Modified social force model based on information transmission toward crowd evacuation simulation

Physica A 469 (2017) 499–509

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Physica A journal homepage: www.elsevier.com/locate/physa

Modified social force model based on information transmission toward crowd evacuation simulation✩ Yanbin Han a,b,c , Hong Liu a,b,∗ a

School of Information Science and Engineering, Shandong Normal University, Jinan, China

b

Shandong Provincial Key Laboratory for Novel Distributed Computer Software Technology, Jinan, China

c

School of Information Science and Engineering, University of Jinan, Jinan, China

highlights • • • •

Information transmission is introduced into social force mode in this paper. The reliability of evacuation information is used for choosing exits. A collision avoidance strategy is proposed and adopted in our model. The results show our model can help to design and optimize evacuation scheme.

article

info

Article history: Received 5 September 2016 Received in revised form 7 November 2016 Available online 16 November 2016 Keywords: Crowd evacuation Exits choosing Information transmission Social force model

abstract In this paper, the information transmission mechanism is introduced into the social force model to simulate pedestrian behavior in an emergency, especially when most pedestrians are unfamiliar with the evacuation environment. This modified model includes a collision avoidance strategy and an information transmission model that considers information loss. The former is used to avoid collision among pedestrians in a simulation, whereas the latter mainly describes how pedestrians obtain and choose directions appropriate to them. Simulation results show that pedestrians can obtain the correct moving direction through information transmission mechanism and that the modified model can simulate actual pedestrian behavior during an emergency evacuation. Moreover, we have drawn four conclusions to improve evacuation based on the simulation results; and these conclusions greatly contribute in optimizing a number of efficient emergency evacuation schemes for large public places. © 2016 Elsevier B.V. All rights reserved.

1. Introduction The research on pedestrian dynamics for emergency evacuation has attracted increasing attention from scholars recently. Many remarkable models simulating the complex behavior of pedestrians have been proposed to analyze evacuation processes in different situations [1–3]. These evacuation models can help create an efficient emergency evacuation scheme to minimize damage and avoid loss of life. The models can be divided into two categories: discrete and continuous, which include the cellular automata [4–6] and lattices models [7–9], and the social force (SF) model [10,11], respectively.

✩ The work described in this paper was supported by grants from the National Natural Science Foundation of China (61472232, 61373149).

∗

Correspondence to: No. 88, Wenhua East Road, School of Information Science and Engineering, Shandong Normal University, Jinan City, P.R. China. E-mail address: [email protected] (H. Liu).

http://dx.doi.org/10.1016/j.physa.2016.11.014 0378-4371/© 2016 Elsevier B.V. All rights reserved.

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Fig. 1. Group shots from the earthquake evacuation in Tang Shan, China on May 28, 2012.

