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

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

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ISSN 1852-4249

Sequential evacuation strategy for multiple rooms toward the samemeans 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 acase study, a medium-rise office building is considered. It was found that the standardstrategy, whereby the simultaneous evacuation of all levels is performed, can be improvedby a sequential evacuation, beginning with the lowest floor and continuing successivelywith each one of the upper floors after a certain delay. The importance of the presentresearch is that it provides the basis for the design and implementation of new evacuationstrategies and alarm systems that could significantly improve the evacuation of multiplerooms through a common means of escape.

I. Introduction

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

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

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

1 Instituto Tecnologico de Buenos Aires, 25 de Mayo 444,1002 Ciudad Autonoma de Buenos Aires, Argentina.

2 Consejo Nacional de Investigaciones Cientıficas yTecnicas, Av. Rivadavia 1917, 1033 Ciudad Autonomade Buenos Aires, Argentina.

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

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

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

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

pending on the synchronization and order in whichthe individual rooms are evacuated, the hallway canbe 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 thedegree of saturation of the hallway. This is becausedensity is a limitation for speed. The relationshipbetween density and velocity in a crowd is called“fundamental diagram of pedestrian traffic” [9–14].Therefore, the performance of the egress from eachroom will depend on the density of people in thehallway, which is difficult to predict from analyt-ical methods. This type of analysis is limited tosimple cases such as simultaneous evacuation of allrooms, assuming a maximum degree of saturationon 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 multistorybuilding is studied.

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

i. Description of the evacuation process

The evacuation process comprises two periods:

- E1, reaction time indicating the time periodbetween the onset of a threat or incident andthe instant when the occupants of the buildingbegin to evacuate.

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

E1 can be subdivided into: time to detect dan-ger, report to building manager, decision-making ofthe person responsible for starting the evacuation,and the time it takes to activate the alarm. Thesetimes are of variable duration depending on the us-age given to the building, the day and time of theevent, 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 durationof E1 is the same for the whole building. In conse-quence, for the present study only the evacuationprocess itself described as period E2 is considered.The total time of a real complete evacuation willbe necessarily longer depending on the duration ofE1.

ii. Hypothesis

This subsection defines the scope and conditionsthat are assumed for the system.

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

2. All floors have the same priority for evacua-tion. The case in which there is a fire at someintermediate 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, ventilationsystem, storage of toxic products, etc., are notincluded in the present analysis.

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

• People walk under normal conditions,without running.

• If high densities are produced, peoplewait without pushing.

• Exits are free and the doors are wideopen.

• The evacuation plan is properly signaled.

• People start to evacuate when the alarmis activated on their own floor, followingthe 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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force model (SFM) [3]. This modification allows abetter approximation to the fundamental diagramof Ref. [12], commonly used in the design of pedes-trian facilities.

The SFM is a continuous-space and force-basedmodel that describes the dynamics considering theforces exerted over each particle (pi). Its Newtonequation reads

miai = FDi + FSi + FCi, (1)

where ai is the acceleration of particle pi. Theequations are solved using standard molecular dy-namics techniques. The three forces are: “DrivingForce” (FDi), “Social Force” (FSi) and “ContactForce”(FCi). The corresponding expressions are asfollows

FDi = mi(vdi ei − vi)

τ, (2)

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

FSi =

Np∑j=1,j 6=i

A exp

(−εijB

)enij , (3)

with Np being the total number of pedestrians inthe system, A and B are constants that determinethe strength and range of the social interaction, en

ij

is the unit vector pointing from particle pj to pi;this direction is the “normal” direction between twoparticles, and εij is defined as

εij = rij − (Ri +Rj), (4)

where rij is the distance between the centers of piand pj and R is their corresponding particle radius.

FCi = (5)

Np∑j=1,j 6=i

[(−εij kn) en

ij + (vtij εij kt) etij

]g(εij),

where the tangential unit vector (etij) indicates the

corresponding perpendicular direction, kn and kt

are the normal and tangential elastic restorativeconstants, vtij is the tangential projection of therelative velocity seen from pj(vij = vi − vj), andthe function g(εij) is: g = 1 if εij < 0 or g = 0otherwise.

