Group Behavior in FDS+Evac Evacuation Simulations

Transcription

1 HELSINKI UNIVERSITY OF TECHNOLOGY Department of Automation and Systems Technology Systems Analysis Laboratory Mat Independent Research Project in Applied Mathematics Group Behavior in FDS+Evac Evacuation Simulations Juha-Matti Kuusinen, 57755S Espoo,

2 Contents 1 Introduction 2 2 Modeling Crowd Dynamics and Group Behavior Helbing s Model for Crowd Dynamics Group Behavior in FDS+Evac The gathering stage The evacuation stage Simulations The Experimental Design Evacuation in an Open Corridor Evacuation Through a Throttle Effect of Throttle Shape Behavior of Groups in a Crowd Results Evacuation in an Open Corridor Evacuation Through a Throttle Effect of Throttle Shape Behavior of Groups in a Crowd Discussion 28 References 32 1

3 1 Introduction A proper fire safety design in large buildings undoubtedly increases the number of survivals in case of fire or other catastrophe. However, if crowd dynamics and behavior of humans are not taken into account, disasters can still have grave consequences. Modeling and computational simulation of evacuation is one way to increase the safety of large constructions. The usability of many current evacuation models is yet questionable because they do not consider the decision making and group behavior of humans. Fire Dynamics Simulator (FDS) with an egress calculation module (Evac) is a state-of-the-art software that enables the simulation of evacuation in case of fire. FDS and the related visualization software Smokeview [1] are developed at National Institute of Standards and Technology (NIST) in the USA. The evacuation module is developed at VTT Technical Research Centre of Finland [7]. The evacuation module exploits the effective flow-calculation algorithms of FDS to create exit routes for the evacuees. FDS is able to calculate a route from any point of a building to any exit. All the routes together form a directional vector field that can be used in modeling the motion of the evacuees. FDS+Evac is made publicly and freely available and can be downloaded from the Internet [2]. Also the source files are available. In FSD+Evac each pedestrian is driven by an equation of motion. This approach allows the treatment of each person as an individual agent. The model behind the movement algorithm is the social force model introduced by Helbing s group [3, 4, 5]. This model has been modified to include a better description of the shape of the human body and to include the rotational degrees of freedom [9, 8]. The model integrates physical and social forces affecting the movement of pedestrians in a crowd. These forces prevent humans, for example, from moving too close to each other or colliding against the walls. Martikainen discusses in her Master s thesis [10] the social psychological ef- 2

4 fects related to the familiarity of the exit routes, grouping of people, decision making under stress, the appearance of panic, and the social effects caused by other pedestrians. Another recent survey on human behavior in emergencies was conducted by Pan [11]. According to Pan, actions taken by the members of a group are not independent. Furthermore, a separated group may try to gather together before exiting and groups that are hierarchically organized, like families, will probably behave differently than those that are not. In conclusion, instead of immediately running to the exits, evacuees gather together with familiar people, consider the alternative courses of action and try to exit together. Heliövaara introduces in his Master s thesis [6] many computational models for human behavior in evacuation situation. Some of these models have already been implemented in FDS+Evac and their effects have been studied through test simulations. The aim of this project is through various simulations study the group behavior model that will be part of later versions of FDS+Evac. One of the main objectives is to find a realistic default value for the parameter GROUP EFF. In FDS+Evac, this parameter is used to describe how eagerly members of a group want to keep the group together. 3

5 2 Modeling Crowd Dynamics and Group Behavior In this section we are going to shortly present Helbing s model for crowd dynamics. In the presentation, human body is modeled by a circle in a twodimensional space. A better description of human body can be achieved with three circles [9] and in the version 1 of FDS+Evac that we used in the simulations, human body is approximated with three circles. One should know that the conversion from one-circle approximation to three-circle approximation does not make Helbing s model inadequate. This is because the interaction forces between two persons and a person and the walls are calculated using those circles of the persons that are closest to each other or that circle of a person that is closest to a wall. Thus, the model is correct for the version of FDS+Evac that we used. The only thing that changes between the two approximations of the human body is that the three-circle approximation introduces rotational degrees of freedom that has to be taken into account in the model. How this is done, see the papers written by Langston et. al [9] and Korhonen et. al [8]. In this section we will also present how one adds group behavior to Helbing s model [6]. 2.1 Helbing s Model for Crowd Dynamics People who are evacuating from a building, for example, in case of fire tend to move faster than normal. They start pushing each other and interactions among a crowd become physical in nature. A throttle on an exit route can cause arching and clogging and jams may build up. In these jams, the pushing of crowd members in the back can cause fatal pressures in the front. In addition, evacuating people show tendency towards mass behavior. 1 Fire Dynamics Simulator, Compilation Date: May 31, 2007, Version: 5 RC5+. FDS+Evac Evacuation Module, FDS+Evac Compilation Date: May 9, 2007, FDS+Evac Version: 1.10b. 4

