Papers in Physics, vol. 6, art. 060013 (2014)

Received: 9 October 2014, Accepted: 13 November 2014
Edited by: G. C. Barker
Licence: Creative Commons Attribution 3.0
DOI: http://dx.doi.org/10.4279/PIP.060013

www.papersinphysics.org

ISSN 1852-4249

Sequential evacuation strategy for multiple rooms toward the same
means of egress

D. R. Parisi,1, 2∗ P. A. Negri2, 3†

This paper examines different evacuation strategies for systems where several rooms evac-
uate through the same means of egress, using microscopic pedestrian simulation. As a
case study, a medium-rise office building is considered. It was found that the standard
strategy, whereby the simultaneous evacuation of all levels is performed, can be improved
by a sequential evacuation, beginning with the lowest floor and continuing successively
with each one of the upper floors after a certain delay. The importance of the present
research is that it provides the basis for the design and implementation of new evacuation
strategies and alarm systems that could significantly improve the evacuation of multiple
rooms through a common means of escape.

I. Introduction

A quick and safe evacuation of a building when
threats or hazards are present, whether natural or
man-made, is of enormous interest in the field of
safety design. Any improvement in this sense would
increase evacuation safety, and a greater number of
lives could be better protected when fast and effi-
cient total egress is required.

Evacuation from real pedestrian facilities can
have different degrees of complexity due to the par-
ticular layout, functionality, means of escape, oc-
cupation and evacuation plans. During the last
two decades, modeling and simulation of pedestrian

∗E-mail: dparisi@itba.edu.ar
†E-mail: pnegri@uade.edu.ar

1 Instituto Tecnológico de Buenos Aires, 25 de Mayo 444,
1002 Ciudad Autónoma de Buenos Aires, Argentina.

2 Consejo Nacional de Investigaciones Cient́ıficas y
Técnicas, Av. Rivadavia 1917, 1033 Ciudad Autónoma
de Buenos Aires, Argentina.

3 Universidad Argentina de la Empresa, Lima 754, 1073
Ciudad Autónoma de Buenos Aires, Argentina.

movements have developed into a new approach to
the study of this kind of system. Basic research on
evacuation dynamics has started with the simplest
problem of evacuation from a room through a single
door. This “building block” problem of pedestrian
evacuation has extensively been studied in the bib-
liography, for example, experimetally [1, 2], or by
using the social force model [3–5], and cellular au-
tomata models [6–8], among many others.

As a next step, we propose investigating the
egress from multiple rooms toward a single means
of egress, such as a hallway or corridor. Examples
of this configuration are schools and universities
where several classrooms open into a single hall-
way, cinema complexes, museums, office buildings,
and the evacuation of different building floors via
the same staircase. The key variable in this kind
of system is the timing (simultaneity) at which the
different occupants of individual rooms go toward
the common means of egress. Clearly, this means
of egress has a certain capacity that can be rapidly
exceeded if all rooms are evacuated simultaneously
and thus, the total evacuation time can be subopti-
mal. So, it is valid to ask in what order the different

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Papers in Physics, vol. 6, art. 060013 (2014) / D. R. Parisi et al.

rooms should be evacuated.
The answer to this question is not obvious. De-

pending on the synchronization and order in which
the individual rooms are evacuated, the hallway can
be saturated in different sectors, which could hin-
der the exit from some rooms and thus, the corre-
sponding flow rate of people will be limited by the
degree of saturation of the hallway. This is because
density is a limitation for speed. The relationship
between density and velocity in a crowd is called
“fundamental diagram of pedestrian traffic” [9–14].
Therefore, the performance of the egress from each
room will depend on the density of people in the
hallway, which is difficult to predict from analyt-
ical methods. This type of analysis is limited to
simple cases such as simultaneous evacuation of all
rooms, assuming a maximum degree of saturation
on the stairs. An example of an analytical resolu-
tion for this simple case can be seen in Ref. [12],
on chapter 3-14, where the egress from a multistory
building is studied.

From now on we will analyze a 2D version of this
particular case: an office building with 7 floors be-
ing evacuated through the same staircase, which
is just an example of the general problem of sev-
eral rooms evacuating through a common means of
egress.

i. Description of the evacuation process

The evacuation process comprises two periods:

- E1, reaction time indicating the time period
between the onset of a threat or incident and
the instant when the occupants of the building
begin to evacuate.