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

The kind of model used allows one to definethe pedestrian characteristics individually. Fol-lowing standard pedestrian dynamics bibliography(see, for example, [3–5, 15]), we considered inde-pendent and uniform distributed values betweenthe ranges: pedestrian mass m ε [70 kg, 90 kg];shoulder width d ε [48 cm, 56 cm]; desired veloc-ity vd ε [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 = 1.2 105 N/m, kt = 2.4 105 kg/m/s.

Beyond the microscopic model, pedestrian be-havior simply consists in moving toward the exitof 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 every0.1 second. From these data, it is possible to calcu-late several outputs; in the present work we focusedon 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 analyticallyin Chapter 3-14 in Ref. [12], only for the case ofsimultaneous 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, wewill only consider the egress of 150 persons towardone of the stairs. Thus, on each floor, 150 people

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

are initially placed along the central corridor thatis 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 centralcorridors 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 ofegress. The effective width of the stairway is 1.4 m.The central corridors of each floor are separated by10.66 m. This separation arises from adding thehorizontal distance of the steps and the landingsbetween floors in the 3D system [12]. So the dis-tance between two floors in the 2D version of theproblem is of the same length as the horizontal dis-tance that a person should walk, also between twofloors, 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 isthe simultaneous evacuation of all floors.

The parameters to be varied in the study are thefollowing:

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 thenfollows in order to the immediately superiorfloors. a.2) “Top-Down” indicates that theevacuation begins on the top floor (7th, in thiscase), and continues to the next lower floor,until the 1st floor is finally evacuated.

b The time delay dt between the start of theevacuation of two consecutive floors. Thiscould be implemented in a real system througha segmented alarm system for each floor, whichtriggers 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 tf0 {BU,TD,SE} indicates the time

when the alarm is activated on floor f . Subindices{BU, TD, SE} are set if the time t belongs to theBottom-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 thealarm on the 2nd floor is triggered after dt seconds,t20 BU = t10 BU + dt, and so on in ascending orderup to the 7th floor . In general, the time when thealarm is triggered on floor f can be calculated as:

tf0 BU = T0 + dt× (f − 1). (6)

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

tf0 TD = T0 + dt× (N − f). (7)

Simultaneous Evacuation is the special case inwhich dt = 0 and thus, it considers the alarms onall the floors to be triggered at the same time:

tf0 SE = T0|f=1,2,...,7. (8)

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III. Results

This section presents the results of simulationsmade by varying the strategy and the time delaybetween the beginning of the evacuation of the dif-ferent levels.

Each configuration was simulated five times, andthus, the mean values and standard deviations arereported. This is consistent with reality, becauseif a drill is repeated in the same building, totalevacuation times will not be exactly the same.

i. Metrics definition

Here we define the metrics that will be used toquantify the efficiency of the evacuation process ofthe 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 theground floor (see Fig. 1), which means that thebuilding is completely evacuated.

The f th Floor Evacuation Time (FETf ) refers tothe time elapsed since initiating the evacuation offloor f until its 150 occupants reach the staircase.It must be noted that this evacuation time does notconsider the time elapsed between the access to thestaircase and the general exit from the building, nordoes it consider as starting time the time at whichthe evacuation of some other level or of the buildingin general begins. It only considers the beginning ofthe evacuation of the current floor. Average FloorEvacuation Time (FET ) is the average of the sevenFETf .

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 inevacuating all the floors having the same priorityat the same time.

Under these conditions, the capacity of the stairssaturates 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 queuesat each level can be observed. The differences inthe length of queues are due to differences in thetemporal evolution of density in front of each door.

Figure 2: Snapshot taken at 73 seconds since thestart of the simultaneous evacuation, where thequeues of different lengths can be observed on eachfloor.

In this evacuation scheme, the first level that canbe emptied is the 1st floor (105± 6 s) and the lastone 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 meanFloor Evacuation Time (FET ) is 195± 55 s.

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

iii. Bottom-Up strategy

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

It can be seen that the Total Evacuation Time(TET ) remains constant for time delays (dt) up to30 seconds. Therefore, TET is the same as the si-multaneous evacuation strategy (dt = 0 s) in thisrange. It is worth noting that 30 seconds is approx-imately one half of the time needed to evacuate afloor if the staircase were empty.