6 These observations encouraged Helbing s group to model the evacuation as a many-particle system in continuous space. This approach is particulary good for evacuation simulations because it includes the real physical forces appearing in such situations. These forces are body forces that counteract body compression and friction forces between two pedestrians and between pedestrians and walls. The equation of motion for pedestrian i is dv i m i dt = m vi 0 (t)e 0 i (t) v i (t) i + f ij + τ i j( i) W f iw + ξ i, (1) where m i vi 0 (t) e 0 i (t) v i (t) τ i f ij j( i) f iw W ξ i is the mass of pedestrian i is the desired speed of pedestrian i is the desired moving direction of pedestrian i is the actual velocity of pedestrian i is a characteristic acceleration time includes the forces between pedestrian i and other pedestrians includes the forces between pedestrian i and the walls is a small random force As shown in Equation (1), acceleration of a pedestrian, considered as a particle in the model, can be caused by difference between the desired velocity vi 0 (t)e 0 i (t) and the actual velocity v i (t), or by the forces caused by other pedestrians, f ij, or by walls, f iw. The small random force ξ i is added to prevent two pedestrians to jam in a head-on encounter. The characteristic acceleration time of pedestrian i, τ i, denotes the time in which the pedestrian accelerates to the desired velocity. Small values of τ i create high accelerations and vice versa. 5

7 The psychological tendency of two pedestrians i and j to stay away from each other is described by a repulsive interaction force, called social force ( A i exp[(r ij d ij )/B i ]n ij λ i + (1 λ i ) 1 + cos(ϕ ) ij), (2) 2 where A i and B i are constants, R ij is the sum of pedestrians radii and d ij = r i r j is the distance between pedestrians centers of mass. Vector n ij = (r i r j )/d ij denotes the normalized vector pointing from pedestrian j to i. The last term of Equation (2) scales the quantity of the social force according to the location of the repulsive occupant. If we select λ i < 1 the occupants in front of the pedestrian have larger impact than the ones behind the pedestrian. The angle ϕ ij (t) denotes the angle between the pedestrian s moving direction v i (t)/ v i (t) and the direction n ij of the occupant exerting the repulsive force, i.e., cos ϕ ij (t) = n ij v i / v i (t). The pedestrians touch each other if their distance d ij is smaller than the sum of their radii R ij. In this case, two forces are added to the model. Body force, defined by k(r ij d ij )n ij counteracts body compression and sliding friction force κ(r ij d ij ) ν t jit ij controls relative tangential motion. Here t ij means the tangential direction between the pedestrians, which is perpendicular to n ij, and ν t ji = (v j v i ) t ij is the tangential velocity difference. Symbols k and κ represent large constants. Now, the interaction forces between two persons can be defined by f ij = κg(r ij d ij ) νjit t ij + (3) { ( A i exp[(r ij d ij )/B i ] λ i + (1 λ i ) 1 + cos(ϕ ) } ij) + kg(r ij d ij ) n ij 2 where the function g(x) is zero if the pedestrians do not touch each other, i.e. d ij > R ij, and otherwise equal to the argument x. 6

8 The interaction between a person and the walls is analogous to the personto-person interactions. The related force can be given by f iw = {A i exp[(r i d iw )/B i ] + kg(r i d iw )}n iw (4) κg(r i d iw )(v i t iw )t iw where d iw is the distance from pedestrian i to wall W, n iw denotes the unit direction perpendicular to the wall. Vector t iw denotes the tangential direction between the wall and the pedestrian. Hence, t iw is perpendicular to n iw. An important benefit of the model is the possibility to easily implement different behavior of the evacuees. This can be done by changing the desired moving direction e i (t) and the desired velocity vi 0 (t). Thus, group behavior can be added to the model by properly adjusting these vectors. Of course, this is not the only way to implement group behavior. For example, an additional force could be used to describe attraction (or repulsion) between humans [8]. In this case group behavior could be added by using strong attractive forces between the members of a group. 2.2 Group Behavior in FDS+Evac In the FDS+Evac model the population is assumed to consist of groups of pedestrians, like families or friends, that often have come to the building together. As stated earlier, these groups will probably also try to leave together, and thus, actions of a group can be divided into two stages. In the gathering stage, the group members walk towards each other to gather the group. In the evacuation stage the group moves together along the chosen exit route. The initial location of pedestrians may affect the outcome of the simulation greatly. When the behavior of groups is taken into account the effect can be even greater. The algorithm for the location of the pedestrians in the beginning of the simulation is presented in [6]. 7

