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Modeling pedestrian evacuation with guiders based on a multi-grid model
Physics Letters A 380 (2016) 540–547
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Physics Letters A www.elsevier.com/locate/pla
Discussion
Modeling pedestrian evacuation with guiders based on a multi-grid model Shuchao Cao a , Weiguo Song a,∗ , Wei Lv b a b
State Key Laboratory of Fire Science, University of Science and Technology of China, Hefei 230027, China Research Center for Crisis & Hazard Management, Wuhan University of Technology, Wuhan 430070, China
a r t i c l e
i n f o
Article history: Received 6 July 2015 Received in revised form 10 November 2015 Accepted 23 November 2015 Available online 30 November 2015 Communicated by R. Wu Keywords: Evacuation Guider Guidance strategy Multi-grid model Pedestrian dynamics
a b s t r a c t Pedestrian evacuation with guidance is investigated by a multi-grid model in this paper. The effects of guider type, guider number, guider distribution and guidance strategy on evacuation are discussed. From the analysis of simulation results, it is found that the identified guiders are more beneficial to evacuation because they can be distinguished easily by pedestrians during evacuation; The optimal guider number exists in view of the human cost and can be obtained in our model; The uniform distribution of guiders covers more area in the room and makes evacuation efficient; Evacuation guidance is more effective when the speed of guider is about 75% of herding pedestrian’s speed in our simulation scenario; The performance of evacuation guidance strategy considering both distance and occupant number is the best when compared to other strategies; The coordination and cooperation between guiders are very important and necessary to facilitate the evacuation. The study may be useful for understanding the importance of guidance in evacuation and developing efficient evacuation strategy for management under emergency. © 2015 Elsevier B.V. All rights reserved.
1. Introduction With the development of modern society, more and more buildings are built to meet the needs of people on living, working and entertainment. Due to the complex structure of the buildings, safe crowd evacuation has been becoming more important and critical in case of emergency. In recent decades, many evacuation models have been proposed by researchers. Generally, evacuation models can be classified into two categories: the continuous model such as the social force model [1–3] and the discrete model such as the cellular automaton model [4–9] and the lattice gas model [10–14]. The dynamic features of pedestrian evacuation such as herding and zipper effect, stop and go, lane formation and clogging effect have been observed and successfully reproduced by these models. In real life, crowd evacuation from large and complex building spaces is usually hindered by people’s not knowing their detailed internal connectivity. In such circumstances, occupants might not be aware of the existence of suitable circulation paths or the most appropriate escape paths. Psychology studies show that occupants usually decide to use familiar exits, such as where they entered the
*
Corresponding author. E-mail address: [email protected] (W. Song).
http://dx.doi.org/10.1016/j.physleta.2015.11.028 0375-9601/© 2015 Elsevier B.V. All rights reserved.
building [15]. Emergency exits or exits not normally used for circulation are often ignored, in addition, the following behavior is also found during evacuation. If a fire occurs, blocking some of those known paths, and smoke further obscuring the vision, the problem might be fatally aggravated and chaos or even disaster may occur which often cause severe casualties. In such emergencies, if people could be guided by evacuation guiders who know the evacuation path to the exits, casualties might be avoided or reduced significantly. It is widely accepted that a proper evacuation could save many lives in emergencies. Therefore, better preparations of evacuation guidance are significant and important for pedestrian evacuation. François and Robert [16] modeled the effect of leadership on crowd flow dynamics. Leaders were divided into embedded leader, peripheral leader and distant leader according to their initial positions. Simulation showed that a mix of leader classes was the most desirable and leaders going about half the speed of other agents led to the most efficient evacuations. Pelechano and Badler [17] simulated crowd and trained leader behavior and different roles such as trained personnel, leaders and follower were considered during building evacuation. Evaluation showed that only a relatively small percentage of trained leaders yielded the best evacuation rates. Then Ji and Gao [18] investigated crowd evacuation with a leader–follower model and result indicated that evacua-
S. Cao et al. / Physics Letters A 380 (2016) 540–547
tion with some leaders would be more efficient as compared to situations without leaders, however, more leaders might not always result in more efficient evacuation because of the chaotic effect caused by too many leaders to the evacuation. Yuan and Tan [19] proposed an extensive cellular automaton model to simulate evacuation from a large crowed smoke-filled compartment with considering the effect of guiders and visibility range, and the phenomenon of “flow with the stream” was modeled. Wang et al. [20] added a communication field to the original floor field model for emergency evacuation under the control of evacuation assistants. The effective locations and optimal numbers of assistants were investigated. Based on the extended dynamic communication field model, they [21] also introduced the centripetal effect of an evacuation assistant. Spartalis et al. [22] studied the impact of guidance on evacuation based on CA model. The evacuation of a retirement house with the help of the nursing staff was simulated and results proved the significance of proper guidance. Yang et al. [23] introduced a modification method for modeling the guided pedestrian group where the navigational force was defined based on social force model and the model was validated by comparing its local density–speed and density–flow diagrams with fundamental diagrams. To our best knowledge, although some research on evacuation guidance has been done by many scholars, studies on different guidance strategies during evacuation are very few. It is important and necessary to investigate the effect of these factors on pedestrian evacuation. Because of the low computational efficiency of continuous model and inaccuracy of traditional discrete model, in this paper, an extensive model based on multi-grid model [24–28] is proposed to simulate pedestrian evacuation with guidance. The rest of this paper is organized as follows: A multi-grid model considering the guidance of evacuation assistant is introduced in section 2. In section 3, the effects of guider type, guider number, guider distribution, guider speed and guidance strategy on pedestrian evacuation are surveyed and simulation results are discussed. In section 4, conclusion is made and the paper is closed. 2. Model 2.1. Model description Pedestrians involved in the model include two kinds: guider and herding occupant. Guider gives the evacuation guidance about exit location to occupants, and it can be categorized into two types: identified guider and unidentified guider. The unidentified guider assumed to be the same with other occupants in appearance but know the exit and have a subtle influence on other pedestrians in the influence radius R inf . This influence is similar with the soft control [29] and occupants are guided unconsciously by the unidentified guider to the exit. The identified guider assumed to wear special uniform that are different from other occupants and could be distinguished easily by other people. Pedestrians are strongly influenced by the identified guiders and must follow the evacuation guidance when they are located in the influence radius of identified guiders, which is clearly different from the soft control of the unidentified guider. The herding occupants cannot evacuate from the room by themselves and need other people’s assistance. If herding occupants find the identified guider in the influence radius, they must follow the guidance of the identified guider closest to them. Otherwise, they will follow the majority of people who have found the exit no matter she or he is guider or herding occupant in their influence radius. As for evacuation guidance, there are two kinds of guidance for guiders during evacuation assistance: (1) Static guidance that guiders do not move and only lead people on the fixed position
