Route choice in pedestrian evacuation under conditions of good and zero visibility: Experimental and simulation results

Transportation Research Part B 46 (2012) 669–686

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Transportation Research Part B journal homepage: www.elsevier.com/locate/trb

Route choice in pedestrian evacuation under conditions of good and zero visibility: Experimental and simulation results Ren-Yong Guo a,⇑, Hai-Jun Huang b, S.C. Wong c a

College of Computer Science, Inner Mongolia University, Hohhot 010021, China School of Economics and Management, Beijing University of Aeronautics and Astronautics, Beijing 100191, China c Department of Civil Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, China b

a r t i c l e

i n f o

Article history: Received 7 September 2011 Received in revised form 5 January 2012 Accepted 5 January 2012

Keywords: Pedestrian experiment Pedestrian model Evacuation Route choice Visibility

a b s t r a c t The route choice of pedestrians during evacuation under conditions of both good and zero visibility is investigated using a group of experiments conducted in a classroom, and a microscopic pedestrian model with discrete space representation. Observation of the video recordings made during the experiments reveals several typical forms of behavior related to preference for destination, effect of capacity, interaction between pedestrians, following behavior and evacuation efficiency. Based on these forms of behavior, a microscopic pedestrian model with discrete space representation is developed. In the model, two algorithms are proposed to describe the movement of pedestrians to a destination under conditions of both good and zero visibility, respectively. Through numerical simulations, the ability of the model to reproduce the behavior observed in the experiments is verified. The study is helpful for devising evacuation schemes and in the design of internal layouts and exit arrangements in buildings that are similar to the classroom. Ó 2012 Elsevier Ltd. All rights reserved.

1. Introduction Pedestrian evacuation is a strategy commonly used to handle emergency situations, and has been studied using various modeling methods (e.g., Helbing et al., 2000; Kirchner and Schadschneider, 2002; Guo et al., 2011). Pedestrians during evacuations exhibit complex and variable patterns of behavior, and understanding these patterns is extremely important for improving evacuation procedures and relevant regulations. One of the critical behavioral reactions of pedestrians, which affects evacuation efficiency, is the choice of route for leaving a building. The route choice of pedestrians can be formulated in pedestrian models using either continuous space representation (e.g., Hoogendoorn and Bovy, 2003, 2004; Asano et al., 2010) or discrete lattice space (e.g., Lo et al., 2006; Varas et al., 2007; Huang and Guo, 2008; Xia et al., 2008; Huang et al., 2009; Kretz, 2009; Zhao and Gao, 2010; Guo and Huang, 2010, 2011; Hartmann, 2010; Alizadeh, 2011). In models that use discrete lattice space, the route choice of pedestrians can be formulated using the potential of the lattice, that is to say the floor field (Burstedde et al., 2001; Kirchner and Schadschneider, 2002). The potential is generally used to measure the route distance from the lattice site to the destination, the congestion of pedestrians on routes to the destination, or the capacity of routes to the destination; this allows these factors to be taken into account in a unified and simple way. Varas et al. (2007) and Huang and Guo (2008) proposed a category of algorithms to compute the potential of a lattice that considered only route distance, to formulate the route choice of pedestrians to multiple exits. Zhao and Gao (2010) formulated the route choice of pedestrians to multiple exits, taking into consideration the distance potential of space and pedestrian ⇑ Corresponding author. Tel.: +86 15148066375. E-mail addresses: [email protected], [email protected] (R.-Y. Guo). 0191-2615/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.trb.2012.01.002

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congestion near exits, under the premise that pedestrians were distributed heterogeneously. Guo and Huang (2010) used the logit-based discrete choice principle to formulate the stochastic route choice of pedestrians to multiple exits, taking into consideration the disutility of pedestrians going to exits, which was determined by route distance, the width of the exits, and the number of pedestrians selecting each exit. Alizadeh (2011) used a class of lattice potentials that weighted the distance of the route, human psychology and behavior, pedestrian distribution, and various other factors to formulate pedestrians’ route choice in rooms with obstacles. In the above three studies, pedestrian congestion at the front of routes is considered in the route choice; however, a pedestrian on one route is not necessarily affected by congestion on other routes. Kretz (2009) and Hartmann (2010) considered not only the effects of both route distance and pedestrian congestion on route choice using the potential of space, but also distinguished frontal congestion on different routes. Guo and Huang (2011) developed a method for computing the potential of a lattice that measured several factors affecting pedestrians’ route choice, including route distance, pedestrian congestion and route capacity. They also distinguished frontal congestion on different routes. In most studies on pedestrian evacuation, it is assumed that visibility in the pedestrian facility is good. However, this is often not the case. In some accidents, such as fire emergencies and terrorist attacks, a failure of the electrical power supply at night or smoke reduces the visibility significantly. Isobe et al. (2004) studied the evacuation process of pedestrians from a room with no visibility by means of experiments and simulations, and found that the evacuation of these pedestrians consists of two processes: the biased random walk from an initial position to the wall, and the second walk following the wall. On this basis, Nagatani and Nagai (2004) analyzed the probability density distributions of (1) the number of steps of the biased random walk to the wall, (2) the first contact point on the wall, and (3) the number of steps of the second walk along the wall. Nagai et al. (2004) studied the effects of the configuration of the exits on pedestrian evacuation from a room with no visibility. In the above studies, there are no any internal obstacles in the room and the effects of internal obstacles on the evacuation of pedestrians are not considered. However, in the real world there are normally internal obstacles in buildings. These studies also only consider two cases in which one and ten pedestrians evacuate from the room. The small sample size limits the reliability of the results. Xia et al. (2009) pointed out the importance of the effect of memory on the pedestrian evacuation process in an environment with diminished visibility. Yue et al. (2010) simulated pedestrian evacuation flow with an impaired field of vision using a model of cellular automata and studied the effects of the radius of pedestrian sight on evacuation time. Jeon et al. (2011) analyzed the evacuation behavior of pedestrians under visually handicapped conditions through experiments that were conducted in different conditions of visibility at underground facilities. Pedestrians in condition of zero visibility cannot see the pedestrian dynamics on frontal routes, and visibility affects their route-choice behavior. Thus, studying the route-choice behavior of pedestrians under condition of zero visibility raises considerable problems. To date, the dynamics of pedestrian evacuation from classrooms has been studied by means of modeling and by experimental methods. Helbing et al. (2003) conducted an experiment on pedestrian evacuation from a classroom and compared these results, especially the spatial dependence of pedestrians’ evacuation time on their initial positions, with simulations based on a lattice gas model of pedestrian flows. Zhang et al. (2008) found several typical characteristics of pedestrians evacuating a classroom by watching video recordings of their movement in the classroom, and also simulated the evacuation of pedestrians from the classroom using an improved multi-grid model. Liu et al. (2009) used an experiment conducted in a classroom and a cellular automaton model to study the distribution of pedestrians’ evacuation times as a function of their initial position and the dynamics of their evacuation. This study considered the impact of pedestrian density around exits on pedestrian behavior in evacuation. Zhu and Yang (2011) analyzed the difference among evacuation efficiencies induced by different exit positions and different layouts inside classrooms by simulating pedestrian evacuation from a classroom using a cellular automaton model. Internal obstacles, such as desks, chairs and platforms, are generally found in classrooms. These obstacles divide the space of the classrooms into interlaced aisles and routes, and affect the evacuation efficiency of pedestrians. The classification of pedestrian evacuations from these classrooms is applicable to the study of the route-choice behavior of pedestrians during an evacuation. In this paper, we investigate the route-choice behavior of pedestrians during evacuation, not only under condition of good visibility, but also under condition of zero visibility using experimental and modeling methods. We focus on the effects of visibility on route choice in pedestrian evacuation, and compare the results obtained from experiments and from simulations. In Section 2, we first introduce a group of experiments on pedestrian evacuation from a classroom with a single exit and interlaced routes formed by internal obstacles, under both good and zero visibility conditions. Zero visibility condition is achieved by having the participants wear an eye-patch. Several typical forms of behavior related to the route choice of pedestrians under these conditions are then described. In Section 3, a microscopic pedestrian model with discrete lattice space, as a cellular automata model, is presented to simulate pedestrian evacuation in the classroom, and two algorithms for the potential of the pedestrian space are developed to describe how pedestrians leave the classroom under conditions of good and zero visibility. In Section 4, numerical results are given to illustrate the ability of the model to describe several typical forms of behavior related to the route choice of pedestrians under conditions of good and zero visibility. The evacuation times of pedestrians in experiments and simulations are also compared. Section 5 concludes the paper.