- E2, the evacuation time itself is measured from
the beginning of the egress, when the first per-
son starts to exit, until the last person is able
leave the building.

E1 can be subdivided into: time to detect dan-
ger, report to building manager, decision-making of
the person responsible for starting the evacuation,
and the time it takes to activate the alarm. These
times are of variable duration depending on the us-
age given to the building, the day and time of the
event, the occupants training, the proper function-
ing of the alarm system, etc. Because period E1
takes place before the alarm system is triggered, it

must be separated from period E2. The duration
of E1 is the same for the whole building. In conse-
quence, for the present study only the evacuation
process itself described as period E2 is considered.
The total time of a real complete evacuation will
be necessarily longer depending on the duration of
E1.

ii. Hypothesis

This subsection defines the scope and conditions
that are assumed for the system.

1. The study only considers period E2 (the evac-
uation process itself) described in subsection
I. i. above.

2. All floors have the same priority for evacua-
tion. The case in which there is a fire at some
intermediate floor is not considered.

3. The main aspect to be analyzed is the move-
ment of people who follow the evacuation plan.
Other aspects of safety such as types of doors,
materials, electrical installation, ventilation
system, storage of toxic products, etc., are not
included in the present analysis.

4. After the alarm is triggered on each floor, the
egress begins under conditions similar to those
of a fire drill, namely:

• People walk under normal conditions,
without running.

• If high densities are produced, people
wait without pushing.

• Exits are free and the doors are wide
open.

• The evacuation plan is properly signaled.
• People start to evacuate when the alarm

is activated on their own floor, following
the evacuation signals.

• There is good visibility.

II. Simulations

i. The model

The physical model implemented is the one de-
scribed in [15], which is a modification of the social

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Papers in Physics, vol. 6, art. 060013 (2014) / D. R. Parisi et al.

force model (SFM) [3]. This modification allows a
better approximation to the fundamental diagram
of Ref. [12], commonly used in the design of pedes-
trian facilities.

The SFM is a continuous-space and force-based
model that describes the dynamics considering the
forces exerted over each particle (pi). Its Newton
equation reads

miai = FDi + FSi + FCi, (1)

where ai is the acceleration of particle pi. The
equations are solved using standard molecular dy-
namics techniques. The three forces are: “Driving
Force” (FDi), “Social Force” (FSi) and “Contact
Force”(FCi). The corresponding expressions are as
follows

FDi = mi
(vdi ei − vi)

τ
, (2)

where mi is the particle mass, vi and vdi are the
actual velocity and the desired velocity magnitude,
respectively. ei is the unit vector pointing to the de-
sired target (particles inside the corridors or rooms
have their targets located at the closest position
over the line of the exit door), τ is a constant re-
lated to the time needed for the particle to achieve
vd.

FSi =

Np∑
j=1,j 6=i

A exp

(
−�ij
B

)
enij, (3)

with Np being the total number of pedestrians in
the system, A and B are constants that determine
the strength and range of the social interaction, enij
is the unit vector pointing from particle pj to pi;
this direction is the “normal” direction between two
particles, and �ij is defined as

�ij = rij − (Ri + Rj), (4)
where rij is the distance between the centers of pi
and pj and R is their corresponding particle radius.

FCi = (5)

Np∑
j=1,j 6=i

[
(−�ij kn) enij + (v

t
ij �ij kt) e

t
ij

]
g(�ij),

where the tangential unit vector (etij) indicates the
corresponding perpendicular direction, kn and kt

are the normal and tangential elastic restorative
constants, vtij is the tangential projection of the
relative velocity seen from pj(vij = vi − vj), and
the function g(�ij) is: g = 1 if �ij < 0 or g = 0
otherwise.

Because this version of the SFM does not pro-
vide any self-stopping mechanism for the particles,
it cannot reproduce the fundamental diagram of
pedestrian traffic as shown in Ref. [15]. In conse-
quence, the modification consists in providing vir-
tual pedestrians with a way to stop pushing other
pedestrians. This is achieved by incorporating a
semicircular respect area close to and ahead of the
particle (pi). While any other pedestrian is inside
this area, the desired velocity of pedestrians (pi) is
set equal to zero (vdi = 0). For further details and
benefits of this modification to the SFM, we refer
the reader to Ref. [15].