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until all other occupants have evacuated from the room during evacuation. (2) Dynamic guidance that guiders lead people through moving in the room and they evacuate with other people together when evacuation begins. 2.2. Model mechanism Once evacuation begins, pedestrians must choose an exit firstly, after that, they move to their target exit immediately. Therefore, it is very important to understand the exit selection and pedestrian movement process in the model. 2.2.1. Exit selection The exit selection for guiders in this model is based on random utility theory [30], and the usefulness perceived by the decision maker n about the m alternative is represented by the following formula:
U mn = V mn + εmn
(1)
The first one V mn is the main or expected value of the perceived utility. The second term εmn , called the random residual, represents the deviation of the average utility from the real value. According to different distribution of random residue, the Mixed Logit Models (MLMs) based on the hypothesis that the random residues are independent and identically distributed according to a Gumbel random distribution with a mean equal to zero and a λ parameter [31] is used in this paper. Therefore, the probability of selecting exit m among the k exits for pedestrian n is given as follows:
exp(λ V mn ) pmn = k j =1 exp(λ V jn )
(2)
V mn = kdis (1 − pdismn ) + kden (1 − pdenmn )
(3)
pdismn = pdenmn =
dismn max(dis1n , · · · , dismn , · · · , diskn ) denmn max(den1n , · · · , denmn , · · · , denkn )
(4) (5)
where dismn denotes the distance from the position of pedestrian n to the exit m; denmn is the number of pedestrians who select exit m and their distance to the exit m is nearer than pedestrian n; pdismn and pdenmn are the proportion of dismn and denmn to their maximum value respectively; kdis and kden are the scaling constants, and we ensure kdis + kden = 1 in this paper. For herding occupants, they cannot find the exit by themselves and need to be guided during evacuation. There are three situations should be considered: (1) If herding occupants are located in the identified guider’s influence radius, they will receive the exit information from guiders and find the exit location, then follow the guidance to the exit. If there are more than one identified guiders in the influence radius, the occupant will follow the closest guider’s leading. (2) If they are not, occupants will choose the exit selected by the largest number of people in their influence radius. (3) If no people or people in the influence radius also do not find the exit, occupants will move randomly without aim until they find the exit. 2.2.2. Pedestrian movement A floor field model is used to simulate pedestrian movement under emergency. The size of one cell is 0.1 m × 0.1 m and every pedestrian occupies 25 cells. The shuffled update is adopted in this model, and each pedestrian can move a distance equal to one cell per update to any of the eight directions based on the transition probabilities just as shown in Fig. 1.
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Fig. 1. Possible transitions and corresponding transition probabilities.
Once an occupant chooses the target exit m, the transition probability of selecting the neighborhood cell (i , j) in the next step is calculated as follows:
P i j = N nor I ine exp k S S m i j (1 − ni j )αi j
(6)
where N nor denotes the normalization factor for ensuring that P i j = 1; I ine represents the inertial parameter; k S is the parameter for scaling the static floor field; ni j indicates whether the cell (i , j) is occupied, it is 1 if the cell is occupied and 0 otherwise; αi j is related to the existence of obstacle in the cell, the value is 0 if the cell is occupied by obstacle and 1 otherwise. The static floor field S m initialized at the beginning of the model run is set inij versely proportional to the distance from the exit m to the cell (i , j). In this model, we set one time step t = 0.1 s, I ine = 1.2 for the movement direction that is the same with the movement direction in last time step, otherwise I ine = 1. k S = 0.8 and R inf represents the influence radius of pedestrian in this paper.
Fig. 2. (a) The schematic illustration of the room, (b) the static floor field graph of the room.
2.3. Model scene Simulation scenario is displayed in Fig. 2. The size of the room is 20 m × 10 m inside, which is discretized into 200 cells × 100 cells. The thickness of the wall is 0.5 m. Two exits whose width is 1 m are located in the center of walls respectively. The number of guider and herding occupant in the simulation is N g and N h , and the total pedestrian number N = N g + N h . The movement speed is v g and v h for guiders and herding occupants respectively. Simulation is carried out fifty times for every scenario. The overall simulation process is shown as a flowchart in Fig. 3. 3. Simulation and results At first, we should set the values of kdis and kden . Fig. 4 shows the evacuation time of different values of kdis . We can find the optimal evacuation time is achieved when kdis = 0.4 (kden = 1 − kdis ). So kdis = 0.4 and kden = 0.6 are set in this paper. In Fig. 5, the average evacuation time decreases with the increase of the influence radius R inf . It is easy to understand because the larger of the influence radius can make more pedestrians be covered by the guidance. But if the influence radius is large enough, the evacuation time does not change anymore. R inf = 2 m is adopted in the following simulations. 3.1. The effect of guider type and number on evacuation In Fig. 6, evacuation time decreases with the increase number of guiders and curves can be split into three parts. The decline of evacuation time is sharp in the first part, and it decreases from 70 s (55 s) to 50 s (50 s) for identified (unidentified) guider in Fig. 6(a). In Fig. 6(b), it falls from 61 s (47 s) to 44 s (40 s). The significant reduction indicates guiders are the most beneficial to
evacuation at the first stage. Then the decrease of evacuation time in the second part is not as obvious as that in the first part. At the last part, the curves become flat and the decrease hardly happens, which means guidance has saturated during the evacuation when guider number is large enough. Therefore, it is necessary and meaningful to find the optimal guider number considering the human cost and evacuation time during evacuation. In Fig. 6, the optimal guider number is 4 for evacuation in this scenario. As shown in Fig. 6, the guidance of identified guider is more conducive to evacuation than the unidentified guider’s guidance. As mentioned before, the mechanism of guidance between two types of guider is very different. The strong influence of identified guiders has a direct effect on herding occupants, which makes them have an optimal exit selection based on this compulsory guidance. However, the soft control of unidentified guiders weakens the guidance effect on evacuation and pedestrians may not follow the optimal guidance on exit selection even though they have received the unidentified guider’s guidance, because other pedestrians in the influence radius will also have an effect of same intensity on pedestrian’s exit choice. As a result, evacuation time under the guidance of unidentified guider is longer than that of the identified guider’s guidance. In the following part of this paper, only the identified guider is discussed and simulated. When compared Fig. 6(a) with Fig. 6(b), we can find that the evacuation time with static guidance is always longer than that with dynamic guidance when the guider number is the same. Therefore, the dynamic guidance is more effective to evacuation than the static guidance. The reason is that the dynamic guiders will assist more herding occupants and their influence areas are larger when they move together with other pedestrians after evacuation begins. However, the static guidance takes effect only when
S. Cao et al. / Physics Letters A 380 (2016) 540–547
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Fig. 3. The flowchart of the overall simulation process.