9 This section describes how the group behavior is added to Helbing s model by changing the value of e 0 i (t). All of the models and equations presented here are based on [6] The gathering stage In the gathering stage, each pedestrian attempts to move towards the center of the group, and thus, vector e 0 i (t) of each group member points to the center of the group. The gathering stage continues until all of the group members are within a certain radius r(n) from the center. It is assumed that the radius depends on n, which denotes the size of the group. This dependence is modeled with function r(n) = r 0 + nr 1 (5) where r 0 and r 1 are constants. Once the group has been gathered, it begins to evacuate The evacuation stage In the evacuation stage, each pedestrian has two objectives. The first is to move along the chosen exit route. The second is to keep the group together. Thus, the desired moving direction vector e 0 i (t) can be given by e 0 i (t) = αe 0 C,i(t) + (1 α)e 0 F,i(t) (6) where e 0 C,i (t) is a normalized vector pointing to the center of the group and e 0 F,i (t) is a normalized vector pointing to the direction of the vector field, i.e., the exit route direction calculated by FDS. The parameter α [0, 1] is called group effect. It is denoted with GROUP EFF in FDS+Evac. The larger the group effect parameter is, the more eagerly the group members try to keep the group together during the evacuation. When a group starts to move towards an exit, the desired moving speeds v 0 i (t) are set equal for all group members. Without equalizing the speeds, 8

10 the faster group members would run away from the others. This could be prevented with other ways too, for example, by slowing down the group members who are ahead and by accelerating the members who are behind. Anyway, in the current version of FDS+Evac the desired moving speed of each group member is determined to be the desired moving speed of the slowest group member. The moving speed of each evacuee is drawn from user specified distribution 2 which can be different for every type of evacuee. 3 Simulations 3.1 The Experimental Design We are interested in how the evacuation speed and the behavior of groups changes when the value of the parameter GROUP EFF changes. It is also of interest to study how the evacuation of a small crowd consisting of autonomous pedestrians differs from that of a small group of pedestrians. In FDS+Evac, there are five default human types defined: adult, male, female, child and elderly [2]. The crowds and the groups in the simulations will consist of three or six adults. A small group of three adults could represent, for example, two parents with an adult child. A group of six adults can be regarded as a group of grown up friends. Intuitively, we should get results indicating that a crowd consisting of autonomous adults evacuates faster than a group of adults because the movement of the group is affected, for example, by the group s desire to stay together. In most of the experiments we will quantitatively measure the average evacuation speed of a crowd and a group of similar size and compare the results. We will also do some qualitative studies concerning, for example, the movement of a group through a two-piece throttle and the behavior of groups in a large crowd. 2 The distribution of the moving speed is by default uniform distribution whose width depends on the human type. In FDS+Evac there are five default human types [2]. 9

11 Figure 1: Snapshot of the Probabilistic Fire Simulator 3 The average evacuation speed is calculated using values obtained from several simulations executed with help of Probabilistic Fire Simulator 3 (PFS3), see Figure 1. PFS3 is an Excel based software developed at VTT. It is used for Monte-Carlo simulations using different fire models. With PFS3 we can run, for example, 1000 simulations for different values of the parameter GROUP EFF so that we don t need to change the value of the parameter between simulations manually. PFS3 does it automatically facilitating the simulations and increasing their number. PFS3 is not yet publicly available. In almost all of the configurations the directional vector field that is used to calculate the evacuation routes to the exit is created by placing a sucking vent in the bottom of the room. In the last configuration the vent is placed behind the main exit. 10