An important criterion for an evaluation model is self-organization, which reflects the non-linear interactions among different objects or subjects and refers to the spontaneous establishment of qualitatively new behavior [12]. Six types of crowd self-organization phenomena are analyzed in literature, among them, the SF model, proposed by Helbing, can simulate five of those phenomena better than other models [2]. Moreover, the SF model can also represent a whole range of realistic motion-base cases. Thus, it is often chosen and modified to simulate various evacuation types [13–16]. The current research is also based on the SF model. According to Ref. [17], evacuation is not only an individual action, but a group behavior, such that its entire efficiency is affected by individual capability and group cooperation [18,19]. Cooperation is based on information exchanges realized through information transmissions. However, the original SF model does not describe this phenomenon. To refine the cooperation mechanism and increase evaluation safety, evacuation leader [20], guided pedestrian [21], and mutual information [22], are applied to the original SF model. In the guided pedestrian model, common individuals are guided to escape from the scenario by their choosing a nearest guider [21], and which is only standard. Leadership effect can assist ordinary pedestrians to move according to the position and moving direction of the chosen leader [20], however, cooperation is absent among common pedestrians. Mutual information highlights the influence of the location and velocity direction of pedestrians, as well as considers the environment density during evacuation [22]; however, the driving force is calculated only according to the position of the chosen exit. In conclusion, the modifications for the SF model mostly have focused on introducing a new force according to specific applications, with less attention paid on pedestrians’ perception on the evacuation environment and the cooperation among individuals. In actual evacuations, pedestrians can learn evacuation information in numerous means, including learning from themselves, other pedestrians (cooperation), and signs. Thus, information transmission is important during evacuation and worthy of focused attention. In this paper, information transmission mechanism is presented to simulate the dissemination of evacuation information, including exit’s position, distance, and density, among the crowd by modifying the original SF model. Fig. 1 shows that information transmission exists in the actual evacuation. The pictures in Fig. 1 are from an earthquake evacuation video from a school in Tang Shan, China on May 28, 2012. We chose two examples to explain information transmission in an evacuation process. One is shown in Fig. 1(a1–a3), and the other is presented in Fig. 1(b1–b3). In the first example, one student found that the right staircase was free (Fig. 1(a1)), and she informed her classmate to choose the right direction as the escape path. In the second example, another student found the same situation (Fig. 1(b1)), pulled his classmate, and chose the right direction to escape. Thus, information transmission is constant in the evacuation process, and it reflects the cooperation among pedestrians. When pedestrians aim to escape from a scenario as quickly as possible under an emergency evacuation, they face two critical problems: how to obtain all the exit information, and how to choose the proper exit as their escape path [23]. The two problems are especially important for pedestrians who are unfamiliar with the evacuation environment. To find an appropriate path, pedestrians collect information, such as the exit’s distance and evacuation capacity, from their neighbors, which refers to the information transmission and analysis process. In this paper, a novel evacuation model, which includes the information transmission mechanism, is presented to simulate this process by modifying the original SF model. Simulation results show that this modified model can reproduce the evacuation process, as well as effectively

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reduce evacuation time with increased pedestrians. Moreover, this paper has drawn four conclusions that help improve the efficiency and minimize the damage in evacuations. The remainder of the paper is organized as follows. Section 2 introduces the information transmission mechanism and the modified SF model. Section 3 discusses a specific simulation process. Section 4 shows and analyzes the simulation results, and we conclude the paper and outline our future work in Section 5. 2. Modified SF model based on information transmission mechanism 2.1. Original SF model The original SF model has three social forces: driving force toward the desired target (F⃗d ), repulsive force from the neighbor pedestrian (F⃗ij ), and repulsive force from the wall (F⃗iw ). The resultant force (F⃗i ) acting on each pedestrian can be expressed by Eq. (1). F⃗i = F⃗d +



F⃗ij +



F⃗iw

(1)

where i, j, and w are the pedestrian’s number, the neighbor pedestrian’s number, and the wall’s number, respectively. The repulsive force from neighbor pedestrian (F⃗ij ) between pedestrians i and j include three forces: repulsive interaction, body, and sliding friction forces. F⃗ij is expressed by Eq. (2)

⃗ij + kg rij − dij n⃗ij + κ g rij − dij 1vijt ⃗tij F⃗ij = Ai e[(rij −dij )/Bi ] n 

[(rij −dij )/Bi ] ⃗







(2)

⃗ij , and κ g rij − dij 1v ⃗ correspond to the repulsive force above the interaction, body, where Ai e nij , kg rij − dij n and sliding friction forces, respectively; rij is sum of two pedestrians’ radii. If ri and rj are the radii of pedestrians i and j, ⃗ij is a respectively, then, rij = ri + rj . Ai and Bi are constant; dij is distance between two pedestrians’ centers of mass; n normalized vector, the direction of which is from pedestrians j to i; k and κ are constant; ⃗tij is the tangential direction. vj − v⃗i )⃗tij is the tangential velocity difference; and v⃗j and v⃗i respectively correspond to the velocities of pedestrians 1vjit = (⃗ i and j. Function g (x) equals to zero if two pedestrians has no physical contact (dij > rij ), and otherwise equals to argument x. According to g (x), body and sliding friction forces act on pedestrians i and j when their distance dij is smaller than rij . 







t ij tij

F⃗iw is similar to F⃗ij , and is expressed by Eq. (3).