The kind of model used allows one to define
the pedestrian characteristics individually. Fol-
lowing standard pedestrian dynamics bibliography
(see, for example, [3–5, 15]), we considered inde-
pendent and uniform distributed values between
the ranges: pedestrian mass m � [70 kg, 90 kg];
shoulder width d � [48 cm, 56 cm]; desired veloc-
ity vd � [1.1 m/s, 1.5 m/s]; and the constant val-
ues are: τ = 0.5 s, A = 2000 N, B = 0.08 m,
kn = 1.2 10

5 N/m, kt = 2.4 10
5 kg/m/s.

Beyond the microscopic model, pedestrian be-
havior simply consists in moving toward the exit
of the room and then toward the exit of the hall-
way, following the evacuation plan.

From the simulations, all the positions and veloc-
ities of the virtual pedestrians were recorded every
0.1 second. From these data, it is possible to calcu-
late several outputs; in the present work we focused
on evacuation times.

ii. Definition of the system under study

As a case study, we have chosen that of a medium-
rise office building with N = 7, N being the num-
ber of floors. This system was studied analytically
in Chapter 3-14 in Ref. [12], only for the case of
simultaneous evacuation of all floors.

The building has two fire escapes in a symmet-
ric architecture. At each level, there are 300 occu-
pants. Exploiting the symmetric configuration, we
will only consider the egress of 150 persons toward
one of the stairs. Thus, on each floor, 150 people

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Papers in Physics, vol. 6, art. 060013 (2014) / D. R. Parisi et al.

Figure 1: Schematic of the two-dimensional system
to be simulated. Each black dot indicates one per-
son.

are initially placed along the central corridor that
is 1.2 m wide and 45 m long. In total, 1050 pedes-
trians are considered for simulating the system.

For the sake of simplicity, we define a two-
dimensional version of a building where the central
corridors of all the floors and the staircase are con-
sidered to be on the same plane as shown in Fig.
1.

The central corridors can be identified with the
“rooms” of the general problem described in sec-
tion I. and the staircase is the common means of
egress. The effective width of the stairway is 1.4 m.
The central corridors of each floor are separated by
10.66 m. This separation arises from adding the
horizontal distance of the steps and the landings
between floors in the 3D system [12]. So the dis-
tance between two floors in the 2D version of the
problem is of the same length as the horizontal dis-
tance that a person should walk, also between two
floors, along the stairway in the 3D building.

iii. Evacuation strategies

The objective of proposing a strategy in which dif-
ferent floors start their evacuation at different times

is to investigate whether this method allows an im-
provement over the standard procedure, which is
the simultaneous evacuation of all floors.

The parameters to be varied in the study are the
following:

a The order in which the different levels are evac-
uated. In this sense, we study two procedures:
a.1) “Bottom-Up”: indicates that the evacua-
tion begins on the lowest (1st) floor and then
follows in order to the immediately superior
floors. a.2) “Top-Down” indicates that the
evacuation begins on the top floor (7th, in this
case), and continues to the next lower floor,
until the 1st floor is finally evacuated.

b The time delay dt between the start of the
evacuation of two consecutive floors. This
could be implemented in a real system through
a segmented alarm system for each floor, which
triggers the start of the evacuation in an inde-
pendent way for the corresponding floor.

The initial time, when the first fire alarm is trig-
gered in the building, is defined as T0.

The instant t
f
0 {BU,T D,SE} indicates the time

when the alarm is activated on floor f. Subindices
{BU,TD,SE} are set if the time t belongs to the
Bottom-Up, Top-Down, or Simultaneous Evacua-
tion strategies, respectively.

The Bottom-Up strategy establishes that the 1st

floor is evacuated first: t10 BU = T0. Then the
alarm on the 2nd floor is triggered after dt seconds,
t20 BU = t

1
0 BU + dt, and so on in ascending order

up to the 7th floor . In general, the time when the
alarm is triggered on floor f can be calculated as:

t
f
0 BU = T0 + dt× (f − 1). (6)

The Top-Down strategy begins the building evac-
uation on the top floor (7th, in this case): t70 T D =
T0. After a time dt, the evacuation of the floor
immediately below starts, and so on until the evac-
uation of the 1st floor:

t
f
0 T D = T0 + dt× (N −f). (7)

Simultaneous Evacuation is the special case in
which dt = 0 and thus, it considers the alarms on
all the floors to be triggered at the same time:

t
f
0 SE = T0|f=1,2,...,7. (8)

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Papers in Physics, vol. 6, art. 060013 (2014) / D. R. Parisi et al.