Fig. 4. 150 pedestrians are distributed randomly in the room (N = N g = 150, v g = 2 m/s).
Fig. 5. The effect of influence radius R inf on evacuation time (N = 150, N g = 4, v g = v h = 2 m/s).
pedestrians enter into the influence radius of the fixed guiders. Therefore, in contrast with the dynamic guidance, the effect of static guidance on evacuation is limited.
room. As shown in Fig. 8, the uniform guider distribution has the least average evacuation time than other distributions. The reason is that the uniform distribution makes guiders cover more areas in the room and influence more people within the same amount of time when compared to other distributions. Therefore, it is beneficial for evacuation when guiders are distributed uniformly in this scene. But for a specific or known distribution of occupants, the result may be different. Because it is highly related to the real distribution of occupants in the room. However, under this circumstance, the model can still be used to simulate pedestrian
3.2. The effect of guider distribution on evacuation The effect of guider distribution on evacuation is investigated in this part and N g = 4 (the optimal guider number in section 3.1) is adopted. Fig. 7 displays the guider distribution in different scenarios. Pedestrians except the guiders are distributed randomly in the
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Fig. 6. Pedestrians are distributed randomly in the room (N = 150, v g = v h = 2 m/s). (a) Static guidance, (b) dynamic guidance.
3.3. The effect of guider speed on evacuation
Fig. 7. The black circles represent guiders’ positions in the room. (a) Random distribution, (b) center distribution, (3) uniform distribution, (4) exit distribution.
evacuation and compare the performance of different guider distribution, finally find the optimal guider distribution for the specific occupant distribution.
In this part, pedestrians are randomly distributed in the room and the effect of guider’s speed on evacuation guidance is investigated. Obviously, when v g = 0 m/s, guider becomes static guider, otherwise, it is dynamic guider. When evacuation begins, guiders will move to the exit immediately. As shown in Fig. 9, evacuation time declines firstly and it slumps from 50 s to its lowest 37 s, then it rises to 41 s with the increase of guider’s speed. In this scene, the optimal speed of guider is v g = 1.5 m/s for v h = 2 m/s. The reason can be found that evacuation is hindered when guider’s speed is small (v g < 1 m/s in this scene), because they cannot lead other pedestrians quickly. However, when guider’s speed is large (v g > 2 m/s in this scene), they move too fast to assist enough pedestrians and many pedestrians have not found the exit before guiders leave the room. Therefore, if we want to reduce the evacuation time, guider should assist people as much as possible with a speed as fast as possible. In Fig. 9, the most effective evacuation guidance is obtained when guider’s speed is about 75% of herding occupant’s speed. Nonetheless, the simulation scenario is limited
Fig. 8. Pedestrians are randomly distributed in the room (N = 150, N g = 4 and v g = v h = 2 m/s). (a) Static guidance, (b) dynamic guidance.
S. Cao et al. / Physics Letters A 380 (2016) 540–547
Fig. 9. The effect of guider speed on evacuation time (N = 150, N g = 4 and v h = 2 m/s).
and more investigation should be done to find the optimal speed of guider in different situations in the future. 3.4. The effect of guidance strategy on evacuation The guider’s guidance strategy in the above simulation is toward the exit and their target is the exit all the time, which means dynamic guider will go to the exit immediately when evacuation begins. This kind of evacuation guidance strategy is not bad when the total pedestrian number is large (e.g. N = 150), but it does not work efficiently when pedestrian density in the room is too low (e.g. N = 10). Due to no other pedestrians in the influence radius or pedestrians around them do not find the exit either, some pedestrians cannot find the exit and evacuate from the room successfully in low density. In a word, many pedestrians will not receive the guidance directly or indirectly and fail the evacuation finally under this condition. There are two methods to solve this problem in low density. One is adding the guider number, but the human cost will increase too. The other way is replanning the guidance strategy and changing guider’s movement target from the exit to the pedestrian who still has not found the exit, which means guider should search for occupants needing assistance and move to them, then lead them to the exit. After current target pedestrian has received the guidance and found the exit, guider will go to the next target pedestrian immediately and they do not leave the room until all the pedestrians in the room find the exit at last. Therefore, the effect of different guidance strategies on pedestrian evacuation is studied in this part. 3.4.1. Guidance strategy for single guider At first, the simple situation N g = 1 is investigated and different strategies are adopted based on different criteria of choosing target pedestrian. Strategies for single guider are as follows: (S 1 ) The shortest distance principle that guider chooses the target pedestrian closest to him or her; (S 2 ) The largest number principle that guider selects the target pedestrian who has the maximum number of occupants who have not found the exit in his or her influence radius; (S 3 ) The distance and number principle that guider considers both the distance to him or her and the occupant number in the influence radius. In fact, it is a combination of strategies S 1 and S 2 . The formula is as follows:
Pi = Pd •
d gi dmax
− (1 − P d ) •
ni nmax
(7)
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Fig. 10. The effect of P d on evacuation guidance (N g = 1, v g = v h = 2 m/s).