⃗iw + kg (ri − diw ) n⃗iw − κ g (ri − diw ) v⃗i⃗tiw ⃗tiw F⃗iw = Ai e[(ri −diw )/Bi ] n 



(3)

⃗iw denotes the perpendicular direction to the wall; and ⃗tiw is the where diw is the distance from pedestrian i to wall w ; n tangential direction. When the resultant force (F⃗i ) of pedestrian i is calculated by Eq. (1), the new velocity (⃗ vi′ ) is obtained by Eq. (4): v⃗i′ = v⃗ i +

F⃗i mi

τi

(4)

where mi is the mass of pedestrian i; τi is the acceleration time reasonably estimated as 0.5 s. If P⃗i0 is the current position of pedestrian i, the new position (P⃗i ) is calculated as follows: P⃗i = P⃗i0 + v ⃗i′ τi .

(5)

The driving force leading pedestrians to move forward is an important factor, and its direction depends largely on the chosen exit. Thus, we have modified the driving force (F⃗d ) in this study using the information transmission mechanism to simulate how pedestrians choose an appropriate moving direction by directly or indirectly learning evacuation information. 2.2. Modified SF model based on information transmission mechanism In this paper, the new driving force (F⃗′ d ) is calculated by the information transmission mechanism, and among the factors deciding its direction is the information obtained by the pedestrians from their neighbors, instead of the nearest exit. The new expression is as follows: F⃗i = F⃗′ d +



F⃗ij +



F⃗iw

(6)

where F⃗d′ reflects how pedestrians obtain and choose one appropriate exit according to their obtained information, as expressed by Eq. (7):

  F⃗d′ = e−α F⃗d + 1 − e−α F⃗dik ,

α ∈ Z+

(7)

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where e−α is the reserving factor; e−α F⃗d is the reserved exit’s information after spreading; and α is the number of information transmission, with an initial value of zero. When information is spread by one pedestrian, 1 is added to α . In Eq. (7), F⃗dik represents the attractive force from the neighbor who provides exit information; and 1 − e−α describes the pedestrian’s trust in his chosen neighbors. If the exit is in the pedestrian’s vision, the pedestrian can obtain exit information directly, and no information is lost (α = 0). When a pedestrian has to obtain exit information from neighbors, information loss (α ̸= 0) and attractive force (F⃗dik ) from neighbor. When information spreads further (α is bigger), information becomes more unreliable (e−α is smaller), and pedestrians depend more on their neighbors (1 − e−α is bigger) to escape. The new driving force from one exit is the same as the original SF model. If vi0 , v ⃗i , ⃗ei , and mi respectively correspond to desired rate, current velocity, desired direction, and mass of pedestrian i, then F⃗d is expressed in Eq. (8): F⃗d = mi

1

τi

(vi0 ⃗ei − v⃗i )

(8)

where τi is a certain relaxation time; and ⃗ ei is the direction from the current position of pedestrian i to the exit position, which can be expressed by Eq. (9):

⃗) (P⃗i − EP  ⃗ei =   ⃗ ⃗ ) (Pi − EP

(9)

⃗ is the position of the chosen exit. where P⃗i is the current position of pedestrian i, and EP F⃗dik represents the attractive force from the selected neighbor who provides exit information, which is expressed as follows:  1  0 F⃗dik = mi vi ⃗eik − v⃗i (10) τi

where ⃗ eik is a unit vector, which describes the current position’s direction of pedestrian i to neighbor k. Similar to Eq. (9), ⃗ eik is expressed as follows:

(P⃗i − P⃗k ) . ⃗eik =   ⃗ ⃗  (Pi − Pk )

(11)

With the limited vision field of pedestrians, most of them have to obtain exit information from their neighbors. Considering all factors affecting pedestrians’ choice of exit, such as distance, density, width (capacity), and exit information reliability, we propose the information transmission model is expressed in Eq. (12) k1 e−dsij + k2 e−dej + k3 (1 − e−dwj )

 Sij = e

−α



(12) k1 + k2 + k3 where i is the number of neighbor pedestrians; j is the number of exits chosen by neighbor pedestrians; dsij is the distance from the position of pedestrian i to exit j; dej is the density of exit j; dw j is the width of exit j; k1 , k2 , and k3 are the weights of dsij , dej and dw j , respectively; and α is the reserved factor (see Eq. (7)). In general, pedestrians will obtain multiple exit information from their neighbors, and the same exit information may vary because of the different neighbors. Thus, it is important how pedestrians choose one neighbor from their surroundings when obtaining exit information. If n neighbors are around the pedestrians, the number of chosen neighbor is calculated by the next equation. ic = arg(max{Si }),

i = 1, . . . , n.