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2. Experiments 2.1. Description of the experiments The group of experiments was conducted in a classroom illustrated schematically in Fig. 1. The size of the classroom was 5.70  13.10 m2. The exit, with a width of 0.85 m, was located in the north wall, at a distance of 0.80 m from the west wall. Three obstacles, a platform, a lectern, and a computer workbench, were placed on the west side of the classroom and 78 pairs of desks and chairs were arranged in 10 rows of 8. The obstacles and the desks are denoted in the schema by light grey rectangles, and the initial positions of individuals are denoted by green circles and are numbered from 1 to 78. The desks and chairs were divided into six sections by two horizontal aisles and one vertical aisle. The transverse distance between desks in each section was 0.9 m, the width of the horizontal aisles was 0.6 m, and the width of the vertical aisle was 0.8 m. The chairs folded automatically, so when individuals stood up, the chairs folded up and left space for the individuals to move between the desks. Two video cameras were mounted at the southwest corner of the classroom and near the middle of the east wall, respectively. The first camera was used to record the pedestrian outflow from the exit, and the second camera was used to record the evacuation process of pedestrians in the classroom. Thirty students were recruited and asked to evacuate from the classroom. Six pairs of experiments were carried out. In each pair of experiments, the pedestrians were asked to perform two evacuation processes, starting from identical initial positions. In the first evacuation process, each pedestrian wore an eye-patch and evacuated under condition of zero visibility. In the second evacuation process, the eye-patches were removed and the participants evacuated under condition of good visibility. In the sequences, Experiment i–j represents the jth evacuation process in the ith pair of experiments. The initial positions of the individuals are shown in Tables 3–8 (see Appendix A). All individuals stood up from their seats and moved towards the exit as soon as the command to evacuate was given. Once the individuals arrived at the exit, they left the classroom. An individual’s evacuation time is defined as the time elapsed between when the command to evacuate is given and the moment the individual exits the classroom. The evacuation times of pedestrians in the experiments are given in Tables 3–8. Each evacuation was recorded by the two cameras. Figs. 2 and 3 show pedestrian evacuation from the classroom in Experiment 2-1 at 0, 6, 10 and 14 s, and in Experiment 2-2 at 0, 4, 8 and 12 s, respectively.

2.2. Behavior of pedestrians in experiments The analysis of the video recordings reveals several typical patterns of behavior related to the choice of route of pedestrians in these experiments. First, under condition of good visibility, the pedestrians can see the routes in front and the exit, and hence it is reasonable for them to consider the route distance to the exit in selecting movement routes, and thus minimize the distance as a strategy in route choice. Under condition of zero visibility, the pedestrians cannot see the surrounding dynamics, but they can still consider the route distance to the exit in selecting movement routes. Their memory of the internal layout and position of the exit guides their evacuation. This phenomenon occurs when pedestrians are familiar with the internal layout and the position of the exits in buildings. When buildings have more complex internal layouts or are larger, the use of memory to enhance evacuation efficiency is liable to diminish. Second, the number of pedestrians moving south and north along the rows of seats in columns 3–6 in each experiment are given in Table 1. The seats in column 3 consist of those numbered 3, 11, 19, 27, 35, 43, 51, 59, 67 and 73 (see Fig. 1). The

0.80 0.85 0.70 0.90 Exit

5.70

0.80

1 2

9 10

17 18

25 26

33 34

41 42

49 50

57 58

65 66

3 4 5 6

11 12 13 14

19 20 21 22

27 28 29 30

35 36 37 38

43 44 45 46

51 52 53 54

59 60 61 62

67 68 69 70

73 74 75 76

2.00

7 8

15 16

23 24

31 32

39 40

47 48

55 56

63 64

71 72

77 78

1.40

13.10 Fig. 1. Schematic illustration of the classroom.

1.10

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Experiment2-1: 0s

Experiment2-1: 6s

Experiment2-1: 10s

Experiment2-1: 14s

Fig. 2. Photographs of pedestrian evacuation from the classroom in Experiment 2-1 at 0, 6, 10 and 14 s.

Experiment2-2: 0s

Experiment2-2: 4s

Experiment2-2: 8s

Experiment2-2: 12s

Fig. 3. Photographs of pedestrian evacuation from the classroom in Experiment 2-2 at 0, 4, 8 and 12 s.

other columns can be defined similarly. In the table, the total numbers of pedestrians moving south and north in each column, under conditions of both good and zero visibility, are recorded in the two right-hand columns. It can be seen that in each experiment, under conditions of both good and zero visibility, all pedestrians whose initial positions are in the seats in columns 3 and 4 move north. Pedestrians whose initial positions are in the seats in column 6 prefer to move south rather than north, despite the fact that the north route is shorter than the south route. Pedestrians whose initial positions are in the seats in column 5 sometimes move south and sometimes move north. When no individuals are on the folding seats, they are folded and leave space for the pedestrians to move; however, it is inconvenient for pedestrians to cross the aisles occupied by seats. Therefore, these seats affect the capacity of the aisles, and to formulate an appropriate route choice of pedestrians, this effect should be taken into consideration. Third, under condition of good visibility, the movement of pedestrians is affected by the congestion on frontal routes in their line of vision, and they tend to select frontal routes that are unoccupied by other individuals. However, under zero visibility condition, pedestrians cannot see the dynamics on frontal routes, and do not consider their congestion. In this case, pedestrians can only judge whether they are surrounded by others by feeling with their hands or body. To avoid the

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R.-Y. Guo et al. / Transportation Research Part B 46 (2012) 669–686 Table 1 Numbers of pedestrians moving south and north in columns 3–6 in the experiments. Experiment