III. Results

This section presents the results of simulations
made by varying the strategy and the time delay
between the beginning of the evacuation of the dif-
ferent levels.

Each configuration was simulated five times, and
thus, the mean values and standard deviations are
reported. This is consistent with reality, because
if a drill is repeated in the same building, total
evacuation times will not be exactly the same.

i. Metrics definition

Here we define the metrics that will be used to
quantify the efficiency of the evacuation process of
the system under study.

It is called Total Evacuation Time (TET), start-
ing at T0, when everyone in the building (150×7 =
1050 persons) has reached the exit located on the
ground floor (see Fig. 1), which means that the
building is completely evacuated.

The fth Floor Evacuation Time (FETf ) refers to
the time elapsed since initiating the evacuation of
floor f until its 150 occupants reach the staircase.
It must be noted that this evacuation time does not
consider the time elapsed between the access to the
staircase and the general exit from the building, nor
does it consider as starting time the time at which
the evacuation of some other level or of the building
in general begins. It only considers the beginning of
the evacuation of the current floor. Average Floor
Evacuation Time (FET ) is the average of the seven
FETf .

From these definitions, it follows that TET >
FETf for any floor (even the lowest one).

ii. Simultaneous evacuation strategy

In general, the standard methodology consists in
evacuating all the floors having the same priority
at the same time.

Under these conditions, the capacity of the stairs
saturates quickly, and so all floors have a slow evac-
uation. Figure 2 shows a snapshot from one simula-
tion of this strategy. Here, the profile of the queues
at each level can be observed. The differences in
the length of queues are due to differences in the
temporal evolution of density in front of each door.

Figure 2: Snapshot taken at 73 seconds since the
start of the simultaneous evacuation, where the
queues of different lengths can be observed on each
floor.

In this evacuation scheme, the first level that can
be emptied is the 1st floor (105 ± 6 s) and the last
one is the 6th floor (259 ± 3 s).

The Total Evacuation Time (TET ) of the build-
ing for this configuration is 316±8 s, and the mean
Floor Evacuation Time (FET) is 195 ± 55 s.

For reference, the independent evacuation of a
single floor toward the stairs was also simulated.
It was found that the evacuation time of only one
level toward the empty stair is 65 ± 4 s.

iii. Bottom-Up strategy

Figure 3(a) shows the evacuation times for different
time delays dt following the Bottom-Up strategy.

It can be seen that the Total Evacuation Time
(TET ) remains constant for time delays (dt) up to
30 seconds. Therefore, TET is the same as the si-
multaneous evacuation strategy (dt = 0 s) in this
range. It is worth noting that 30 seconds is approx-
imately one half of the time needed to evacuate a
floor if the staircase were empty.

Furthermore, the mean Floor Evacuation Time
(FET) declines as dt increases, reaching the

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Papers in Physics, vol. 6, art. 060013 (2014) / D. R. Parisi et al.

−20 0 20 40 60 80 100
0

100

200

300

400

500

600

700

dt (s)

E
v
a
c
u
a
ti
o
n
 T

im
e
 (

s
)

 

 

TET

FET

(a)

−20 0 20 40 60 80 100
0

100

200

300

400

500

600

700

dt (s)

E
v
a

c
u

a
ti
o

n
 T

im
e

 (
s
)

 

 

TET

FET

(b)

Figure 3: TET and FET, obtained from simulations for different phase shifts (dt) following sequential
evacuation: (a) Bottom-Up strategy, (b) Top-Down strategy. The symbols and error bars indicate one
standard deviation.

asymptotic value for 65 seconds, which is the evac-
uation time of a single floor considering the empty
stairway. As expected, if the levels are evacuated
one at a time, with a time delay greater than the
duration of the evacuation time of one floor, the
system is at the limit of decoupled or independent
levels. In these cases, TET increases linearly with
dt.

Since TET is the same for dt < 30 s and FET
is significantly improved (it is reduced by half) for
dt = 30 s, this phase shift can be taken as the best
value, for this strategy, to evacuate this particular
building.