dmax = nmax =
212 + 112 = 23.7 m
πR
2
0.25
= 50.2
(8) (9)
where P d ∈ [0, 1] represents the weight of distance factor; d gi denotes the distance between the guider g and pedestrian i; dmax is the diagonal length of the room; ni stands the pedestrian number in the influence radius of pedestrian i and nmax is the maximum number in pedestrian’s influence radius (the occupy size of each person in the model is 0.25 m2 ). Guider chooses the target pedestrian with the smallest P i in this strategy; (S 4 ) The shortest distance principle that guider chooses the target pedestrian closest to the exit; (S 5 ) The largest distance principle that guider selects the target pedestrian who has the longest distance to the exit. The effect of different P d on evacuation time is shown in Fig. 10. There is one point should be noticed that when P d = 1 and P d = 0, strategy S 3 actually becomes strategies S 1 and S 2 respectively. We can see the trend of curves decreases firstly then increases at last. It is interesting that the optimal evacuation time is achieved at P d = 0.3, which indicates the evacuation guidance is the most effective when considering both the distance and pedestrian number factors. By analyzing the reason we find that guider only assists one occupant once at most time and most occupants still cannot find the exit if guider only considers the distance factor (S 1 ). The evacuation efficiency is low and the exit is not fully used under this circumstance. However, guider needs more time to assist the target occupant if only considering the pedestrian number factor (S 2 ), and then pedestrian needs more time to reach the exit when evacuation begins. Just as shown in Fig. 11, the average time of first arrival to the exit in different situations is t S 1 < t S 3 ( P d =0.3) < t S 2 . The disadvantage of only considering distance factor is that the flow is small and exit is not fully used during evacuation, while the weakness of only considering occupant number factor is that it needs more time to guide pedestrians during evacuation. Therefore, taking account of both factors makes the guidance efficient for evacuation. There is one interesting point that the evacuation time of N = 50 is smaller than that of N = 10 when P d ≤ 0.1 in Fig. 10. Guider prefers to assist pedestrian who has a relatively large number of occupants in the influence radius when P d is small. Compared to the situation of N = 10, pedestrians distributed randomly in the room are more likely to form small groups in their influence radius when N = 50. In this case, it becomes easy for people to find the exit and evacuate from the room in a short time when guider
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Fig. 11. The effect of P d on the time of first arrival to exit (N g = 1, v g = v h = 2 m/s).
Fig. 12. Evacuation time of different strategies for guider (N g = 1, v g = v h = 2 m/s).
gives more consideration of pedestrian number in the influence radius. Therefore, a relatively larger density in the room is positive to evacuation when P d is small. Fig. 12 shows the evacuation time of different guidance strategies. The evacuation time T S 3 ( P d =0.3) < T S 4 < T S 1 < T S 2 < T S 5 . Therefore, when compared to other four strategies, the strategy S 3 ( P d = 0.3) is the most effective strategy for guiders. 3.4.2. Guidance strategy for multi-guider When fire or other accident occurs, pedestrians must evacuate from the room as soon as possible. Only one guider is not enough, therefore, more guiders are needed to lead pedestrians. In this part, the effect of guidance strategy for multi-guider on evacuation is surveyed. The situation is more complex when there are more than one guider during evacuation. There are two problems needing to be solved: (1) Should guiders cooperate with each other? (2) What strategies do guiders adopt during evacuation? Firstly, we assume two relationships exist between guiders. The first one is cooperation that guiders have communication and share information with each other. Therefore, they know each other’s target and will not choose the same target pedestrian during guidance. The other situation is noncooperation that guiders ignore the existence of other guiders and they lead their target pedestrian to the exit no matter the target is chosen by other guiders or not.
Fig. 13. Evacuation time of different strategies for guiders (N g = 2, v g = v h = 2 m/s).
Secondly, taking two guiders as an example. The strategies adopted by two guiders are as follows: (1) S 3 + S 3 , both guiders consider the distance and occupant number factors and use the strategy S 3 ( P d = 0.3); (2) S 4 + S 4 , guiders choose the target pedestrian who has the shortest distance to exit; (3) S 5 + S 5 , both guiders select the target pedestrian who has the largest distance to exit; (4) S 3 + S 4 , one guider uses S 3 ( P d = 0.3) and the other adopts S 4 ; (5) S 3 + S 5 ; (6) S 4 + S 5 . The evacuation time of different strategies for two guiders is displayed in Fig. 13. It is found the communication and cooperation between guiders facilitate pedestrian evacuation. Because guiders know each other’s target pedestrian before they choose their own target under this circumstances, so they will avoid guiding the same target during evacuation, which makes evacuation efficient when compared to evacuation in noncooperation situation. Among the six strategies for two guiders, strategies S 3 + S 3 and S 3 + S 4 are the most effective and evacuation time in both strategies are the least. The result is also consistent with the evacuation situation with only one guider (evacuation time in S 3 and S 4 for single guider are the least). 4. Conclusion In this paper, a multi-grid model based on random theory is introduced to investigate the effect of evacuation guidance on pedestrian evacuation in different situations. Guider type, guider number, guider distribution and different guidance strategies are studied. Simulation results are summarized as follows: (1) The identified guider is more beneficial to evacuation when compared to the guidance of unidentified guider. Therefore, in reality, guiders should have something special from the outside to make themselves be distinguished easily by other people during evacuation. (2) Adding guider number reduces the evacuation time but the effect is not obvious when guider number is large enough, and a proper number of guiders in view of the human cost can be obtained in our model. (3) The uniform distribution of guider is more conducive to evacuation when pedestrians are distributed randomly in the room, which suggests that guiders are supposed to cover as large area as they can when they choose their positions. That is usually the case because it is hard to predict exact distribution of pedestrians.