12 3.1.1 Evacuation in an Open Corridor The evacuation geometry, presented in Table 1 and Figure 2, consists of four meters wide and ten meters long open corridor 3. We will first examine the evacuation speed of crowds consisting of three and six autonomous adults. We have placed two counters 4.25 meters away from each other to be able to calculate the instants of time when the last adult crosses the first and the second counter. It is not necessarily the same adult that crosses last the both counters. The evacuation speed is the distance between the counters divided by the time difference of the two instants of time. We will run once 500 Monte-Carlo simulations for both crowd sizes. Evacuation geometry 4.0 m x 10.0 m corridor Crowd size 3 and 6 Counter position First counter: y = 5.25 Second counter: y = 1.0 Initial position of adults 3 adults: , (x 0 x),(y 0 y) 6 adults: , Table 1: The evacuation geometry We will also run simulations for groups of three and six adults. An important difference compared to the situation above is that the group behavior has to be taken into account through the parameter GROUP EFF. In the first run, the parameter will receive the following values: 0.05, 0.1, 0.15, 0.2, 0.25, 0.3 and In the second run, as we want to study the effect of the parameter more precisely, it will receive values from 0.2 to 0.3 with a step size The number of Monte-Carlo simulations will be adjusted so that the there will be approximately 100 simulations per value of the parameter. Since a group of six adults needs more space than a group of three adults, FDS+Evac more often fails to place the bigger group into the desired area in the beginning of the 3 In all Figures of this project work, x-axis denotes horizonal and y-axis vertical direction. 11

13 Figure 2: The evacuation geometry. Each pedestrian is described with three squares simulation. Thus, the number of Monte-Carlo simulations will be larger for group size six and we will get a reasonable number of succeeded simulations for every combination of group size and the parameter Evacuation Through a Throttle The evacuation geometry, presented in Table 2 and Figure 3, consists of a 10 meters wide and long room containing one meter wide throttle. The throttle may represent a door or an exit. There are again two counters 4.25 meters away from each other. In Figure 3 can also be seen the vector field used in the evacuation calculation. The desired moving direction of an adult is the direction of the vector field in the position of the evacuation grid that the adult is occupying. We will first examine the evacuation speed of a crowd of three adults by running once 500 Monte-Carlo simulations from two initial positions: center and upper left corner, see Table 2. We do not need to run simulations starting from the upper right corner as the results would be analogous to those 12

14 Evacuation geometry 10.0 m x 10.0 m room Crowd or group size 3 and 6 Counter position First counter: y = 5.25 Second counter: y = 1.0 Initial position of adults 3 adults: Center , Upper left corner , adults: Center , , Upper left corner , Throttle position left obstacle: , right obstacle: , Table 2: The evacuation geometry Figure 3: The evacuation geometry obtained starting from the upper left corner. Then we will run 1000 Monte- Carlo simulations for a group of three adults starting from the same initial positions. The parameter will receive values 0.05, 0.1, 0.15, 0.2, 0.25, 0.26, 0.27, 0.28, 0.29 and 0.3. Thus, there will be approximately 100 simulations 13

15 per value of the parameter. We will also run the same simulations for crowd and group size six. In this case, the area where the adults are initially put will be larger, see Table 2, and the number of Monte-Carlo simulations for group size six will be 2000 to ensure enough succeeded simulations Effect of Throttle Shape We want to examine the effect of throttle shape on the average evacuation speed of groups of three and six adults. The room geometry is the same as above except that in the first configuration we will use one two meters wide throttle and in the second, the throttle will consists of two one meter wide sections with 0.4 meters wide obstacle between them, see Figure 4. Initial position of the adults is in the horizontal center of the room. We are also interested in the value of the parameter which causes the whole or the majority of the group to evacuate through the same section of the twopiece throttle. We will study this qualitatively with the help of Smokeview. The parameter will receive values 0.15, 0.2, 0.25 and We will run 10 simulations per value of the parameter for both group sizes. An important thing to be observed is how a group uses the two-piece throttle, i.e., does the group split up or stay together. In addition to the qualitative study, we will quantitatively examine the way of using the two-piece throttle. In this test the idea is to define the number of simulations in which the majority of a group of six adults passes through the same section of the throttle. If the group effect parameter has some effect, we should get results indicating that the larger the value of the parameter, the larger the number of the simulations in which the majority used the same section. We determine the majority to be four out of six adults, i.e., zero, one or two adults passes through different section of the throttle than the others. We will place one counter behind each section of the throttle. If the absolute value of the difference between the counters is more than zero, we know that the majority passed through the same section. In this case, the 14