Column Column Column Column

3 4 5 6

1-1

2-1

3 4 5 6

4-1

5-1

6-1

Total

S

N

S

N

S

N

S

N

S

N

S

N

S

4 4 2 0

0 0 2 4

6 3 1 0

0 0 0 5

5 3 1 1

0 0 1 4

5 3 2 0

0 0 1 5

4 3 2 0

0 0 2 2

5 4 0 0

0 0 2 3

29 20 8 1

0 0 8 23

N

S

N

S

N

S

N

S

N

S

N

S

N

S

4 4 2 0

0 0 2 4

6 3 0 0

0 0 1 5

5 3 1 0

0 0 1 5

5 3 2 0

0 0 1 5

4 3 2 0

0 0 2 2

5 4 0 0

0 0 2 3

29 20 7 0

0 0 9 24

1-2

Column Column Column Column

3-1

N

2-2

3-2

4-2

5-2

6-2

Total

Note: ‘‘N’’ denotes north and ‘‘S’’ denotes south.

surrounding obstacles or walls and find a feasible route easily, pedestrians generally follow other pedestrians in front of them, who they can feel or touch. Fourth, under zero visibility condition, to avoid bumping into walls or obstacles and to find a route to their destination, pedestrians generally prefer to touch or feel the boundary of walls and obstacles and move along that boundary. This behavior can also be found in other studies, such as those of Isobe et al. (2004) and Jeon et al. (2011). Fifth, we observe the evacuation times of pedestrians. Fig. 4 shows the bar charts delineating the evacuation times of pedestrians in the experiments. In the figure, the location in row x and column y corresponds to the individual’s position, numbered 8(x  1) + y in the classroom. For instance, in the first bar chart the location in row 4 and column 3 represents the position numbered 27. One can see that, if there is more than one pedestrian in a line in one section of desks and chairs, the individuals closer to the two horizontal aisles generally have shorter evacuation times than individuals who do not have aisle seats. That is to say, if there are pedestrians in a line of seats, the evacuation time of an individual in column 1 is longer than that of the one in column 2, the evacuation time of an individual in column 8 is longer than that of one in column 7, and the evacuation time of a pedestrian in column 4 or 5 is not shorter than that of one in column 3 or 6, generally. Similarly, if there is more than one individual in a column, then on the whole, the individuals on the west side, who are closer to the exit, have shorter evacuation times than those on the east side. This is understandable. The two horizontal aisles and the aisles occupied by seats are narrow and it is difficult for individuals to walk beside each other in those aisles, or to pass other people. The two phenomena can be observed in cases of both good and zero visibility. Furthermore, in each experiment pedestrians located in the northeast seats generally need more time to leave the classroom than those in the southeast seats, despite the fact that the northeast seats are closer to the exit than the southeast seats. The pedestrians in the northeast seats can leave the classroom by the north horizontal aisle. They can also first cross the aisles occupied by seats in columns 3–6, and then leave the classroom by the south horizontal aisle. The route distance in the second case is longer than that in the first case, thus they hardly consider the second case. Pedestrians in the southeast seats can leave the classroom by the south horizontal aisle. They can also first cross the aisles occupied by seats in columns 3–6 or the vertical aisle, and then leave by the north horizontal aisle. The route distances in the two cases are almost identical. In the second option, they share the north horizontal aisle with those pedestrians in the northeast seats. Due to congestion, the pedestrians in the northeast seats have to slow down. The above phenomenon can be observed in conditions of both good and zero visibility. Fig. 5 displays the comparison between the evacuation time of pedestrians under good and zero visibility conditions in the experiments. In the figure, the horizontal and vertical coordinates of each point denote the evacuation times of an individual under good and zero visibility conditions, respectively. It can be seen that all data points in each pair of experiments are above the diagonal, which indicates that the evacuation time of each individual under zero visibility condition is greater than that under good visibility condition. With zero visibility, pedestrians move along the boundary of walls or obstacles, and their travel distance is longer than when they have good visibility. In addition, under condition of zero visibility, pedestrians need to find the evacuation route by touch, and to avoid obstacles at the same time. Thus, they have to slow down. This indicates that visibility is one of the critical factors affecting the efficiency of pedestrian evacuation. In Fig. 5, the data points in each pair of experiments are fitted by a linear function. One can see that as the time of the experiment increases, the slope of the fitting line decreases on the whole. The reason for this phenomenon is that under zero visibility condition, pedestrians have to select their route depending on memory and previous experience; as the time of the experiment increases, they become more familiar with the layout and exit position in the classroom, which helps to make their evacuation more efficient. This suggests that evacuation exercises are helpful for improving the efficiency of evacuation under condition of zero visibility.

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Experiment 1-2

Experiment 1-1

30

Time (s)

Time (s)

80 60 40 20

20 10

0

0

Exit 1

Exit 1

2

3

4

Column

5

6

7

8

1

2

3 4

5

6

7

8

9

5

6

7

8

1

2

3 4

5

6

7

8

9

Row

30

Time (s)

Time (s)

4

Experiment 2-2

60 40 20

20 10

0

0

Exit 1

Exit 1

2

3

4

Column

5

6

7

8

1

2

3 4

5

6

7

8

9

2

3

4

Column

5

6

Row

Experiment 3-1

7

8

1

2

3 4

5

6

7

8

9

Row

Experiment 3-2 30

Time (s)

60

Time (s)

3

Column

Row

Experiment 2-1

40 20

20 10

0

0

Exit 1

Exit 1

2

3

4

Column

5

6

7

8

1

2

3 4

5

6

7

8

9

2

3

4

Column

Row

Experiment 4-1

5

6

7

8

1

2

3 4

5

6

7

8

9

Row

Experiment 4-2 30

Time (s)

60

Time (s)

2

40 20

20 10

0

0

Exit 1

Exit 1

2

3

4

Column

5

6

7

8

1

2

3 4

5

6

7

Row

8

9

2

3

4

Column

5

6

7

8

1

2

3 4

5

Fig. 4. Bar charts delineating the evacuation times of pedestrians in the experiments.

6

7

Row

8

9

675

R.-Y. Guo et al. / Transportation Research Part B 46 (2012) 669–686

Experiment 5-1

Experiment 5-2 30

Time (s)

Time (s)

60 40 20

20 10

0

0

Exit 1

Exit 1

2

3

4

Column

5

6

7

8

1

2

3 4

5

6

7

8

9

3

4

Column

Row

Experiment 6-1

5

6

7

8

1

2

3 4

5

6

7

8

9

Row

Experiment 6-2 30

Time (s)

60

Time (s)

2

40 20

20 10

0

0

Exit 1

Exit 1

2

3

4

Column

5

6

7

8

1

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3 4

5

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8

9

2

3

4

Column

Row

5

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1

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40

20

Experiment 1 0 0

20

40

60

60

40

20

Experiment 2 0 0

80

80

60

40

20

Experiment 4 0 0

20

40

60

80

Time under good visibility (s)

40

60

80

60

40

20

Experiment 3 0 0

80

Time under good visibility (s) Time under zero visibility (s)

Time under zero visibility (s)

Time under good visibility (s)

20

Time under zero visibility (s)

60

80

80

60

40

20

Experiment 5 0 0

20

40

60

80

Time under good visibility (s)

20

40

60

80

Time under good visibility (s) Time under zero visibility (s)

80

Time under zero visibility (s)

Time under zero visibility (s)

Fig. 4 (continued)

80

60

40

20

Experiment 6 0 0

20

40

60

80

Time under good visibility (s)

Fig. 5. Comparison between the evacuation times of pedestrians under good and zero visibility conditions in the experiments.

