

, l

The coefficients (α, β, γ) are added to regulate the

importance of the individual criterion. Besides a

length the safest path criterion provides important

information about people’s density and fire hazards

spreading on an escape route section.

3.5 Routing Algorithm

The criteria presented in the previous section are

incorporated in a route choice algorithm, which

evaluates the safest path during the evacuation. The

algorithm is described in Figure 2. The Re-routing is

triggered when a better route than the current is

identified. The necessary input data for the algo-

rithm (the numbers of pedestrians, the value of fire

hazards on the escape route sections) are updated

every 10 seconds.

Once the safest path criterion φ is calculated, the

optimal escape route is determined using the Floyd-

Warschall algorithm. It is suitable to use the algo-

rithm of Floyd-Warschall in this case (Evans and

Minieka, 1992) since the location of the fire is un-

predictable and it is always necessary to compute all

possible paths. This algorithm finds the shortest path

between between all pairs of edges in a graph.

Normally, the means of the algorithm are expressed

by following equation (Evans and Minieka, 1992):







min











,







(6)

where:







– the shortest distance from i – vertex to

j-vertex.

m – intermediate vertices of path.

For our task we used the safest path criterion φ in-

stead of the shortest distance. Actually our criterion

Length

Timeliness

Obstruction

→ min

DevelopmentofaSafestRoutingAlgorithmforEvacuationSimulationinCaseofFire

687

has already contained information related to distance

(see section 3.3).

For our task we used the safest path criterion φ as

the weight of the edges. At each time step the algo-

rithm evaluate the need for a re-routing on the sec-

tion. The directions of the pedestrians are updated in

the case that they are not already on the safest route.

Figure 2: Safest route algorithm. t

is the current

evacuation time and t

the step time (10 seconds)

4 CASE STUDY

We investigate a section of a shopping mall in the

centre of Moscow. Figure 3 shows the plan of the

simulated object. The two exits are annotated on the

plan.

Figure 3: Plan of the simulated shopping mall.

Figure 4 shows the structure of the graph extracted from

the plan. The vertices of the graph are located at the cross-

ing of escape routes and represented by dark circles. The

rescue areas are represented by the green circles. The

edges are weighted by the safest path criterion φ defined in

the previous section.

5 SIMULATION

The simulation is conducted in two scenarios. In the

first scenario we did not used the safest route algo-

rithm therefore the evacuated people did not change

their current route. After simulating the first scenario

we got evacuation and fire hazard spreading’s data

which would be compared with data of the second

scenario.

In the second scenario we used the

safest route

algorithm described in Figure 2. For both scenarios

we used a flow model for people movement

(Kholsgevnikov, Shields, et al., 2003) and FDS (K.,

Simo Hostikka, S. et al., 2007) for the simulation of

the fire hazards spreading. Also, pedestrians are in

both scenarios first directed to the shortest route to

the outside. In the second scenario however, they

change their initial route after some time.

The following constraints were used in the simu-

lations:

- 1323 persons were randomly distributed in the

plan presented in Figure 3;

- The pre-evacuation time is set to 60 seconds;

Yes

Start

Next simulation step

Getting data from

detecto

s on sections

Re-routing

needed?

Evacuation

completed?

Direction people

by the newly

defined

ath

= t

Calculating

the safest direction

The End

Direction

people by the

current path

Cross of escape routes

Exit 2

Exit 1

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688

- All people were healthy and the initial space occu-

pied by each person is 0,125 m

For the simulations the maximum density D

max

chosen 9 persons/m

based on the following sources

(Kholsgevnikov et al, 2008; German Fire Protection

Association, 2012; Huang et al, 2013), the maximal

length of a section measured is 58 meters (section 6-

8, figure 4).

Scenario 1

The simulation results from scenario 1 are presented

in table 1. The percentage use of each exit gives

information about how long this exit was effectively

used during the entire evacuation. It is calculated as

the ratio of the evacuation time through the consid-

ered escape to the total evacuation time.

Table 1: Simulation results of simulation by scenario 1

without the safest path algorithm.

Exit

umber of

evacuated

ersons

Evacua-

tion time,

[s]

Percentage

use (%)

1 395 124,6 25,2

2 928 316,8 100,0

From the results presented in Table 1 it can be in-

ferred that 30% of people are evacuated during the

first minute (from the start moving). The remaining

70 % of people are evacuated during the last 4

minutes. The escape 1 had been available for 145

seconds, but people were still going to the escape 2.

A section is avoided in the simulation only if the fire

hazards reach its critical value on that section. Dur-

ing the process of evacuation the fire hazards did not

spread as fast as the pedestrians were evacuated and

therefore did not reach its critical value in the places

where pedestrians were going. By the end of evacua-

tion the fire hazards spread up to the node 8.

Scenario 2

In this scenario, the safest route algorithm described

in Figure 2 is used. The following weight coeffi-

cients were used in (5): a – 0,7; b – 0; l – 0,3. Those

coefficients values were chosen because from our

point of view the a-criterion (which reflects people

density) is more important than l-criterion. The val-

ue of b is zero because the fire hazards did not reach

a critical value. Actually, the definition of the coef-

ficients is another task which can be investigated in

future work. The simulation results from scenario 2

are presented in Table 2.

The results of people evacuation show that evac-

uation time is reduced. Moreover, re-routing for

pedestrians take place at time 120 sec in the node 5.

The re-routing of evacuation flows happened when

Table 2: Simulation results of simulation by scenario 2

using the safest path algorithm.

Exit

umber of

evacuated

ersons

Evacua-

tion time,

[s]

Percentage

use (%)

1 707 190,5 82,8

2 616 230,6 100,0

section 5-4, 4-1 were empty and section 5-6, 6-2 had

a density of approximately 3 persons/m

6 ANALYSIS

The comparison of the results of simulation leads to

several conclusions. Firstly, the pedestrians were

directed to the shortest path (scenario 1) and as the

result the non-evenly distribution evacuation flows

through exits took place. Also there are many evi-

dences about non-evenly distribution evacuation

flows through exits during evacuation (Kobes et al,

2010; Benthorn and Frantzich, 1996). However,

application of the safest route algorithm distributed

the pedestrians more evenly and reduced the overall

time of evacuation.

Secondly, the main criteria of the evacuation

process such as the time of evacuation and distribu-

tion of people through the exits depend on the re-

routing time. Thus, the re-routing time happened

when the people’s density reached 3 persons/m

the second scenario. It is still not a critical density

that could affect people’s safety. Nevertheless it has

an influence on people’s velocity and on the evacua-

tion time. It means that the optimal balance between

the weight coefficients in (5) should at least aims at

reducing the evacuation time.

7 CONCLUSIONS AND FUTURE

WORK

The presented algorithm computes the optimal safest

route based on input data from smoke detectors and

other sources. The results are therefore influenced

by the quality of the input data. We also

acknowledge that the algorithm must be coupled to

an evacuation system to give the instructions during

the evacuation process using dynamic indicators.

This could be very useful for guiding impaired per-

sons for instance. A major problem is to give a guid-

ance that will be accepted by the evacuees. In the

further work we plan to improve the algorithms and

integrate them within a pedestrian simulator. In

addition proper validation criteria must also be in-

DevelopmentofaSafestRoutingAlgorithmforEvacuationSimulationinCaseofFire

689

vestigated. In this contribution we limit ourselves to

the evacuation time.

ACKNOWLEDGEMENTS

The performed researches are in the framework of

an internship supported by the scholarship of the

President of the Russia Federation in 2013/2014

academic year.

We would like to thank the anonymous review-

ers for their helpful comments.

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