16 Figure 4: The evacuation geometry with a two-piece throttle outcome of the simulation will be one. Otherwise it will be zero. By summing all the outcomes of the simulations, we will know in how many simulations the majority used the same section. We will run 1600 simulations with PFS3. The initial positions of the adults will be , , i.e., upper left corner and , , i.e., center. The group effect parameter will receive the following values: 0.1, 0.15, 0.2 and Behavior of Groups in a Crowd We will qualitatively study how the behavior of groups in a crowd varies as the value of the parameter varies. We are interested in the following matters: evacuation formation of groups, values of the parameter that causes groups either to stay together or spread out to the crowd and value of the parameter that causes groups to wander around unreasonably. The evacuation geometry is presented in Figure 5. It consist of a 40 meters long and 25 meters wide congress center. Four rooms are placed inside the center: three auditoriums (large rooms) and a toilet (small room). There is a two meters wide and long pillar in the middle 15

17 Figure 5: The evacuation geometry Figure 6: Initial positions of the groups in a crowd of the building. There is also a four meters long and 0.5 meters wide desk with a chair in the lobby. The main exit is two meters wide and the room doors are one meter wide. We will place in total 400 adults inside the building. To be able to study the group behavior, we will place one group of three and one group of six adults in each of the bigger rooms. There will also be a group of three adults in the upper left corner room, a group of six adults between the 16

18 two upper rooms and a group of three adults between the two rooms in the left. The parameter will receive the following values: 0.05, 0.1, 0.15, 0.2, 0.25 and 0.3. The duration of the gathering stage of the groups will be set to five seconds. 3.2 Results Evacuation in an Open Corridor The average evacuation speeds of a crowd of three and six autonomous adults were m/s and m/s. Thus, a crowd of three adults evacuates faster than a crowd of six adults. This is a consequence of the fact that the desired moving speed of each adult is a random number drawn by FDS+Evac from a uniform distribution whose width is given as [1.25 m/s±0.30] [2]. It is likely that the minimum value of a bigger sample is smaller than the minimum value of a smaller sample when the values of the samples are drawn from the same uniform distribution. For the same reason, the evacuation speed of a crowd of three autonomous adults is on average smaller than the mean 1.25 m/s. The social forces have probably also some influence on the evacuation speed. This influence is stronger in a crowd of six adults as there are more social forces influencing the movement of each adult. From Figures 7 and 8 we can state that the evacuation speed of a group of three adults is faster than that of a group of six adults. It seems also that a group of three adults moves slower in an open corridor than a crowd of three autonomous adults. This applies for six adults too. An interesting feature is that the evacuation speed of the groups starts to considerably decrease approximately after the value 0.28 of the group effect parameter. The main reason for this decrease is probably that the moving directions become unreasonable. For example, groups might not be moving towards the exit all the time. This is not realistic behavior. We can conclude that if one wants to add group behavior to the simulations, the value of the 17

19 Figure 7: The average evacuation speed (m/s) of a crowd and a group of three and six adults as a function of the group effect parameter Figure 8: The average evacuation speed (m/s) of a crowd and a group of three and six adults as a function of the group effect parameter parameter should not be larger than To leave some margin, a good default value for the parameter in an open corridor or room would be Evacuation Through a Throttle The results for the case where a crowd and a group of three adults are evacuating through the throttle are presented in Figures 9 and 10. Naturally, the average evacuation speed is slower when the evacuation starts from the upper left corner. It seems also that the evacuation speed of a group of three adults is faster than that of a crowd of three autonomous adults when the group effect parameter receives values equal to or smaller than

20 Figure 9: The average evacuation speed (m/s) of a crowd and a group of three adults, initial position: center Figure 10: The average evacuation speed (m/s) of a crowd and a group of three adults, initial position: upper left corner The main reason for this result lies in the vector field. It works properly for a fluid or a gas, but is not always suitable for modeling the evacuation of humans. Let us assume that an autonomous adult starts, for example, from the upper left corner of Figure 3. Depending on the specific speed, orientation and weight of the adult, the momentum will drive the adult to the frames and not straight through the throttle. Also, in case of a crowd of autonomous adults, the social forces can drive the adults far away from the horizontal center, and thus, their trajectories become such that they will be driven to the frames of the throttle. In case of groups, the parameter keeps the groups together especially when it receives large values. In addition, groups use some seconds to gather together before the evacuation starts, i.e., each 19