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3. Model 3.1. Model description We simulate pedestrian evacuation in the classroom using a proposed microscopic model with discrete lattice space. The space is represented by a two-dimensional square lattice. In traditional pedestrian models with discrete lattice space, the size of each lattice site is 0.4  0.4 m2, and a pedestrian occupies one lattice site. The sizes of most aisles and obstacles in the classroom are not integral multiples of the size of the lattice. For instance, the width of the two horizontal aisles is 0.6 m, which is 1.5 times the size of the lattice. Previous studies using this type of model have introduced and investigated the notion of a finer discretization of the space (e.g., Kirchner et al., 2004; Weng et al., 2007; Guo and Huang, 2008; Zhang et al., 2008). To represent geometrical structures more accurately and in a natural way, and to guarantee the computational efficiency of the model, we introduce a finer discretization of the space for our model, and have pedestrians occupy 2  2 lattice sites. The size of each lattice site is 0.2  0.2 m2. The classroom is divided into 31  62 lattice sites (including sites occupied by walls). The width of the exit is 4 lattice sites. The position of the first lattice site beginning from the west, occupied by the exit, is designated (6, 31). The transverse distance between desks in each section of desks and chairs is 4 lattice sites. The lengthwise widths of the two sections of desks and chairs in the north, middle and south are 6, 10 and 7 lattice sites, respectively. In each update time step, pedestrian positions are updated in random sequence, and each pedestrian moves the distance of one lattice site to the east, south, west or north, or does not move. As the time of the experiment increases, these pedestrians’ evacuation becomes more efficient. This means that the velocities of pedestrians in each experiment are different. Thus, the size of the time step is determined by the experimental data. Let ae, as, aw and an denote whether pedestrian movements to the east, south, west or north are available, respectively. If two neighboring lattice sites to the east are not occupied by other individuals or obstacles, then movement to the east is available, and the ae value equals 1; otherwise it is 0. The other three parameters can be defined in a similar fashion. When all four directional movements are not available, the pedestrian stays still. When at least one direction of movement is available, the choice of direction is governed by the transition probability, which represents the possibility that the pedestrian moves the distance of a lattice site in each direction. Let Pe, Ps, Pw and Pn denote the transition probability to the east, south, west and north, respectively; they are computed as follows:

Pe ¼ Nae expðepe þ ue Þ;

ð1Þ

Ps ¼ Nas expðeps þ us Þ;

ð2Þ

Pw ¼ Naw expðepw þ uw Þ;

ð3Þ

Pn ¼ Nan expðepn þ un Þ;

ð4Þ

where

N¼

1 : ae expðepe þ ue Þ þ as expðeps þ us Þ þ aw expðepw þ uw Þ þ an expðepn þ un Þ

ð5Þ

pe, ps, pw and pn represent the sum of potentials of two neighboring lattice sites to the east, south, west and north, respectively. The potential modifies the transition probabilities in such a way that a movement in the direction of a smaller potential is preferred. e (>0) is a sensitive parameter for scaling the sum of potentials. When its value takes 0, pedestrians select the direction of movement randomly; when its value is relatively large, pedestrians select the direction with the smallest potential as the direction of movement. ue, us, uw and un are four inertia parameters. For the selected direction of movement at  ; for the other three directions, the inertia paramthe previous time step, the inertia parameter’s value is a positive number u eter values equal 0. This avoids abrupt and random changes of direction in pedestrian movement. This can also be used to guarantee that pedestrians move towards a boundary of walls or obstacles to follow the boundary under condition of zero visibility (Isobe et al., 2004). In the following sections, the algorithms for computing the potential of pedestrian space under both good and zero visibility conditions are developed. 3.2. Potential of pedestrian space under condition of good visibility For the pedestrian space under condition of good visibility, the potential of each lattice site is used to reflect the total effects of the route distance from the lattice site to the exit, the degree of pedestrian congestion on the frontal route to the exit, and the capacity of the frontal route passing the lattice site. The potential is directly proportional to the route disij denote the potential of lattice tance and the degree of congestion, and is inversely proportional to the route capacity. Let p site (i, j). The algorithm for computing the potential of lattices in the classroom under condition of good visibility is summarized by the following steps. Parameters cij, ao, ad and d, which are used in the algorithm, are specified below.

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677

ij ¼ þ1 and is fixed. For each lattice site Step 1. For each lattice site (i, j) occupied by a wall or obstacle, its potential is p ij ¼ 0, and is also fixed. (i, j) occupied by an exit, its potential is p Step 2. For each lattice site (i, j) that has neighboring lattices occupied by exits in the horizontal or vertical direction, set ij ¼ 1; its potential is fixed and is added into the set of lattices that need to be checked. Set d p 0. ij < d þ 1, then first check the neighStep 3. For each lattice site (i, j) in the set of lattices that need to be checked, if d 6 p boring lattice sites (i0, j0) in all eight directions then remove the lattice site (i, j) from the set of lattices that need to be ^i0 j0 in checked. If the potential of the lattice site (i0, j0) has not been determined, then compute a temporary potential p terms of the following four cases: – If lattice site (i0, j0) is not occupied by a pedestrian, and is in the horizontal or vertical direction, then

ij þ ð1 þ cij Þ; ^ i0 j 0 ¼ p p

ð6Þ

– if lattice site (i0, j0) is occupied by a pedestrian, and is in the horizontal or vertical direction, then

ij þ ð1 þ ao Þð1 þ cij Þ; ^ i0 j 0 ¼ p p

ð7Þ

– if lattice site (i0, j0) is not occupied by a pedestrian, and is in the diagonal direction, then

^ i0 j 0 ¼ p ij þ ð1 þ ad Þð1 þ cij Þ; p

ð8Þ

– and if lattice site (i0, j0) is occupied by a pedestrian, and is in the diagonal direction, then