(13)

Once the ic is determined, the exit chosen by the pedestrian is the same exit chosen by neighbor ic . The new driving force is then calculated based on Eq. (7). Different values of parameters (k1 , k2 , k3 ) reflect different emphasis that pedestrians consider in choosing an exit. If k2 = 0, k3 = 0, and Sij = e−α e−dsij , the distance to the exit is considerably important because it requires less time to finish a shorter path. If k1 = 0, k2 = 0, and Sij = e−α e−dwj , pedestrians will focus more on the width (capacity) of exits, because a much wider exit means a much higher evacuation ability. By setting proper values for all parameters, Eq. (13) ascertains that the exit with the higher reliability, lower density, and wider width is chosen by pedestrians. In an actual evacuation, pedestrian behavior is exceptionally complex, and most pedestrians consider different factors in various evacuation stages. In the initial evacuation stage, if the pedestrians are far from the exit, they always choose exits that are wider with low density. Conversely, when pedestrians are nearby some exits, they always choose the nearest exit to save on evacuation time, especially in the last stage. Thus, in our study, a decreasing strategy is designed for k2 and k3 , which is expressed in Eq. (14) k(t ) = k0 e−t

(14)

where t is the evacuation time, and t is the simulation iterations in this paper; k0 is the initial values of k2 or k3 (k1 is a constant, 1.0); and k(t ) describes the different considerations in various stages. As time passes, k(t ) quickly tends to reach 0, which represents that pedestrians focus more on the distance from the exit.

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Fig. 2. Collision avoidance strategy; (a) collision condition; (b) new position.

2.3. Collision avoidance strategy The original SF model fails to ensure that all pedestrians avoid collision during the evacuation process [24]. One of collision avoidance methods is self-stopping, which is proposed by Parisi [25]. Based on this method, a simple collision avoidance strategy is adopted in our study. If pedestrian j is one person whose current position(P⃗j ) lies  on themovement direction of pedestrian i, the new movement

  position (P⃗i ) of pedestrian i should be checked. If dij dij = P⃗j − P⃗i  < rij (Section 2.1), a collision will occur between two pedestrians, as shown in Fig. 2(a). Thus, pedestrian i should find a new position (P⃗i′ ) that satisfies above condition (dij ≥ rij ). The new position is shown in Fig. 2(b). In Fig. 2, P⃗i0 is the current position of pedestrian i; ri and rj are the radii of pedestrians i and j, respectively; P⃗i′ is the new position which lies on the movement direction of pedestrian i, and dij (the distance between P⃗i′ and P⃗j ) equals to rij (in Fig. 2(b)). 3. Simulation processes of the modified SF model Because information transmission is introduced into the traditional SF model in this study, there are some differences compared with the original SF model in the new simulation process. Two obvious differences exist. First, a process for calculating the density of all exits is available. According to Section 2.2, exit information is composed of three parts transferred by pedestrians, such as position, density, and width. Exit position and width are constant during the evacuation process. However, exit density is calculated with time, making it necessary to add a process to calculate the density of all exits in every simulation step. Second, the pedestrian’s nearest exit information should be firstly obtained because exit information transmission goes from its position to distance, according to Eqs. (12) and (13). If no exit is available in sight, pedestrians have to obtain exit information from their neighbors, which lead to information loss. Once information is spread, 1 is added to α from neighbors (see Section 2.2). The simulation procedure is specified and described as follows: Step 1 Step 2 Step 3 Step 4

Set the number of pedestrians and initialize their positions and all parameter values. Check the pedestrians’ statuses. If all pedestrians left the scenario, go to Step 6. Calculate the density of all exits, and then calculate the exit information for every pedestrian using Eq. (13). Calculate the resultant force, new velocity, and position of every pedestrian using Eqs. (6), (4), and (5), respectively. Afterward, adjust the pedestrians’ positions according to Section 2.3. Step 5 Calculate k2 and k3 using Eq. (14), and then go to Step 2. Step 6 Finish the simulation. 4. Simulations and results All of our simulation parameters are set as follows. For each pedestrian, radius r = 0.25 m, mass M = 80 kg, desired pedestrian velocity vi0 = 2.5 m/s, constant k = 1.2 × 105 , κ = 2.4 × 105 , A = 200, B = 0.1, and τi = 0.5. To analyze the effects of the exit density and width on evacuation efficiency, two rooms (shown in Fig. 3) with the same size (15 m × 15 m) and different exit distributions are used in our simulations. In the first room (Fig. 3(a), Room A), the width of all exits are the

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Fig. 3. Two-room structures in which (a) the width of all exits is 1 m; (b) the width of one exit is 2 m.