21 member of a group first moves towards the center of the group and then starts to evacuate. This causes the members who initially are far away from the horizontal center to be placed closer to it before the evacuation starts. Thus, there is a bigger chance that all the members avoid hitting the frames. The results seem to be similar for both initial positions of the adults. We managed to increase the evacuation speed of a crowd of autonomous adults by adding blowing vents to the side walls of the room. This transformed the vector field to such that the moving formation of the crowd resembled that of a group with the normal vector field. Even if it was possible to make the vector field work better for evacuation calculation of a crowd in this simple geometry, in a more complex geometry, it would be too troublesome to add blowing vents on the sides of the obstacles and walls. Thus, the vector field has to modified at least near the doors. Figure 11: The average evacuation speed (m/s) of a crowd and a group of six adults, initial position: center The results for six adults, see Figures 11 and 12, are comparable to those obtained with three adults. Figures 13 and 14 illustrate the difference between the evacuation of a crowd and a group of six adults. In the simulation, the initial position was horizontally in the center of the room and the group effect parameter received value 0.2. In the first frame of the both figures, the elapsed time is one second, so the group has already gathered together. In the other frames, elapsed times are 20

22 Figure 12: The average evacuation speed (m/s) of a crowd and a group of six adults, initial position: upper left corner Figure 13: The evacuation of a crowd of six autonomous adults Figure 14: The evacuation of a group of six adults 5.05 and 8.05 seconds. The evacuation of the group seems to be much more organized and therefore faster than the evacuation of a crowd of autonomous adults. An important result concerning these simulations is that the parameter should not receive values above the value As discovered earlier, with larger values the moving directions of the groups become unreasonable. Again, to leave some margin, the chosen parameter value in evacuation simulations through a throttle should not be larger than

23 3.2.3 Effect of Throttle Shape It seems, see Figure 15, that the evacuation speed of a group of three adults is faster through one wide throttle than through a two-piece throttle. This is what one would expect to happen in a real situation. The difference in the evacuation speed between the two throttle shapes is, however, very big. Even with the smallest studied value of the parameter, the moving speed of the group through the two-piece throttle is unreasonably slow. Figure 15: The average evacuation speed (m/s) of a group of three adults evacuating through different throttle shapes The qualitative study revealed the source of this problem. The vector field in Figure 16 is such that it drives the evacuees against the middle obstacle and not through the sections of the throttle. In a real situation the evacuees would not hit the obstacle, especially, when the room is not packed of other evacuees and high pressures in front of the throttle do not occur. This explains the significant difference in average evacuation speed between the two throttle shapes. It was also checked that an autonomous adult, starting horizontally from the coordinates of the left section of the throttle, can and probably will hit the obstacle. We tried to sidestep this problem by changing the geometry and the position of the vents but the vector field, and thus, the behavior of 22

24 the evacuees did not improve. Besides, one should not use too complicated tricks to improve the vector field because in that case the model loses its applicability. Figure 16: The vector field in the two-piece throttle geometry It was learned that, in case of a two-piece throttle, the initial position of the adults have more impact on the way of using the throttle than the group effect parameter. Another observation was that the group seeks to move in line like formation as shown in Figure 17. The consequence is that if the first adult of the group hits the middle obstacle then the second adult will hit the first and the third will hit the second, etc. This causes the adults to crash against each other which in turn causes them to bounce to the sides. This behavior is very arbitrary and unrealistic, which makes it very hard to analyze how the way of using the two-piece throttle varies as the parameter varies. In Figure 18 are presented the results for the quantitative study. The percentage value indicates the number of simulations in which the majority of the group passed through the same section of the two-piece throttle. We can state that when the initial position of the group is the upper left corner of 23

25 Figure 17: A group in line like formation just before the first adult hits the obstacle Figure 18: The number of simulations where the majority passed through the same section of the throttle the room the majority of the group almost always uses the same section. The group parameter does not have any effect on the way of using the throttle. When the initial position of the group is horizontally in the center of the room, the parameter has some effect. Between the values 0.1 and 0.2 of the parameter the way of using the throttle does not vary significantly. The value 0.25 has a distinguishable effect. In conclusion, the vector field does not work correctly in a geometry including two piece throttles but some group behavior 24

26 can be added to the model with the value 0.25 of the group parameter Behavior of Groups in a Crowd The first observation concerning all the simulations was that the vector field very often drives the evacuees against the obstacles. As stated earlier, this is not a lifelike phenomenon. It was noticed that the best way to find differences between the simulations executed with different values of the group effect parameter, is to observe the trajectories of the evacuees: if the trajectory of the group members is clearly different from that of the autonomous adults, the parameter probably has some effect. Presumably, the social forces have some effect too. However, the effect of these forces is similar in all of the simulations, and thus, all the observed differences should be caused by the varying value of the parameter. The results are presented below separately for every studied value of the parameter. 1. GROUP EFF = 0.05: One cannot distinguish the behavior of the group members from that of the autonomous adults. The group members follow the trajectory given by the vector field and their choices concerning the desired moving direction are independent from one another. 2. GROUP EFF = 0.1: No change occurs in the behavior compared to the previous configuration. The groups spread out to the crowd and all the evacuees follow the same trajectories to the main exit. As shown in Figure 19, in front of the main exit, groups are not in group formation and the last group arriving to the main exit is spread out. 3. GROUP EFF = 0.15: The trajectory of some group members is altered by the parameter. 25