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(4) It is good for evacuation when guider’s speed is about 75% of herding occupant’s speed in our scene. In this case, guider can assist enough people with a relatively large speed at the same time. However, it still needs more investigation to get the optimal speed of guider in different situations. (5) In comparison with other strategies discussed in this paper, the guidance strategy of considering both guider-pedestrian distance and occupant number is the most effective to evacuation. In addition, cooperation between multiple guiders is very necessary and should be adopted during evacuation guidance. We think the study can help to develop efficient evacuation strategy and give suggestions to management under emergency. It should be noted that the psychological factor of pedestrian during evacuation guidance is not taken into account in this paper, and it will be investigated carefully in the future work. Acknowledgements Project supported by the National Natural Science Foundation of China (Grant Nos. 51178445, 51308526, 51120165001), Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20133402110009), the Shanghai Postdoctoral Sustentation Fund of China (Grant No. 14R21422200) and the foundation supports from the State Key Laboratory of Fire Science in University of Science and Technology of China (HZ2015-KF11). References [1] [2] [3] [4]
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Discussion
Modeling pedestrian evacuation with guiders based on a multi-grid model Shuchao Cao a , Weiguo Song a,∗ , Wei Lv b a b
State Key Laboratory of Fire Science, University of Science and Technology of China, Hefei 230027, China Research Center for Crisis & Hazard Management, Wuhan University of Technology, Wuhan 430070, China
a r t i c l e
i n f o
Article history: Received 6 July 2015 Received in revised form 10 November 2015 Accepted 23 November 2015 Available online 30 November 2015 Communicated by R. Wu Keywords: Evacuation Guider Guidance strategy Multi-grid model Pedestrian dynamics
a b s t r a c t Pedestrian evacuation with guidance is investigated by a multi-grid model in this paper. The effects of guider type, guider number, guider distribution and guidance strategy on evacuation are discussed. From the analysis of simulation results, it is found that the identified guiders are more beneficial to evacuation because they can be distinguished easily by pedestrians during evacuation; The optimal guider number exists in view of the human cost and can be obtained in our model; The uniform distribution of guiders covers more area in the room and makes evacuation efficient; Evacuation guidance is more effective when the speed of guider is about 75% of herding pedestrian’s speed in our simulation scenario; The performance of evacuation guidance strategy considering both distance and occupant number is the best when compared to other strategies; The coordination and cooperation between guiders are very important and necessary to facilitate the evacuation. The study may be useful for understanding the importance of guidance in evacuation and developing efficient evacuation strategy for management under emergency. © 2015 Elsevier B.V. All rights reserved.
1. Introduction With the development of modern society, more and more buildings are built to meet the needs of people on living, working and entertainment. Due to the complex structure of the buildings, safe crowd evacuation has been becoming more important and critical in case of emergency. In recent decades, many evacuation models have been proposed by researchers. Generally, evacuation models can be classified into two categories: the continuous model such as the social force model [1–3] and the discrete model such as the cellular automaton model [4–9] and the lattice gas model [10–14]. The dynamic features of pedestrian evacuation such as herding and zipper effect, stop and go, lane formation and clogging effect have been observed and successfully reproduced by these models. In real life, crowd evacuation from large and complex building spaces is usually hindered by people’s not knowing their detailed internal connectivity. In such circumstances, occupants might not be aware of the existence of suitable circulation paths or the most appropriate escape paths. Psychology studies show that occupants usually decide to use familiar exits, such as where they entered the
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Corresponding author. E-mail address: [email protected] (W. Song).
http://dx.doi.org/10.1016/j.physleta.2015.11.028 0375-9601/© 2015 Elsevier B.V. All rights reserved.
building [15]. Emergency exits or exits not normally used for circulation are often ignored, in addition, the following behavior is also found during evacuation. If a fire occurs, blocking some of those known paths, and smoke further obscuring the vision, the problem might be fatally aggravated and chaos or even disaster may occur which often cause severe casualties. In such emergencies, if people could be guided by evacuation guiders who know the evacuation path to the exits, casualties might be avoided or reduced significantly. It is widely accepted that a proper evacuation could save many lives in emergencies. Therefore, better preparations of evacuation guidance are significant and important for pedestrian evacuation. François and Robert [16] modeled the effect of leadership on crowd flow dynamics. Leaders were divided into embedded leader, peripheral leader and distant leader according to their initial positions. Simulation showed that a mix of leader classes was the most desirable and leaders going about half the speed of other agents led to the most efficient evacuations. Pelechano and Badler [17] simulated crowd and trained leader behavior and different roles such as trained personnel, leaders and follower were considered during building evacuation. Evaluation showed that only a relatively small percentage of trained leaders yielded the best evacuation rates. Then Ji and Gao [18] investigated crowd evacuation with a leader–follower model and result indicated that evacua-
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tion with some leaders would be more efficient as compared to situations without leaders, however, more leaders might not always result in more efficient evacuation because of the chaotic effect caused by too many leaders to the evacuation. Yuan and Tan [19] proposed an extensive cellular automaton model to simulate evacuation from a large crowed smoke-filled compartment with considering the effect of guiders and visibility range, and the phenomenon of “flow with the stream” was modeled. Wang et al. [20] added a communication field to the original floor field model for emergency evacuation under the control of evacuation assistants. The effective locations and optimal numbers of assistants were investigated. Based on the extended dynamic communication field model, they [21] also introduced the centripetal effect of an evacuation assistant. Spartalis et al. [22] studied the impact of guidance on evacuation based on CA model. The evacuation of a retirement house with the help of the nursing staff was simulated and results proved the significance of proper guidance. Yang et al. [23] introduced a modification method for modeling the guided pedestrian group where the navigational force was defined based on social force model and the model was validated by comparing its local density–speed and density–flow diagrams with fundamental diagrams. To our best knowledge, although some research on evacuation guidance has been done by many scholars, studies on different guidance strategies during evacuation are very few. It is important and necessary to investigate the effect of these factors on pedestrian evacuation. Because of the low computational efficiency of continuous model and inaccuracy of traditional discrete model, in this paper, an extensive model based on multi-grid model [24–28] is proposed to simulate pedestrian evacuation with guidance. The rest of this paper is organized as follows: A multi-grid model considering the guidance of evacuation assistant is introduced in section 2. In section 3, the effects of guider type, guider number, guider distribution, guider speed and guidance strategy on pedestrian evacuation are surveyed and simulation results are discussed. In section 4, conclusion is made and the paper is closed. 2. Model 2.1. Model description Pedestrians involved in the model include two kinds: guider and herding occupant. Guider gives the evacuation guidance about exit location to occupants, and it can be categorized into two types: identified guider and unidentified guider. The unidentified guider assumed to be the same with other occupants in appearance but know the exit and have a subtle influence on other pedestrians in the influence radius R inf . This influence is similar with the soft control [29] and occupants are guided unconsciously by the unidentified guider to the exit. The identified guider assumed to wear special uniform that are different from other occupants and could be distinguished easily by other people. Pedestrians are strongly influenced by the identified guiders and must follow the evacuation guidance when they are located in the influence radius of identified guiders, which is clearly different from the soft control of the unidentified guider. The herding occupants cannot evacuate from the room by themselves and need other people’s assistance. If herding occupants find the identified guider in the influence radius, they must follow the guidance of the identified guider closest to them. Otherwise, they will follow the majority of people who have found the exit no matter she or he is guider or herding occupant in their influence radius. As for evacuation guidance, there are two kinds of guidance for guiders during evacuation assistance: (1) Static guidance that guiders do not move and only lead people on the fixed position