Fig. 4. Evacuation times versus the number of pedestrians in two rooms.

same (1 m), thus, the exit distance and density are considered important factors affecting evacuation efficiency. Conversely, the other room (Fig. 3(b), Room B) has one exit with a 2-m width. Therefore, the evacuation capacities of all exits differ in the second room, which are used to analyze the effects of exit evacuation capacity on evacuation efficiency. In every experiment, the numbers of pedestrians are 50, 100, 150, 200, and 250, and the vision radius of pedestrians is 3 m. Considering that pedestrians focus on different evacuation information across various stages, the initial values of parameters k2 and k3 are 50 and 60, respectively. Parameter k1 is constant at 1.0. Parameters k2 and k3 are decreased by Eq. (14). For each simulation, the initial position of every pedestrian is random and not overlapping each other. The evacuation time in each result is the average of multiple experiments. For each simulation, the density of pedestrians at exit j can be calculated as follows, dej =

Nrp2 0.5(1.5edj )2

(15)

where rp is the radius of a pedestrian, and edj is the width of exit j, N is the number of pedestrians in a semicircular area whose center is at the center of exit j and radius is 1.5 times of the width of exit j. 4.1. Crowd evacuation simulation 1 In this simulation, the modified evacuation model is applied in two rooms to simulate crowd evacuation. Given that one exit in Room B (Fig. 3(b)) has a 2-m width, we discuss how the exit width can affect evacuation efficiency by comparing the results between the two rooms in this simulation. The results are presented in Fig. 4. As shown in Fig. 4, the exit width is also important during the evacuation process. Thus, if the exit width is fully learned by pedestrians, evacuation efficiency is improved (evacuation in Room B). However, the effect of the exit width becomes smaller (evacuation time difference between Rooms A and B) when the evacuation number of pedestrians increased, which agrees with real situations. This simulation demonstrates that the modified model can simulate crowd evacuation. The next series of simulations indicate that exit density and width should be paid with increased attention during evacuation by comparing with other models.

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Fig. 5. Evacuation times of Helbing model and our model in Room A.

Fig. 6. Exit density changes with evacuation time in Room A; (a) the simulation result in Helbing behavior model; (b) the simulation result in our model.

4.2. Crowd evacuation simulation 2 To validate that the exit width is important for crowd evacuation, the modified model in this paper and the Helbing behavior model [10] are used to simulate crowd evacuation in Room A, where the exits have the same widths, and k3 is an invalid parameter. In this simulation, the vision radius of pedestrians in the Helbing model is unrestricted. Results are shown in Fig. 5; one is from the Helbing behavior model, and the other is from our model. The modified model, which can reduce evacuation time and improve evacuation efficiency when exit density is considered during evacuation, is shown in Fig. 5. When pedestrians increased, the effect is more evident (time difference between two models becomes bigger). Results demonstrate the validity of our model. In Fig. 6, the change of exit density with time is shown in one simulation. The density change in the Helbing behavior model and the result of our model are shown in Fig. 6(a) and (b), respectively. Compared with the results in Fig. 6(a) and (b), the evacuation time of our model is shorter than that of the Helbing model because all room exits are fully utilized during the evacuation. In Fig. 6(a), pedestrians are no longer seen around Exit 2 after 65 s; although many pedestrians are still in the room, so Exit 2 is not fully utilized. This situation is improved in our model (Fig. 6(b)). The results suggest that evacuation time is effectively shortened and evacuation efficiency is improved if all exits are fully used. Thus, fully utilizing all exits in a scenario by guiding pedestrians during evacuation is a key problem, and our model clearly performs better. This conclusion is also verified by the next simulation. 4.3. Crowd evacuation simulation 3 We used Room B to validate our model in this simulation; and parameter k3 is valid because of a 2-m wide exit (Exit No. 1). Therefore, the evacuation capacity of Exit 1 is bigger than those of others. Results from the two models, the Helbing behavior and the proposed model are shown in Fig. 7. The modified model has obvious advantages compared with the Helbing behavior model when the width of one exit is bigger than those of others, as shown in Fig. 7. The evacuating effect becomes more obvious as depicted in Fig. 5 specifically as pedestrians increased. We also used the density change of every exit with time to explain this kind of phenomenon, and Fig. 8 shows these results. The density change in the Helbing behavior model is shown in Fig. 8(a), whereas Fig. 8(b) depicts the result in our model. Given that the Exit 1 capacity is bigger than the others’, Exit 1 should be fully used to shorten evacuation time. As shown in Fig. 8(a), density of Exit 1 becomes zero prematurely in 66 s. Thus, no pedestrians are left in the room after such time, such that, Exit 1 utilization and evacuation time are considerably low. In Fig. 8(b), Exit 1 utilization is better than the former (its