27 Figure 19: Some groups in front of the main exit, no recognizable group formation This is visible especially for those groups that are initially in a room and whose members exit the room at different times. The members who come out first try to stay close to those group members who are still inside the room. Thus, they move closer to the room walls than the autonomous adults coming out from the same room. 4. GROUP EFF = 0.2: Now, the effect of the parameter truly emerges. As shown in Figure 20, two members of the group of six adults initially placed in the lower left corner room are clearly following a trajectory that keeps them close to the other group members. They first move close to the room wall and later follow a different trajectory than the autonomous adults. In addition, there can be seen some groups in front of the main exit. 5. GROUP EFF = 0.25: The effect of the parameter is very strong. Those members who are first to come out of a room stay and wait for the other group members. Since the groups are now very tight, their moving speed is clearly slower and 26

28 Figure 20: First, two group members move close to the room wall and later follow a different trajectory than the autonomous adults they can disturb the evacuation, for example, an autonomous adult can get stuck in the middle of a group. The parameter should not receive larger values than this because, even if the group behavior would get stronger, this value is in the boundary of reasonableness. It is possible to point out all the groups from Figure 21. Figure 21: All the groups in recognizable group formation 6. GROUP EFF = 0.3: It seems that with this value of the parameter all the groups move in group formation. However, the moving speed and direction of the groups are unreasonable. As shown in Figure 22, the last group moves 27

29 about two meters, i.e, the length of the pillar in about 12 seconds even if there is no one in front of the group. The effect of the parameter is too strong and does not realistically describe the group behavior. Figure 22: Evacuation simulation at elapsed times and seconds 4 Discussion FDS+Evac, Fire Dynamics Simulator developed at National Institute of Standards and Technology (NIST) in the USA, with an evacuation module developed at VTT Technical Research Center in Finland, is a simulation software that combines fire and evacuation simulation. In FDS+Evac, the basic dynamics of the crowd are modeled with Helbing s model. The model allows the simulation of the sociopsychological and physical forces influencing the behavior of humans in a crowd. A crowd may include groups, like families. Pan [11] states that the actions taken by the members of the same group are not independent. In an evacuation situation, a group may first try to gather together and then start exiting the building. These observations have encouraged the improvement of Helbing s model to enable the simulation of group behavior. The computational model for group behavior in FDS+Evac is developed by Heliövaara [6]. In the model, the desired moving direction of each evacuee consists of a vector pointing to the center of the group and a vector pointing to the direction of the vector field. Various group behaviors can be achieved by 28

30 altering the parameter GROUP EFF which determines the interrelationship between the two vectors. Thus, the goal of the project was to find a proper default value for the parameter. The simulations were run with the help of Probabilistic Fire Simulator 3 (PFS3), an Excel based software developed at VTT. PFS3 enabled an automated simulation process through which it was easy to gather a large number of experiment data, and thus, obtain more reliable results. We studied the effect of the parameter in four different configurations. In the first one, crowds of three and six autonomous adults and same sized groups were evacuating in a four meters wide and ten meters long open corridor. It was found that a crowd of three autonomous adults evacuates faster than a group of three adults. This was also true for six adults. Another result was that a crowd of three adults evacuates faster than a crowd of six adults. This is consequence of the uniform distribution that FDS+Evac uses to set the initial speeds for the adults. The most important result obtained here was that the maximum value of the parameter should not be larger than After this value, the group behavior is at risk to become unrealistic. In the second configuration, the evacuation took place in a ten meters wide and long room that included one meter wide throttle. We wanted to study the difference in the evacuation speed between a crowd and a group and of course the effect of the parameter. A slightly surprising result was that when the parameter received a value equal to or smaller than 0.28, groups evacuated faster trough the throttle than crowds, regardless of the initial position. The main reason for this is the unsuitable vector field that causes autonomous adults to hit the frames of the throttle. In addition, the parameter weakens the effect of the social forces and changes the desired walking direction of each group member to such that they move closer to each other and in line like formation. This accelerates the evacuation through a throttle. A good value for the parameter in this kind of configuration would again be The purpose of the third configuration was to study the effect of throttle 29