ij þ ð1 þ ad Þð1 þ ao Þð1 þ cij Þ: ^ i0 j 0 ¼ p p

ð9Þ

Step 4. For each lattice site (i0, j0), which is evaluated according to the temporary potential in Step 3, its potential takes the minimum value among all its temporary potentials, is fixed and is added into the set of lattices that need to be checked. Step 5. Set d d + 1; if there are no lattices for which the potential has not been determined, then stop; otherwise go to Step 3. In this algorithm, parameter cij is one intensity parameter, which scales the effect of the route capacity on the potential of lattice site (i, j). If lattice site (i, j) is in an aisle containing seats, then cij ¼ c ð> 0Þ; otherwise cij = 0. Eqs. (6)–(9) indicate that the increasing rate of the potential of a lattice site is relatively large, if it is in an aisle containing seats (i.e., the capacity of an aisle containing seats is small). The intensity parameter ao (P0) scales the effect of pedestrian congestion on the potential. Eqs. (6)–(9) indicate that the rate of increase of the potential for a lattice site occupied by a pedestrian is not less than that of a lattice site unoccupied by a pedestrian. The intensity parameter ad ð2 ½0; 1Þ scales the increase rate of the neighboring lattice site potential in the diagonal direction. It indicates that the increase rate of the potential of a neighboring lattice site in the diagonal direction is not less than that of a neighboring lattice site in the vertical or horizontal direction. For each iteration, an interval [d, d + 1) is determined. If the potential of a lattice site in the set of lattices that need to be checked is in the interval, then the potentials of its neighboring lattices are computed. In this way, as the parameter d increases, the potentials of more lattices are computed and fixed. It is ruled that the upstream route of a lattice site comprises lattices for which the potential computation precedes the potential computation of the lattice site, and also those for which the potentials affect the potential of the lattice site. The algorithm can guarantee that an individual at a lattice site is only affected by the seats and pedestrians on the route containing the lattice site and upstream of the lattice site, and is not affected by the seats and pedestrians on other routes, especially those routes that target the same destination as the route containing the lattice site. When the above potential algorithm is used to simulate pedestrian evacuation in the classroom, with the specified pedestrian moves, the potential distribution in the classroom needs to be recomputed. The potential algorithm is a type of flood fill method, and it is in principle fairly rapid to run. Even if the potential distribution is computed at each time step of the simulation, the computation time of the simulation is relatively tolerable. To improve the computational efficiency of the simulation, the potential distribution can be computed at intervals of a certain number of time steps. The potential algorithm is a simplified version of that in Guo and Huang (2011), and needs less computational time. The simplification lies in the following two aspects. First, in this algorithm, the potential of each lattice site is computed using the capacity of the link containing the lattice site. In Guo and Huang (2011), the potential of each lattice site is computed using the minimum among its own capacity and the capacities of upstream lattices. Second, in this algorithm, the interval [d, d + 1) is easily determined in each iteration. In Guo and Huang (2011), the corresponding interval is determined by two parameters, one of which is determined with difficultly. If the parameter takes a relatively larger value, then the algorithm fails to iterate from one step to the next; if the parameter takes a relatively smaller value, then their algorithm needs more computational time and it becomes inefficient.

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3.3. Potential of pedestrian space under condition of zero visibility In Section 2.2, we stated that, under condition of zero visibility, pedestrians could still consider the route distance to the exit in selecting movement routes, that seats affect the capacity of the aisles in which they are situated, that pedestrians generally follow individuals in front of them, who they can feel or touch, and that they generally prefer to move along the boundary of walls or obstacles. In addition, under such conditions, pedestrians can only feel or touch other individuals and obstacles in a relatively small surrounding area and pedestrian congestion on the frontal route does not affect their route choice. Thus, for the pedestrian space under condition of zero visibility, the potential of each lattice site is used to reflect the total effects of the route distance, the capacity of the route, and the behavior of following the boundary of obstacles and other individuals around them. ~ij be the potential of lattice site (i, j), which is the weighted sum of three classes of potential p1ij , p2ij and p3ij ; that is, Let p ~ pij ¼ w1 p1ij þ w2 p2ij þ w3 p3ij . Here, w1 (P0), w2 (P0) and w3 (P0) are three parameters scaling the three classes of potential. The first class of potential p1ij reflects the effects of the route distance and the capacity of the route. The second class of potential p2ij formulates the behavior of pedestrian movement along the boundary of walls or obstacles. The third class of potential p3ij formulates the following behavior of pedestrians. In each simulation of pedestrian evacuation under condition of zero visibility, the first class of potential p1ij of each lattice site (i, j) in the space is directly computed by the previous algorithm in Section 3.2 at the initial time of the simulation. In the algorithm, the factor of pedestrian congestion is removed; therefore, the value of the intensity parameter ao is 0. We propose the following algorithm to compute the second class of potential p2ij of each lattice site (i, j) in the space. Step 1. For each lattice site (i, j) occupied by a wall or obstacle, its second class of potential is p2ij ¼ þ1 and is fixed. For each lattice site (i, j) occupied by an exit, its second class of potential is p2ij ¼ 0 and is also fixed. Step 2. For each lattice site (i, j) which has horizontal, vertical or diagonal neighboring lattices occupied by an exit, wall or obstacle, set its second class of potential p2ij ¼ 0, which is fixed and is added into the set of lattices that need to be checked. Set d 1. Step 3. For each lattice site (i, j) in the set of lattices that need to be checked, check its neighboring lattice sites (i0, j0) in all eight directions. If the second class of potential of the lattice site (i0, j0) has not been determined, then its second class of potential is p2i0 j0 ¼ 0 and is fixed. Remove the lattice site (i, j) from the set of lattices that need to be checked. Step 4. For each lattice site (i0, j0) that is evaluated in Step 3, add it to the set of lattices that need to be checked. Set d d + 1. Step 5. If d = da, then set the second class of potentials of the other lattices, the second class of potentials which have not been determined, as 1 and stop; otherwise go to Step 3. In the algorithm, counter d is used to record the time of iteration. Parameter da is the distance in which the following behavior takes effect, and is measured by the number of lattices. For all lattices close to walls or obstacles, or occupied by exits, their second class of potentials are set as 0, and the second class of potentials of the lattices unoccupied by walls or obstacles are set as 1. Pedestrians prefer to move in the direction with the smaller second class of potential, and thus, when they touch or feel the boundary of walls or obstacles, they will follow the boundary. Pedestrians generally feel or touch walls or obstacles by hand or body, and hence the distance da takes the value of three lattice sites, (i.e., 0.6 m). The algorithm is computed at the initial time of each simulation. We propose the following algorithm for computing the third class of potential p3ij of each lattice site (i, j) in the space. Step 1. For each lattice site (i, j) occupied by a wall or obstacle, its third class of potential is p3ij ¼ þ1 and is fixed. Step 2. For each lattice site (i, j) occupied by a pedestrian, its third class of potential is p3ij ¼ 1 and is fixed, and it is added into the set of lattices that need to be checked. Set d 0. Step 3. For each lattice site (i, j) in the set of lattices that need to be checked, check its neighboring lattice sites (i0, j0) in all eight directions. If the third class of potential of the lattice site (i0, j0) has not been determined, and also its first class of potential p1i0 j0 P p1ij , then its third class of potential is p3i0 j0 ¼ 0 and is fixed. Remove the lattice site (i, j) from the set of lattices that need to be checked. Step 4. For each lattice site (i0, j0) that is evaluated in Step 3, add it to the set of lattices that need to be checked. Set d d + 1. Step 5. If d = da, then set the third class of potentials of the other lattices, the third class of potentials which have not been determined, as 1 and stop; otherwise go to Step 3. In the algorithm, counter d is used to record the time of iteration. Parameter da is the distance in which the following behavior takes effect, and is measured by the number of lattices. For those lattice sites close to a pedestrian, if their potentials are larger than the potential of the neighboring lattice site occupied by the pedestrian, then their potentials are set as 0, and the potentials of the other lattices are set as 1. Pedestrians generally feel or touch other pedestrians by hand or body, and hence the distance da also takes the value of three lattice sites, (i.e., 0.6 m). The algorithm assumes that pedestrians follow others in front, who they can feel. The third class of potential obtained by the algorithm cannot be used directly to formulate the following behavior of pedestrians. To guarantee that the third class of potential generated by individuals in this simulation does not cause them to move backwards, or, at the same time, have an

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80 70 60 50 40 30 20 10 0 Fig. 6. Potentials of lattices in the classroom, computed by the potential algorithm in Section 3.2, as parameters c ¼ 2, ao = 0 and ad ¼

Step: 0

Step: 50

Step: 150

Step: 300

pffiffiffi 2  1.