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Fig. 7. Evacuation times versus the number of pedestrians in Room B.

Fig. 8. Exit densities change with evacuation time in Room B; (a) the simulation result in Helbing behavior model; (b) the simulation result in our model.

Fig. 9. Distribution of 250 pedestrians at different evacuation times in Room B for the (a) initial crowd distribution; (b) Helbing behavior model; (c) proposed model.

density nearly becomes zero at the end of evacuation time), and all exits are fully utilized during the evacuation. The results in Fig. 8(b) show that most pedestrians chose Exit 1 to escape Room B. Thus, we draw another conclusion that if wider exits are fully utilized, evacuation time is effectively shortened and evacuation efficiency is improved. Fig. 9 shows pedestrian distributions across different evacuation stages; it also demonstrates the above conclusion. Fig. 9(a) is the initial distribution of the 250 pedestrians, and Fig. 9(b) and (c) respectively correspond to the distributions of two models in later evacuation stages. In Fig. 9(b), a few pedestrians are near Exit 1, and the majority is around the other three exits. Furthermore, evacuation time increases because the evacuation capacity of Exit 1 is larger than those of others. This phenomenon is improved in Fig. 9(c). As shown in Fig. 9, Exit 1 is fully used, which then shortened evacuation time. This result can be attributed to pedestrians considering exit density as an important parameter in choosing an exit (see Eq. (12)). 4.4. Crowd evacuation simulation 4 This simulation is compared with the guide model results [21]. In the guide model, given that the guides are aware of all exits and they only provide their positions to other pedestrians, whereas other pedestrians escape only by the position of their chosen guide. Fig. 10 shows the density changes of the two models during an evacuation when the number of pedestrians is 200 and Room B is selected. Considering that pedestrians are unable to learn more information about the environment except for the guide’s position, they have no option but to follow the nearest guide; the parameter values in the guide model are set by Ref. [21]. Compared

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Fig. 10. Exit density changes with evacuation time in Room B with (a) the simulation result in the guide model; (b) the simulation result in our model.

Fig. 11. Exit density changes with evacuation time in room B with (a) the simulation result in the leadership model; (b) the simulation result in our model.