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until all other occupants have evacuated from the room during evacuation. (2) Dynamic guidance that guiders lead people through moving in the room and they evacuate with other people together when evacuation begins. 2.2. Model mechanism Once evacuation begins, pedestrians must choose an exit firstly, after that, they move to their target exit immediately. Therefore, it is very important to understand the exit selection and pedestrian movement process in the model. 2.2.1. Exit selection The exit selection for guiders in this model is based on random utility theory [30], and the usefulness perceived by the decision maker n about the m alternative is represented by the following formula:
U mn = V mn + εmn
(1)
The first one V mn is the main or expected value of the perceived utility. The second term εmn , called the random residual, represents the deviation of the average utility from the real value. According to different distribution of random residue, the Mixed Logit Models (MLMs) based on the hypothesis that the random residues are independent and identically distributed according to a Gumbel random distribution with a mean equal to zero and a λ parameter [31] is used in this paper. Therefore, the probability of selecting exit m among the k exits for pedestrian n is given as follows:
exp(λ V mn ) pmn = k j =1 exp(λ V jn )
(2)
V mn = kdis (1 − pdismn ) + kden (1 − pdenmn )
(3)
pdismn = pdenmn =
dismn max(dis1n , · · · , dismn , · · · , diskn ) denmn max(den1n , · · · , denmn , · · · , denkn )
(4) (5)
where dismn denotes the distance from the position of pedestrian n to the exit m; denmn is the number of pedestrians who select exit m and their distance to the exit m is nearer than pedestrian n; pdismn and pdenmn are the proportion of dismn and denmn to their maximum value respectively; kdis and kden are the scaling constants, and we ensure kdis + kden = 1 in this paper. For herding occupants, they cannot find the exit by themselves and need to be guided during evacuation. There are three situations should be considered: (1) If herding occupants are located in the identified guider’s influence radius, they will receive the exit information from guiders and find the exit location, then follow the guidance to the exit. If there are more than one identified guiders in the influence radius, the occupant will follow the closest guider’s leading. (2) If they are not, occupants will choose the exit selected by the largest number of people in their influence radius. (3) If no people or people in the influence radius also do not find the exit, occupants will move randomly without aim until they find the exit. 2.2.2. Pedestrian movement A floor field model is used to simulate pedestrian movement under emergency. The size of one cell is 0.1 m × 0.1 m and every pedestrian occupies 25 cells. The shuffled update is adopted in this model, and each pedestrian can move a distance equal to one cell per update to any of the eight directions based on the transition probabilities just as shown in Fig. 1.
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Fig. 1. Possible transitions and corresponding transition probabilities.
Once an occupant chooses the target exit m, the transition probability of selecting the neighborhood cell (i , j) in the next step is calculated as follows:
P i j = N nor I ine exp k S S m i j (1 − ni j )αi j
(6)
where N nor denotes the normalization factor for ensuring that P i j = 1; I ine represents the inertial parameter; k S is the parameter for scaling the static floor field; ni j indicates whether the cell (i , j) is occupied, it is 1 if the cell is occupied and 0 otherwise; αi j is related to the existence of obstacle in the cell, the value is 0 if the cell is occupied by obstacle and 1 otherwise. The static floor field S m initialized at the beginning of the model run is set inij versely proportional to the distance from the exit m to the cell (i , j). In this model, we set one time step t = 0.1 s, I ine = 1.2 for the movement direction that is the same with the movement direction in last time step, otherwise I ine = 1. k S = 0.8 and R inf represents the influence radius of pedestrian in this paper.
Fig. 2. (a) The schematic illustration of the room, (b) the static floor field graph of the room.
2.3. Model scene Simulation scenario is displayed in Fig. 2. The size of the room is 20 m × 10 m inside, which is discretized into 200 cells × 100 cells. The thickness of the wall is 0.5 m. Two exits whose width is 1 m are located in the center of walls respectively. The number of guider and herding occupant in the simulation is N g and N h , and the total pedestrian number N = N g + N h . The movement speed is v g and v h for guiders and herding occupants respectively. Simulation is carried out fifty times for every scenario. The overall simulation process is shown as a flowchart in Fig. 3. 3. Simulation and results At first, we should set the values of kdis and kden . Fig. 4 shows the evacuation time of different values of kdis . We can find the optimal evacuation time is achieved when kdis = 0.4 (kden = 1 − kdis ). So kdis = 0.4 and kden = 0.6 are set in this paper. In Fig. 5, the average evacuation time decreases with the increase of the influence radius R inf . It is easy to understand because the larger of the influence radius can make more pedestrians be covered by the guidance. But if the influence radius is large enough, the evacuation time does not change anymore. R inf = 2 m is adopted in the following simulations. 3.1. The effect of guider type and number on evacuation In Fig. 6, evacuation time decreases with the increase number of guiders and curves can be split into three parts. The decline of evacuation time is sharp in the first part, and it decreases from 70 s (55 s) to 50 s (50 s) for identified (unidentified) guider in Fig. 6(a). In Fig. 6(b), it falls from 61 s (47 s) to 44 s (40 s). The significant reduction indicates guiders are the most beneficial to
evacuation at the first stage. Then the decrease of evacuation time in the second part is not as obvious as that in the first part. At the last part, the curves become flat and the decrease hardly happens, which means guidance has saturated during the evacuation when guider number is large enough. Therefore, it is necessary and meaningful to find the optimal guider number considering the human cost and evacuation time during evacuation. In Fig. 6, the optimal guider number is 4 for evacuation in this scenario. As shown in Fig. 6, the guidance of identified guider is more conducive to evacuation than the unidentified guider’s guidance. As mentioned before, the mechanism of guidance between two types of guider is very different. The strong influence of identified guiders has a direct effect on herding occupants, which makes them have an optimal exit selection based on this compulsory guidance. However, the soft control of unidentified guiders weakens the guidance effect on evacuation and pedestrians may not follow the optimal guidance on exit selection even though they have received the unidentified guider’s guidance, because other pedestrians in the influence radius will also have an effect of same intensity on pedestrian’s exit choice. As a result, evacuation time under the guidance of unidentified guider is longer than that of the identified guider’s guidance. In the following part of this paper, only the identified guider is discussed and simulated. When compared Fig. 6(a) with Fig. 6(b), we can find that the evacuation time with static guidance is always longer than that with dynamic guidance when the guider number is the same. Therefore, the dynamic guidance is more effective to evacuation than the static guidance. The reason is that the dynamic guiders will assist more herding occupants and their influence areas are larger when they move together with other pedestrians after evacuation begins. However, the static guidance takes effect only when
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Fig. 3. The flowchart of the overall simulation process.