Fig. 7. Schema of pedestrian evacuation at update steps 0, 50, 150 and 300 when following-behavior is not considered.

effect on other pedestrians, the third class of potential used in Eqs. (1)–(5) needs to be recomputed. For an individual, if the third class of potential p3i0 j0 ¼ 0 of a neighboring lattice site (i0, j0) in a direction, and also its first class of potential p1i0 j0 is less than the first class of potential of the neighboring lattice site occupied by the individual, then its third class of potential p3i0 j0 ¼ 0 is used in Eqs. (1)–(5); otherwise p3i0 j0 ¼ 1. The algorithm is implemented at each iterative step to update the positions of all individuals in the classroom. The process of computing the third class of potential and formulating the following behavior among pedestrians outlined above, is different from that in Burstedde et al. (2001) and Kirchner and Schadschneider (2002). Burstedde et al. (2001) and Kirchner and Schadschneider (2002) formulated the following behavior among pedestrians using the so-called dynamic floor field. The dynamic floor field is the number of bosons at the lattice site. The bosons depict the virtual traces left by moving pedestrians and these dynamic processes diffuse and decay. In a case in which pedestrians evacuate the classroom under condition of zero visibility, the following behavior cannot be formulated by the dynamic floor field for the following three reasons. First, pedestrians under such conditions generally follow others in front of them, who are closer to the exit in these experiments. However, the bosons dropped by pedestrians can induce individuals or those in front to move backwards. Second, the distance at which the following behavior occurs among pedestrians under zero visibility condition is relatively small. The boson diffuses randomly, and thus the following behavior, as formulated by the dynamic floor field, occurs at a greater distance. Third, the dynamic field is adapted to formulate the following behavior among pedestrians in a room without internal obstacles. However, there are internal obstacles in the classroom considered. 4. Comparison of results from experiments and simulations First, we verify that the potential algorithm in Section 3.2 has the ability to formulate the effect of seats on the capacity of the aisles where they are situated. Fig. 6 gives the potentials of lattices in the classroom, computed by the potential

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Step: 0

Step: 50

Step: 150

Step: 300

Fig. 8. Schema of pedestrian evacuation at update steps 0, 50, 150 and 300 when following-behavior is considered.

pffiffiffi algorithm, as parameters c ¼ 2, ao = 0 and ad ¼ 2  1. The pedestrian congestion is not considered, (i.e., ao = 0), and hence the potential is unchanged throughout the simulation. Pedestrians move in the direction of smaller potential with larger transition probability. Thus, pedestrians whose initial positions are in the southernmost seats of the two sections of desks and chairs between two horizontal aisles, prefer to move south rather than north. Pedestrians, whose initial positions are in the seats neighboring the southernmost seats, sometimes move south and sometimes move north. Pedestrians whose initial positions are in the northernmost two columns of seats in the two sections move north. This is identical to the results observed in the experiments. Second, we verify the ability of the model to formulate the following behavior among pedestrians during evacuation. We simulate two scenes of pedestrian evacuation in the classroom using the potential algorithm in Section 3.3. There are 78  pedestrians initially placed at 78 different positions in the classroom. pffiffiffi The parameters are e = 2 and u ¼ 0 in Eqs. (1)–(5). For the algorithms in Section 3.3, the parameters c ¼ 2 and ad ¼ 2  1. For pedestrians in positions 8, 15, 22, 29, 36, 43, 50, 57 and 78 (i.e., individuals denoted by green circles in Figs. 7 and 8), the weighted parameter w1 = 1, which means that these pedestrians perform biased random walking, and move in the direction of the exit that has the larger probability; for the other pedestrians, (i.e., individuals denoted by red circles in Figs. 7 and 8), the weighted parameter w1 = 0, which means that these pedestrians perform random walking, and do not know the direction of the exit. The weighted parameter w2 = 0, which indicates that the pedestrian behavior of movement along the boundary of walls or obstacles is not considered. In the first simulation, the weighted parameter w3 = 0, which means that there is no following behavior among pedestrians. Fig. 7 displays the schema of pedestrian evacuation at update steps 0, 50, 150 and 300 in the simulation. It can be seen that all pedestrians performing biased random walking, those denoted by green circles, leave the classroom before update step 300. However, nearly all individuals performing random walking, those denoted by red circles, remain in the classroom until update step 300, although a few of them leave the classroom by random movement. In the second simulation, the weighted parameter w3 = 1, which means that there is following behavior among pedestrians. Fig. 8 shows the schema of pedestrian evacuation at update steps 0, 50, 150 and 300 in the simulation. It can be seen that not only pedestrians who perform biased random walking leave the classroom, but also most of the pedestrians who perform random walking leave the classroom before update step 300. In the simulation, the following behavior among pedestrians is considered, and it induces pedestrians performing random walking to follow those in front who are either performing biased random walking or random walking. At the same time, for pedestrians performing random walking in front, their rear neighboring lattice sites are occupied by others following them, and thus they have to move in front or to the side. In addition, a few pedestrians leave the classroom by random movement. This indicates that the following behavior formulated by the potential algorithm in Section 3.3 takes effect, and induces these pedestrians performing random walking to leave the room. Table 2 Lengths of time steps in the simulations. Simulation

1-1

2-1

3-1

4-1

5-1

6-1

Dt

0.52

0.42

0.42

0.41

0.39

0.40

1-2

2-2

3-2

4-2

5-2

6-2

0.18

0.19

0.20

0.19

0.19

0.22

Dt

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R.-Y. Guo et al. / Transportation Research Part B 46 (2012) 669–686

Simulation 1-2

Simulation 1-1

20 40

Time (s)

Time (s)

60

20

10

0

0

Exit 1

Exit 1

2

3

4

Column

5

6

7

8

1

2

3 4

5

6

7

8

9

2

3

4

Column

Row

Simulation 2-1

5

6

7

8

1

2

3 4

5

6

7

8

9

Row

Simulation 2-2

20 40

Time (s)

Time (s)

60

20

10

0

0

Exit 1

Exit 1

2

3

4

5

Column

6

7

8

1

2

3 4

5

6

7

8

9

2

3

4

Column

Row

5

6

7

8

1

2

3 4

5

6

7

8

9

Row

Simulation 3-2

Simulation 3-1

20 40

Time (s)

Time (s)

60

20

10

0

0

Exit 1

Exit 1

2

3

4

Column

5

6

7

8

1

2

3 4

5

6

7

8

9

2

3

4

5

Column

Row

6

7

8

1

2

3 4

5

6

7

8

9

Row

Simulation 4-2

Simulation 4-1

20

Time (s)

Time (s)

60 40 20

10

0

0

Exit 1

Exit 1

2

3

4

Column

5

6

7

8

1

2

3 4

5

6

7

Row

8

9

2

3

4

Column

5

6

7

8

1

2

3 4

5

6

7

8

9

Row

Fig. 9. Bar charts delineating the evacuation times of pedestrians in the simulations.