This result is surprising because the TET of the
building is not affected by systematic delays (dt) at
the start of the evacuation of each floor if dt ≤ 30 s,
which reaches up to 180 seconds for the floor that
further delays the start of the evacuation.

More details can be obtained by looking at the
discharge curves corresponding to one realization
of the building egress simulation. The evacuation
of the first 140 pedestrians (93%) of each floor is
analyzed by plotting the occupation as a function
of time in Fig. 4 for three time delays between the
relevant range dt �[0, 30]. For dt = 0 [Fig. 4(a)]
there is an initial transient of about 10 seconds in
which every floor can be evacuated toward a free
part of the staircase before reaching the congestion

due to the evacuation of lower levels. After that, it
can be seen that the egress time of different floors
has important variations, the lower floors (1st and
2nd) being the ones that evacuate quicker and in-
termediate floors such as 5th and 6th the ones that
take longer to evacuate. After an intermediate sit-
uation for dt = 15 s [Fig. 4(b)] we can observe the
population profiles for the optimum phase shift of
dt = 30 in Fig. 4(c). There, it can be seen that
the first 140 occupants of different floors evacuate
uniformly and very little perturbation from one to
another is observed.

In the curves shown in Fig. 4, the derivative
of the population curve is the flow rate, mean-
ing that low slopes (almost horizontal parts of the
curve such as the one observed in Fig. 4(a) for the
5th floor between 40 and 100 s) can be identified
with lower velocities and higher waiting time for
the evacuating people. Because of the fundamen-
tal diagram, we know that lower velocities indicate
higher densities. In consequence, we can say that
the greater the slope of the population curves, the
greater the comfort of the evacuation (more veloc-
ity, less waiting time, less density). Therefore, it
is clear that the situation displayed in Fig. 4(c) is
much more comfortable than the one in Fig. 4(a).

In short, for the Bottom-Up strategy, the time
delay dt = 30 s minimizes the perturbation among

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Papers in Physics, vol. 6, art. 060013 (2014) / D. R. Parisi et al.

(a) (b) (c)

Figure 4: Time evolution of the number of pedestrians in each floor up to 3 m before the exit to the
staircase. (a) for the simultaneous evacuation (dt = 0); (b) for delay of dt = 15 s and (c) for dt = 30 s.

evacuating pedestrians from successive levels; it re-
duces FET to one half of the simultaneous strategy
(dt = 0 s); it maintains the total evacuation time
(TET ) at the minimum and, overall, it exploits
the maximum capacity of the staircase maintain-
ing each pedestrian’s evacuation time at a mini-
mum. This result is highly beneficial for the gen-
eral system and for each floor, because it can avoid
situations generating impatience due to waiting for
gaining access to the staircase.

iv. Top-Down strategy

Figure 3(b) shows the variation of TET and FET,
as a function of the time delay dt, for the Top-Down
strategy.

It must be noted that TET increases
monotonously for all dt, which is sufficient to
rule out this evacuation scheme.

In addition, for dt < 15 s, FET also increased,
peaking at dt = 15 s. It can be said that for the
system studied, the Top-Down strategy with a time
delay of dt = 15 s leads to the worst case scenario.

For 15 s < dt < 45 s, there is a change of regime
in which FET decreases and TET stabilizes.

For values of dt > 45 s, FET reaches the limit
of independent evacuation of a single floor (see sec-
tion III.ii.). And the TET of the building increases
linearly due to the increasing delays between the
start of the evacuation of the different floors.

In summary, the Top-Down Strategy does not
present any improvement with respect to the stan-
dard strategy of simultaneous evacuation of all

floors (dt = 0).

IV. Conclusions

In this paper, we studied the evacuation of several
pedestrian reservoirs (“rooms”) toward the same
means of egress (“hallway”). In particular, we fo-
cused on an example, namely, a multistory building
in which different floors are evacuated toward the
staircase. We studied various strategies using com-
puter simulations of people’s movement.

A new methodology, consisting in the sequential
evacuation of the different floors (after a time de-
lay dt) is proposed and compared to the commonly
used strategy in which all the floors begin to evac-
uate simultaneously.