31 shape on the evacuation speed of a group. We made two quantitative studies and also statistically and qualitatively studied the way the a group uses a two-piece throttle. In the first quantitative study, a group of three adults evacuated through two different throttle shapes. The results indicated what is intuitively quite clear, i.e., the evacuation was faster through the two meters wide throttle than through the two-piece throttle. The difference in the evacuation speed was, however, unreasonably big. The qualitative study revealed that the reason for this problem was the vector field that directed the evacuees against the middle obstacle. This caused the evacuees to crash against each other and bounce here and there. Thus, the behavior of a group was unrealistic and arbitrary which made it hard to draw any conclusion concerning the effect of the parameter. We concluded that the current vector field is not very suitable for simulations in geometries that include two-piece throttles. The last configuration was a little bit more complex as we wanted to qualitatively study how the behavior of groups in a large crowd changes when the value of the parameter changes. We placed groups of three and six adults inside a 40 meters long and 25 meters wide building in which there were four rooms. Through numerous simulations we carefully studied the behavior of the groups separately for five values of the parameter. The values 0.05 and 0.1 did not have any visible effect. The value 0.15 had a small effect as some of the group members started to have different trajectories than the autonomous evacuees who always follow the trajectory given by the vector field. A strong effect was discovered when the parameter received value 0.2. The exit trajectories of the group members were clearly different from those of the autonomous adults. The effect of this value was especially visible for those groups whose members came out of a room at different times. Those members who came out first tried to stay as close as possible to the other group members who were still in the room, and thus, were moving close to the room walls. The value 0.25 had a very strong effect. In addition to the tendency to stay close to each other, the group members started to wait for 30

32 each other. It was also possible to distinguish all the groups from the crowd. The last value that we studied was 0.3. It seemed that with this value of the parameter all the groups move in group formation and are very tight. However, the moving speed and direction of the groups became unreasonable. The groups started to wander around. Thus, if one wants to add some realistic group behavior to the simulations, the parameter should not receive larger values than It is important to remember that too small values of the parameter do not have any effect at all. We conducted an extensive study concerning the group behavior in FDS+Evac evacuation simulations. We decided to measure the average evacuation speed because we wanted to know how fast the evacuation is completed. We used such small crowds and groups that, for example, measuring the evacuation flow would not have been reasonable. We managed to find a good default value for the parameter in geometries that do not include two-piece throttles. However, the vector field that is currently used to calculate the desired moving direction of the evacuees is not satisfactory and should be modified in the future. This would increase the quality and reliability of the simulations. Despite the small malfunction caused by the vector field in certain geometries, FDS+Evac showed its ability to simulate evacuations including group behavior. 31

33 References [1] [2] [3] Helbing, D. & Molnár, P. Social force model for pedestrian dynamics. Physical Review E, 51(5): , [4] Helbing, D., Farkas, I. & Vicsek, T. Simulating dynamical features of escape panic. Nature, 407: , [5] Helbing, D., Farkas, I.J., Molnár, P. & Vicsek, T. Simulation of pedestrian crowds in normal and evacuation situations. In M. Schreckenberg and S.D. Sharma, editors, Pedestrian and Evacuation Dynamics, pages Springer, [6] Heliövaara, S. Computational Models for Human Behavior in Fire Evacuations. Master s thesis, Helsinki University of Technology, [7] Heliövaara, S., Ehtamo, H., Korhonen, T. & Hostikka, S. Poistumissimuloinnit palotilanteissa. Conference paper, [8] Korhonen, T., Hostikka, S., Heliövaara, S., Ehtamo, H. & Martikainen, K. Integration of an agent based evacuation simulation and the state-of-the-art fire simulation. Paper written to the 7th Asia-Oceania Symposium on Fire Science and Technology, [9] Langston, P.A., Masling, R. & Asmar, B.N. Crowd Dynamics Discrete Element Multi-Circle Model. Safety Science, 44: , [10] Martikainen, K. Käyttäytyminen uhkatilanteessa - Poistumisreitin valintaan vaikuttavat sosiaaliset tekijät tulipalossa. Master s thesis, University of Helsinki,

34 [11] Pan, X. Computational Modeling of Human and Social Behaviors for Emergency Egress Analysis. Master s thesis, Standford University,