In sequences, Simulation i–j represents the jth evacuation process in the ith pair of simulation. Initial positions of pedestrians in Simulation i–j are identical to those in Experiment i–j, and we try to reproduce the evacuation process of pedestrians in Experiment i–j in Simulation i–j.

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Simulation 5-2

Simulation 5-1

20

Time (s)

Time (s)

60 40 20

10

0

0

Exit 1

Exit 1

2

3

4

Column

5

6

7

8

1

2

3 4

5

6

7

8

9

2

3

4

Column

Row

Simulation 6-1

5

6

7

8

1

2

3 4

5

6

7

8

9

Row

Simulation 6-2

20 40

Time (s)

Time (s)

60

20

10

0

0

Exit 1

Exit 1

2

3

4

Column

5

6

7

8

1

2

3 4

5

6

7

Row

8

9

2

3

Column

4

5

6

7

8

1

2

3 4

5

6

7

8

9

Row

Fig. 9 (continued)

Third, we qualitatively and quantitatively reproduce the evacuation processes of pedestrians in these experiments using these simulations, and compare the evacuation times therein. For each evacuation process, 100 simulations are performed, and the evacuation time step of each individual in the process is the average evacuation time step of the individual in these simulations. In simulations of pedestrian evacuation pffiffiffi under condition of zero visibility, the parameters were e = 2 and  ¼ 1:5 in Eqs. (1)–(5). The parameters c ¼ 2, ad ¼ 2  1, w1 = 0.4, w2 = 0.3 and w3 = 0.3 were used in the algorithms in u  Section 3.3. In simulations of pedestrian evacuation under pffiffiffi condition of good visibility, the parameters were e = 2 and u ¼ 1 in Eqs. (1)–(5). The parameters c ¼ 2, ao = 3 and ad ¼ 2  1 were used in the algorithm in Section 3.2. The length Dt of the time step in each evacuation process needs to be determined using data from the corresponding experiment. For each evacuation process, let Si be the evacuation time step of pedestrian i in the simulation, and Ti be the evacuation time of pedestrian i in the experiment. The length of the time step in each evacuation process is computed using the least square method, that is Dt is obtained by the following optimization problem:

min DtP0

X ðSi Dt  T i Þ2 :

ð10Þ

i

Thus,

P Si T i Dt ¼ Pi 2 : i Si

ð11Þ

Table 2 gives the lengths of time steps in these simulations. It can be seen that, for the evacuations under good visibility condition, the difference between the lengths of the time steps in any two simulation processes is smaller. The length of the time step in each simulation is approximately 0.2 s. For the evacuations under condition of zero visibility, the lengths of the time steps vary to a relatively greater extent. In the first experiment the time step is about 0.5 s, but in the subsequent experiments the time step is smaller, about 0.4 s. This indicates that the velocity of pedestrians under condition of zero visibility is about half that of pedestrians under condition of good visibility. This also indicates that evacuation exercises are helpful for improving the efficiency of evacuation under condition of zero visibility. Fig. 9 shows the bar charts delineating the evacuation times of pedestrians in the simulations. In the figure, the location in row x and column y corresponds to the individual’s position numbered 8(x  1) + y in the classroom. One can see that in both good and zero visibility, for the pedestrians in a line in one section of desks and chairs, the individuals closer to the two horizontal aisles have shorter evacuation times than individuals on the inside. For the individuals in a column, people on the west side, closer to the exit, have shorter evacuation times than people on the east side. In each simulation, pedestrians

683

20 0 0

20

40

60

80

30

Simulation 1-2 20

10

0 0

10

20

30

Simulation 4-1 40

20

0 0

20

40

60

Simulation 4-2 20

10

0 0

10

20

30

Time obtained in experiment (s)

0 0

20

40

60

30

Simulation 2-2 20

10

0 0

10

20

30

60

Simulation 5-1 40

20

0 0

20

40

Simulation 5-2 20

10

0 0

10

20

30

Time obtained in experiment (s)

Simulation 3-1 40

20

0 0

20

40

60

30

Simulation 3-2 20

10

0 0

10

20

30

Time obtained in experiment (s)

60

30

60

Time obtained in experiment (s)

Time obtained in experiment (s) Time obtained in simulation (s)

Time obtained in simulation (s)

Time obtained in experiment (s) 30

20

Time obtained in experiment (s) Time obtained in simulation (s)

Time obtained in simulation (s)

Time obtained in experiment (s) 60

40

Time obtained in experiment (s) Time obtained in simulation (s)

Time obtained in simulation (s)

Time obtained in experiment (s)

Time obtained in simulation (s)

40

Simulation 2-1

Time obtained in simulation (s)

60

60

Time obtained in simulation (s)

Simulation 1-1

60

Simulation 6-1 40

20

0 0

20

40

60

Time obtained in experiment (s) Time obtained in simulation (s)

80

Time obtained in simulation (s)

Time obtained in simulation (s)

R.-Y. Guo et al. / Transportation Research Part B 46 (2012) 669–686

30

Simulation 6-2 20

10

0 0

10

20

30

Time obtained in experiment (s)

Fig. 10. Comparison between the evacuation times of pedestrians in the experiments and simulations.

located in the northeast seats generally need longer to leave the classroom than ones in the southeast seats. These phenomena are identical to those observed in the experiments. Fig. 10 depicts the comparison between the evacuation times of pedestrians in the experiments and in the simulations. It can be seen that, for the first group of experiments and simulations, that is Experiments and Simulations 1-1 and 1-2, there are considerable differences in the evacuation times obtained in the simulations and experiments. For the subsequent groups

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R.-Y. Guo et al. / Transportation Research Part B 46 (2012) 669–686

Table 3 Evacuation times (unit: s) of pedestrians in Experiments 1-1 and 1-2. Position

27

33

34

36

37

38

39

42

43

44

Experiment 1-1 Experiment 1-2

11.4 5.5

27.1 13.3

23.9 8.7

37.6 11.0

40.8 14.8

18.7 7.0

21.1 7.6

39.7 9.5

12.9 6.3

29.1 11.7

45

46

47

48

49

50

51

52

53

54

81.3 15.4

49.6 10.5

32.8 9.1

44.9 12.5

55.8 22.9

52.5 22.3

46.2 15.6

48.2 16.6

42.7 14.4

35.2 13.7

55

56

57

58

59

60

61

62

63

64

26.0 18.8

51.1 21.4

79.0 25.4

63.1 19.1

58.2 23.7

73.7 24.8

83.9 25.9

36.4 17.0

69.3 20.2

61.3 18.1

22

23

24

26

27

28

11.8 7.6

13.2 5.3

20.9 7.0

14.2 6.8

10.5 8.1

15.6 9.5

Experiment 1-1 Experiment 1-2

Experiment 1-1 Experiment 1-2

Table 4 Evacuation times (unit: s) of pedestrians in Experiments 2-1 and 2-2. Position Experiment 2-1 Experiment 2-2