Fig. 4. 150 pedestrians are distributed randomly in the room (N = N g = 150, v g = 2 m/s).
Fig. 5. The effect of influence radius R inf on evacuation time (N = 150, N g = 4, v g = v h = 2 m/s).
pedestrians enter into the influence radius of the fixed guiders. Therefore, in contrast with the dynamic guidance, the effect of static guidance on evacuation is limited.
room. As shown in Fig. 8, the uniform guider distribution has the least average evacuation time than other distributions. The reason is that the uniform distribution makes guiders cover more areas in the room and influence more people within the same amount of time when compared to other distributions. Therefore, it is beneficial for evacuation when guiders are distributed uniformly in this scene. But for a specific or known distribution of occupants, the result may be different. Because it is highly related to the real distribution of occupants in the room. However, under this circumstance, the model can still be used to simulate pedestrian
3.2. The effect of guider distribution on evacuation The effect of guider distribution on evacuation is investigated in this part and N g = 4 (the optimal guider number in section 3.1) is adopted. Fig. 7 displays the guider distribution in different scenarios. Pedestrians except the guiders are distributed randomly in the
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Fig. 6. Pedestrians are distributed randomly in the room (N = 150, v g = v h = 2 m/s). (a) Static guidance, (b) dynamic guidance.
3.3. The effect of guider speed on evacuation
Fig. 7. The black circles represent guiders’ positions in the room. (a) Random distribution, (b) center distribution, (3) uniform distribution, (4) exit distribution.
evacuation and compare the performance of different guider distribution, finally find the optimal guider distribution for the specific occupant distribution.
In this part, pedestrians are randomly distributed in the room and the effect of guider’s speed on evacuation guidance is investigated. Obviously, when v g = 0 m/s, guider becomes static guider, otherwise, it is dynamic guider. When evacuation begins, guiders will move to the exit immediately. As shown in Fig. 9, evacuation time declines firstly and it slumps from 50 s to its lowest 37 s, then it rises to 41 s with the increase of guider’s speed. In this scene, the optimal speed of guider is v g = 1.5 m/s for v h = 2 m/s. The reason can be found that evacuation is hindered when guider’s speed is small (v g < 1 m/s in this scene), because they cannot lead other pedestrians quickly. However, when guider’s speed is large (v g > 2 m/s in this scene), they move too fast to assist enough pedestrians and many pedestrians have not found the exit before guiders leave the room. Therefore, if we want to reduce the evacuation time, guider should assist people as much as possible with a speed as fast as possible. In Fig. 9, the most effective evacuation guidance is obtained when guider’s speed is about 75% of herding occupant’s speed. Nonetheless, the simulation scenario is limited
Fig. 8. Pedestrians are randomly distributed in the room (N = 150, N g = 4 and v g = v h = 2 m/s). (a) Static guidance, (b) dynamic guidance.
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Fig. 9. The effect of guider speed on evacuation time (N = 150, N g = 4 and v h = 2 m/s).
and more investigation should be done to find the optimal speed of guider in different situations in the future. 3.4. The effect of guidance strategy on evacuation The guider’s guidance strategy in the above simulation is toward the exit and their target is the exit all the time, which means dynamic guider will go to the exit immediately when evacuation begins. This kind of evacuation guidance strategy is not bad when the total pedestrian number is large (e.g. N = 150), but it does not work efficiently when pedestrian density in the room is too low (e.g. N = 10). Due to no other pedestrians in the influence radius or pedestrians around them do not find the exit either, some pedestrians cannot find the exit and evacuate from the room successfully in low density. In a word, many pedestrians will not receive the guidance directly or indirectly and fail the evacuation finally under this condition. There are two methods to solve this problem in low density. One is adding the guider number, but the human cost will increase too. The other way is replanning the guidance strategy and changing guider’s movement target from the exit to the pedestrian who still has not found the exit, which means guider should search for occupants needing assistance and move to them, then lead them to the exit. After current target pedestrian has received the guidance and found the exit, guider will go to the next target pedestrian immediately and they do not leave the room until all the pedestrians in the room find the exit at last. Therefore, the effect of different guidance strategies on pedestrian evacuation is studied in this part. 3.4.1. Guidance strategy for single guider At first, the simple situation N g = 1 is investigated and different strategies are adopted based on different criteria of choosing target pedestrian. Strategies for single guider are as follows: (S 1 ) The shortest distance principle that guider chooses the target pedestrian closest to him or her; (S 2 ) The largest number principle that guider selects the target pedestrian who has the maximum number of occupants who have not found the exit in his or her influence radius; (S 3 ) The distance and number principle that guider considers both the distance to him or her and the occupant number in the influence radius. In fact, it is a combination of strategies S 1 and S 2 . The formula is as follows:
Pi = Pd •
d gi dmax
− (1 − P d ) •
ni nmax
(7)
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Fig. 10. The effect of P d on evacuation guidance (N g = 1, v g = v h = 2 m/s).