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

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−20 0 20 40 60 80 1000

100

200

300

400

500

600

700

dt (s)

Evacuation T

ime (

s)

TET

FET

(a)

−20 0 20 40 60 80 1000

100

200

300

400

500

600

700

dt (s)

Eva

cu

atio

n T

ime

(s)

TET

FET

(b)

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

asymptotic value for 65 seconds, which is the evac-uation time of a single floor considering the emptystairway. As expected, if the levels are evacuatedone at a time, with a time delay greater than theduration of the evacuation time of one floor, thesystem is at the limit of decoupled or independentlevels. In these cases, TET increases linearly withdt.

Since TET is the same for dt < 30 s and FETis significantly improved (it is reduced by half) fordt = 30 s, this phase shift can be taken as the bestvalue, for this strategy, to evacuate this particularbuilding.

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

More details can be obtained by looking at thedischarge curves corresponding to one realizationof the building egress simulation. The evacuationof the first 140 pedestrians (93%) of each floor isanalyzed by plotting the occupation as a functionof time in Fig. 4 for three time delays between therelevant range dt ε[0, 30]. For dt = 0 [Fig. 4(a)]there is an initial transient of about 10 seconds inwhich every floor can be evacuated toward a freepart of the staircase before reaching the congestion

due to the evacuation of lower levels. After that, itcan be seen that the egress time of different floorshas important variations, the lower floors (1st and2nd) being the ones that evacuate quicker and in-termediate floors such as 5th and 6th the ones thattake longer to evacuate. After an intermediate sit-uation for dt = 15 s [Fig. 4(b)] we can observe thepopulation profiles for the optimum phase shift ofdt = 30 in Fig. 4(c). There, it can be seen thatthe first 140 occupants of different floors evacuateuniformly and very little perturbation from one toanother is observed.

In the curves shown in Fig. 4, the derivativeof the population curve is the flow rate, mean-ing that low slopes (almost horizontal parts of thecurve such as the one observed in Fig. 4(a) for the5th floor between 40 and 100 s) can be identifiedwith lower velocities and higher waiting time forthe evacuating people. Because of the fundamen-tal diagram, we know that lower velocities indicatehigher densities. In consequence, we can say thatthe greater the slope of the population curves, thegreater the comfort of the evacuation (more veloc-ity, less waiting time, less density). Therefore, itis clear that the situation displayed in Fig. 4(c) ismuch more comfortable than the one in Fig. 4(a).

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

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(a) (b) (c)

Figure 4: Time evolution of the number of pedestrians in each floor up to 3 m before the exit to thestaircase. (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 exploitsthe 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 avoidsituations generating impatience due to waiting forgaining 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-Downstrategy.

It must be noted that TET increasesmonotonously for all dt, which is sufficient torule out this evacuation scheme.

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

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

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

In summary, the Top-Down Strategy does notpresent 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 severalpedestrian reservoirs (“rooms”) toward the samemeans of egress (“hallway”). In particular, we fo-cused on an example, namely, a multistory buildingin which different floors are evacuated toward thestaircase. We studied various strategies using com-puter simulations of people’s movement.

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

For the system under consideration, the presentstudy shows that if a strategy of sequential evac-uation of levels begins with the evacuation of the1st floor and, after a delay of 30 seconds (in thisparticular case, 30 s is approximately one half ofthe time needed to evacuate only one floor if thestaircase 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 processimproves. From the standpoint of the evacuation ofthe building, TET is the same as that for the ref-erence state. However, if FET is considered, thereis a significant improvement since it falls to abouthalf. This will make each person more comfortableduring an evacuation, reducing the waiting timeand thus, the probability of causing anxiety thatmay bring undesirable consequences.

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So, one important general conclusion is that asequential Bottom-Up strategy with a certain phaseshift can improve the quality of the evacuation of abuilding of medium height.

On the other hand, the simulations show thatthe sequential Top-Down strategy is unwise for anytime 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 higherthan the reference value at dt = 0). In consequence,the present study reveals that this would be a badstrategy that should be avoided.

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

The results of the present research could formthe basis for developing new and innovative alarmsystems 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” sharea common means of escape.

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

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