with the guide model, the use of all exits is fuller in our model. The Exit 1 density becomes zero after 200 s (Fig. 10(b)), such that, this exit is fully used. Simulation result shows that evacuation time is shortened by 38.3%. 4.5. Crowd evacuation simulation 5 To further validate the effectiveness of our model, this simulation is designed to compare with the leadership model [20]. The parameter setting of the leadership model is the same as [20], and the number of leaders is 4, in which distribution is also the same as [20]. Fig. 11 shows the density changes of the two models, where the pedestrian number is 250, and Room B is selected. As shown in Fig. 11(b), Exit 1 is fully used in our model during the whole evacuation. Result shows that the information transmission effect is better than that of leadership model. The leader can learn more information in the leadership model than the guide model, although common pedestrians use information only about the position and moving direction of the leader. Though pedestrians can randomly choose a leader, they cannot move freely by following their chosen leader, which is the most obvious difference between our model and leadership model. Our model corresponds more to actual evacuation process in comparison, and results show that our model reduces evacuation time by 31.7%. 4.6. Evacuation in a complex scenario Although the validity of our model is confirmed through simple scenarios (Rooms A and B), our model is also be used in complex situations. The size of the whole scene is 32 m × 20 m. In this scenario, there are nine rooms (R1–R9), four halls (H1–H4) and one exit(shown in Fig. 12(a)). In the current simulation, we demonstrate the scene by means of OGRE (Object-Oriented Graphics Rendering Engine), as shown in Fig. 12(b–d). The initial position of pedestrians is randomly set in each room and each hall, and then follows the uniform distribution. In the initial stage of the simulation shown in Fig. 12(b), there are 20 pedestrians in each room and each hall, so the number of pedestrian is 240. Fig. 12(c–d) show the simulation results in different evacuation stages. During the simulation, every pedestrian in the scenario can learn the exit’s information from their neighbors through information transmission, so finally they escape from the exit successfully. As shown Fig. 12(c), most of the pedestrians in the present model choose the path as close as possible to the exit, which is accordant with the actual evacuation situation. This phenomenon indicates our model can describe the behavior of pedestrians in evacuation accurately. In the final stage (Fig. 12(d)), the arch effect formed by the crowds is an important self-organization phenomenon So the proposed model can be used to analyze the evacuation process in emergency [10], and is helpful in creating an effective emergency evacuation scheme to minimize the damage and the loss of life

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Fig. 12. Simulation in a complex scene relative to; (a) complex scene structure; (b) initialization of all the pedestrians’ positions; (c) simulation result in mid-stage; (d) simulation result in late stage.

4.7. Discussion of parameters Three additional parameters from the original SF model are compared with the initial values of 1.0, 50, and 60, respectively, in all simulations. Thus, in this section, we discuss the effect of parameters, especially k2 and k3 , on crowd evacuation. Different parameter values affect the chosen moving target of the pedestrian. They also influence pedestrian distribution, especially in the initial evacuation stage, because values of parameters k2 and k3 tend to become zero over time, according to Eq. (14). Bigger values of parameters k2 and k3 are not necessarily better. Improper values lead to much worse evacuation results than other models. If the parameter values are considerably large, a number of pedestrians wander between some exits, at least initially according to Eq. (13), because exit density is changed frequently. However, if the parameter values are too small, distance becomes the main factor, and the modified model degenerates into the original SF model. Result shows that pedestrians should choose the wider exit with lower density as their evacuation path in the initial evacuation stages, which denotes that the necessary guide is greatly important at the beginning of evacuation. 5. Conclusion and discussion This paper has presented a modified social force model based on information transmission, which is validated by several simulations. In this model, pedestrians can learn exit information by themselves or from their neighbors through information transmission, and then, they choose an appropriate exit as their evacuation path. The information transmission effect of the exit reflects the cooperative operations among pedestrians during an evacuation. Moreover, information loss is considered in our model. This study has drawn four conclusions according to the simulation results and these conclusions will assist crowd evacuation, as well as verify the correctness of the modified model.

• Evacuation time is effectively shortened and evacuation efficiency is improved if all exists are used to the fullest (Section 4.2).

• If wider exits are fully utilized, evacuation time is effectively shortened, and evacuation efficiency is improved (Section 4.3).

• Pedestrians should choose wider exits with lower densities for their evacuation path in the initial evacuation stages (Section 4.7).

• The necessary guide is considerably important at the beginning of an evacuation (Section 4.7). Compared with other models, an information transmission mechanism is introduced into traditional social force model, which help the pedestrians in the scenario learn the whole evacuation situation, so that it will be easier for pedestrians to choose a more appropriate path to evacuate as quickly and safely as possible. But, the pedestrians in the leadership model or in the guide model can only learn evacuation situation from the nearest leader and guider rather than the whole evacuation situation, and then cannot choose other routes freely, so their evacuation efficiency is much lower than ours. However, our model needs more time expense than other models. In addition, when some pedestrians around one pedestrian choose the same destination, he/she may choose the same destination to escape to a great extent, which is the so-called herding in self-organization. Several problems still require further attention in future work. For example, model parameters should be calibrated by real evacuation data. In addition, the influence of barriers in selecting an exit should be also considered.

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