dmax = nmax =
212 + 112 = 23.7 m
πR
2
0.25
= 50.2
(8) (9)
where P d ∈ [0, 1] represents the weight of distance factor; d gi denotes the distance between the guider g and pedestrian i; dmax is the diagonal length of the room; ni stands the pedestrian number in the influence radius of pedestrian i and nmax is the maximum number in pedestrian’s influence radius (the occupy size of each person in the model is 0.25 m2 ). Guider chooses the target pedestrian with the smallest P i in this strategy; (S 4 ) The shortest distance principle that guider chooses the target pedestrian closest to the exit; (S 5 ) The largest distance principle that guider selects the target pedestrian who has the longest distance to the exit. The effect of different P d on evacuation time is shown in Fig. 10. There is one point should be noticed that when P d = 1 and P d = 0, strategy S 3 actually becomes strategies S 1 and S 2 respectively. We can see the trend of curves decreases firstly then increases at last. It is interesting that the optimal evacuation time is achieved at P d = 0.3, which indicates the evacuation guidance is the most effective when considering both the distance and pedestrian number factors. By analyzing the reason we find that guider only assists one occupant once at most time and most occupants still cannot find the exit if guider only considers the distance factor (S 1 ). The evacuation efficiency is low and the exit is not fully used under this circumstance. However, guider needs more time to assist the target occupant if only considering the pedestrian number factor (S 2 ), and then pedestrian needs more time to reach the exit when evacuation begins. Just as shown in Fig. 11, the average time of first arrival to the exit in different situations is t S 1 < t S 3 ( P d =0.3) < t S 2 . The disadvantage of only considering distance factor is that the flow is small and exit is not fully used during evacuation, while the weakness of only considering occupant number factor is that it needs more time to guide pedestrians during evacuation. Therefore, taking account of both factors makes the guidance efficient for evacuation. There is one interesting point that the evacuation time of N = 50 is smaller than that of N = 10 when P d ≤ 0.1 in Fig. 10. Guider prefers to assist pedestrian who has a relatively large number of occupants in the influence radius when P d is small. Compared to the situation of N = 10, pedestrians distributed randomly in the room are more likely to form small groups in their influence radius when N = 50. In this case, it becomes easy for people to find the exit and evacuate from the room in a short time when guider
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Fig. 11. The effect of P d on the time of first arrival to exit (N g = 1, v g = v h = 2 m/s).
Fig. 12. Evacuation time of different strategies for guider (N g = 1, v g = v h = 2 m/s).
gives more consideration of pedestrian number in the influence radius. Therefore, a relatively larger density in the room is positive to evacuation when P d is small. Fig. 12 shows the evacuation time of different guidance strategies. The evacuation time T S 3 ( P d =0.3) < T S 4 < T S 1 < T S 2 < T S 5 . Therefore, when compared to other four strategies, the strategy S 3 ( P d = 0.3) is the most effective strategy for guiders. 3.4.2. Guidance strategy for multi-guider When fire or other accident occurs, pedestrians must evacuate from the room as soon as possible. Only one guider is not enough, therefore, more guiders are needed to lead pedestrians. In this part, the effect of guidance strategy for multi-guider on evacuation is surveyed. The situation is more complex when there are more than one guider during evacuation. There are two problems needing to be solved: (1) Should guiders cooperate with each other? (2) What strategies do guiders adopt during evacuation? Firstly, we assume two relationships exist between guiders. The first one is cooperation that guiders have communication and share information with each other. Therefore, they know each other’s target and will not choose the same target pedestrian during guidance. The other situation is noncooperation that guiders ignore the existence of other guiders and they lead their target pedestrian to the exit no matter the target is chosen by other guiders or not.
Fig. 13. Evacuation time of different strategies for guiders (N g = 2, v g = v h = 2 m/s).
Secondly, taking two guiders as an example. The strategies adopted by two guiders are as follows: (1) S 3 + S 3 , both guiders consider the distance and occupant number factors and use the strategy S 3 ( P d = 0.3); (2) S 4 + S 4 , guiders choose the target pedestrian who has the shortest distance to exit; (3) S 5 + S 5 , both guiders select the target pedestrian who has the largest distance to exit; (4) S 3 + S 4 , one guider uses S 3 ( P d = 0.3) and the other adopts S 4 ; (5) S 3 + S 5 ; (6) S 4 + S 5 . The evacuation time of different strategies for two guiders is displayed in Fig. 13. It is found the communication and cooperation between guiders facilitate pedestrian evacuation. Because guiders know each other’s target pedestrian before they choose their own target under this circumstances, so they will avoid guiding the same target during evacuation, which makes evacuation efficient when compared to evacuation in noncooperation situation. Among the six strategies for two guiders, strategies S 3 + S 3 and S 3 + S 4 are the most effective and evacuation time in both strategies are the least. The result is also consistent with the evacuation situation with only one guider (evacuation time in S 3 and S 4 for single guider are the least). 4. Conclusion In this paper, a multi-grid model based on random theory is introduced to investigate the effect of evacuation guidance on pedestrian evacuation in different situations. Guider type, guider number, guider distribution and different guidance strategies are studied. Simulation results are summarized as follows: (1) The identified guider is more beneficial to evacuation when compared to the guidance of unidentified guider. Therefore, in reality, guiders should have something special from the outside to make themselves be distinguished easily by other people during evacuation. (2) Adding guider number reduces the evacuation time but the effect is not obvious when guider number is large enough, and a proper number of guiders in view of the human cost can be obtained in our model. (3) The uniform distribution of guider is more conducive to evacuation when pedestrians are distributed randomly in the room, which suggests that guiders are supposed to cover as large area as they can when they choose their positions. That is usually the case because it is hard to predict exact distribution of pedestrians.
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(4) It is good for evacuation when guider’s speed is about 75% of herding occupant’s speed in our scene. In this case, guider can assist enough people with a relatively large speed at the same time. However, it still needs more investigation to get the optimal speed of guider in different situations. (5) In comparison with other strategies discussed in this paper, the guidance strategy of considering both guider-pedestrian distance and occupant number is the most effective to evacuation. In addition, cooperation between multiple guiders is very necessary and should be adopted during evacuation guidance. We think the study can help to develop efficient evacuation strategy and give suggestions to management under emergency. It should be noted that the psychological factor of pedestrian during evacuation guidance is not taken into account in this paper, and it will be investigated carefully in the future work. Acknowledgements Project supported by the National Natural Science Foundation of China (Grant Nos. 51178445, 51308526, 51120165001), Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20133402110009), the Shanghai Postdoctoral Sustentation Fund of China (Grant No. 14R21422200) and the foundation supports from the State Key Laboratory of Fire Science in University of Science and Technology of China (HZ2015-KF11). References [1] [2] [3] [4]
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