For the system under consideration, the present
study shows that if a strategy of sequential evac-
uation of levels begins with the evacuation of the
1st floor and, after a delay of 30 seconds (in this
particular case, 30 s is approximately one half of
the time needed to evacuate only one floor if the
staircase were empty), it follows with the evacua-
tion of the 2nd floor and so on (Bottom-Up strat-
egy), the quality of the overall evacuation process
improves. From the standpoint of the evacuation of
the building, TET is the same as that for the ref-
erence state. However, if FET is considered, there
is a significant improvement since it falls to about
half. This will make each person more comfortable
during an evacuation, reducing the waiting time
and thus, the probability of causing anxiety that
may bring undesirable consequences.

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Papers in Physics, vol. 6, art. 060013 (2014) / D. R. Parisi et al.

So, one important general conclusion is that a
sequential Bottom-Up strategy with a certain phase
shift can improve the quality of the evacuation of a
building of medium height.

On the other hand, the simulations show that
the sequential Top-Down strategy is unwise for any
time delay (dt). In particular, for the system stud-
ied, the value dt = 15 s leads to a very poor evacu-
ation since the TET is greater than that of the ref-
erence, and it maximizes FET (which is also higher
than the reference value at dt = 0). In consequence,
the present study reveals that this would be a bad
strategy that should be avoided.

The perspectives for future work are to generalize
this study to buildings with an arbitrary number of
floors (tall buildings), seeking new strategies. We
also intend to analyze strategies where some inter-
mediate floor must be evacuated first (e.g., in case
of a fire) and then the rest of the floors.

The results of the present research could form
the basis for developing new and innovative alarm
systems and evacuation strategies aimed at enhanc-
ing the comfort and security conditions for peo-
ple who must evacuate from pedestrian facilities,
such us multistory buildings, schools, universities,
and other systems in which several “rooms” share
a common means of escape.

Acknowledgements - This work was financially
supported by Grant PICT2011 - 1238 (ANPCyT,
Argentina).

[1] T Kretz, A Grnebohm, M Schreckenberg, Ex-
perimental study of pedestrian flow through a
bottleneck, J. Stat. Mech. P10014 (2006).

[2] A Seyfried, O Passon, B Steffen, M Boltes,
T Rupprecht, W Klingsch, New insights into
pedestrian flow through bottlenecks, Transport.
Sci. 43, 395 (2009).

[3] D Helbing, I Farkas, T Vicsek, Simulating dy-
namical features of escape panic, Nature 407,
487 (2000).

[4] D R Parisi, C Dorso, Microscopic dynamics
of pedestrian evacuation, Physica A 354, 608
(2005).

[5] D R Parisi, C Dorso, Morphological and dy-
namical aspects of the room evacuation pro-
cess, Physica A 385, 343 (2007).

[6] A Kirchner, A Schadschneider, Simulation of
evacuation processes using a bionics-inspired
cellular automaton model for pedestrian dy-
namics, Physica A 312, 260 (2002).

[7] C Burstedde, K Klauck, A Schadschneider,
J Zittartz, Simulation of pedestrian dynam-
ics using a two-dimensional cellular automa-
ton, Physica A 295, 507 (2001).

[8] W Song, X Xu, B H Wang, S Ni, Simulation of
evacuation processes using a multi-grid model
for pedestrian dynamics, Physica A 363, 492
(2006).

[9] U Weidmann, Transporttechnik der eu-
ssgänger, transporttechnische eigenschaften
des fussgängerverkehrs, Zweite, Ergänzte
Auflage, Zürich, 90 (1993).

[10] J Fruin, Pedestrian planning and design, The
Metropolitan Association of Urban Design-
ers and Environmental Planners, New York
(1971).

[11] A Seyfried, B Steffen, W Klingsch, M Boltes,
The fundamental diagram of pedestrian move-
ment revisited, J. Stat. Mech. P10002 (2005).

[12] P J Di Nenno (Ed.), SFPE Handbook of fire
protection engineering, Society of Fire Protec-
tion Engineers and National Fire Protection
Association (2002).

[13] D Helbing, A Johansson, H Al-Abideen, Dy-
namics of crowd disasters: An empirical study,
Phys. Rev. E 75, 046109 (2007).

[14] http://www.asim.uni-wuppertal.de/datab
ase-new/data-from-literature/fundament

al-diagrams.html, accessed November 27,
2014.

[15] D R Parisi, B M Gilman, H Moldovan, A mod-
ification of the social force model can reproduce
experimental data of pedestrian flows in nor-
mal conditions, Physica A 388, 3600 (2009).

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