Experiment 2-1 Experiment 2-2

Experiment 2-1 Experiment 2-2

10 5.8 3.4

11 7.1 4.1

18

19

8.1 4.8

9.1 5.7

31

34

35

36

38

39

40

41

42

43

22.3 9.0

26.1 10.5

16.7 11.5

27.7 14.3

24.6 10.8

33.3 12.1

37.7 14.8

39.4 17.5

30.2 13.1

35.0 15.1

45

46

49

50

52

54

55

58

59

62

44.4 16.7

32.2 13.5

52.0 22.6

40.5 18.9

53.1 24.7

27.4 15.9

36.6 17.7

50.3 21.2

42.7 16.4

47.2 20.1

27

29

30

31

33

34

11.4 9.9

17.6 12.6

15.4 8.0

23.0 9.1

31.7 11.1

19.6 8.4

Table 5 Evacuation times (unit: s) of pedestrians in Experiments 3-1 and 3-2. Position

22

24

25

Experiment 3-1 Experiment 3-2

14.9 7.0

13.1 5.8

14.0 7.2

35

37

38

39

40

42

43

44

46

47

21.4 14.3

26.7 14.2

41.8 11.7

24.6 10.3

30.2 13.1

25.9 15.5

32.2 17.6

33.3 19.5

27.4 13.7

28.3 15.2

50

51

52

55

56

58

59

60

62

63

38.2 21.5

36.5 19.9

43.4 23.8

45.3 20.7

47.0 22.6

52.9 25.0

50.9 25.7

56.6 26.9

54.2 18.7

35.5 16.8

Experiment 3-1 Experiment 3-2

Experiment 3-1 Experiment 3-2

26 9.8 6.4

Table 6 Evacuation times (unit: s) of pedestrians in Experiments 4-1 and 4-2. Position Experiment 4-1 Experiment 4-2

Experiment 4-1 Experiment 4-2

Experiment 4-1 Experiment 4-2

18 9.9 5.1

19 8.1 4.1

21

23

27

30

31

32

34

35

17.6 7.6

15.0 5.5

14.1 6.2

16.9 6.9

22.4 8.2

25.2 9.3

16.2 8.8

19.4 9.7

38

39

40

41

42

44

45

46

47

51

23.4 12.2

20.4 11.4

26.5 10.5

39.3 18.6

21.5 10.8

27.7 13.3

32.8 16.2

43.8 14.1

29.1 13.1

34.0 15.1

52

54

55

56

59

60

61

62

63

64

46.5 19.8

36.2 15.7

30.5 17.8

39.0 22.3

38.0 17.3

42.0 21.8

48.1 23.8

51.3 21.5

39.9 19.2

45.2 23.2

of experiments and simulations, the evacuation times obtained in the simulations are similar to those obtained in the experiments. This is understandable. In the first group of experiments, pedestrians are unfamiliar with the rules of the experiments and are also less familiar with the layout in the classroom. As a result, their evacuation times are affected. In fact, this can be observed in the video recordings of the first group of experiments when, after the command to evacuate is given, several pedestrians remain in their seats for a moment. Additionally, some pedestrians are indecisive in selecting a moving route. However, in simulations, these psychological factors are not considered. Therefore, the reasons for the differences

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R.-Y. Guo et al. / Transportation Research Part B 46 (2012) 669–686 Table 7 Evacuation times (unit: s) of pedestrians in Experiments 5-1 and 5-2. Position Experiment 5-1 Experiment 5-2

Experiment 5-1 Experiment 5-2

Experiment 5-1 Experiment 5-2

18 6.1 4.5

26 9.3 5.6

28

33

34

35

37

38

39

40

11.1 9.0

18.2 16.0

16.2 6.8

15.3 9.7

23.9 10.4

14.3 7.6

19.1 8.5

27.2 11.3

41

42

43

45

46

48

49

50

51

52

36.9 24.6

21.9 11.8

20.1 10.7

32.3 13.4

29.7 13.8

38.2 15.6

45.2 22.7

31.3 14.9

28.1 12.8

34.5 15.9

53

55

56

57

58

59

60

61

63

64

42.3 14.3

40.6 16.8

44.4 18.5

49.4 19.3

35.8 21.8

47.5 17.6

50.7 20.3

52.7 23.6

39.5 20.1

46.7 21.0

Table 8 Evacuation times (unit: s) of pedestrians in Experiments 6-1 and 6-2. Position

17

25

26

27

28

30

31

33

34

35

Experiment 6-1 Experiment 6-2

17.2 7.0

17.6 11.1

15.8 9.3

19.4 7.5

22.5 10.0

14.9 7.9

18.5 8.4

24.3 16.9

20.1 11.8

23.0 13.1

36

37

38

39

40

41

42

43

44

46

27.3 14.4

27.8 13.6

26.0 12.8

36.2 10.5

32.7 17.6

41.7 20.9

34.8 19.3

29.3 18.8

38.3 22.2

33.0 16.1

47

50

51

52

55

58

59

61

63

64

38.6 15.4

32.0 24.2

44.7 24.8

50.6 26.7

34.4 18.5

48.1 26.0

46.7 27.4

43.0 23.0

35.3 19.9

40.1 21.6

Experiment 6-1 Experiment 6-2

Experiment 6-1 Experiment 6-2

between the evacuation times obtained in the first groups of experiments and simulations are obvious. In the subsequent experiments, pedestrians adapt to the process of evacuation and their evacuation is less affected by these factors. Thus, the evacuation times obtained in the subsequent experiments and simulations are similar to each other. 5. Conclusions In this paper, we use experimental and modeling methods to investigate the choice of route in pedestrian evacuation under conditions of both good and zero visibility. Several qualitative and quantitative features of route choice are observed in a group of experiments on pedestrian evacuation conducted in a classroom. These features are summarized as follows: (1) in both conditions of good and zero visibility, pedestrians consider the route distance to the exit when selecting movement routes and always minimize the distance as a strategy in route choice; (2) under both conditions, pedestrians prefer to select routes unoccupied by seats, despite the fact that these may be longer than others; (3) under condition of good visibility, pedestrians are liable to select the frontal routes that are unoccupied by other individuals; however, under zero visibility condition, they generally follow other pedestrians in front, who they can feel or touch; (4) under condition of zero visibility, pedestrians generally prefer to touch or feel the boundary of walls and obstacles and move along them; and (5) under both conditions, for the pedestrians in a line in one section of desks and chairs, the individuals on the outside (i.e. in aisle seats) in general, have shorter evacuation times than individuals with inside seats. For the individuals in a column, those on the west side have shorter evacuation times than those on the east side on the whole. Pedestrians located in the northeast seats generally need longer evacuation times than those in the southeast seats. In the same evacuation scenario, pedestrian evacuation time under zero visibility condition is longer than that under condition of good visibility. As the number of the experiments increases, the evacuation of these pedestrians under condition of zero visibility becomes more efficient. Based on the phenomena observed in the experiments, a microscopic pedestrian model with discrete lattice space is proposed to simulate pedestrian evacuation in the classroom. In the model, the route choice of pedestrians under both conditions is formulated using two developed algorithms for the potential field of pedestrian space. The potential of the lattice under condition of good visibility reflects the total effects of the route distance from the lattice to the destination, the degree of pedestrian congestion on the route in front, and the capacity of the frontal route to the destination. The potential of the lattice under zero visibility condition reflects the total effects of the route distance, the capacity of the route, and the behavior of following the boundary of obstacles and other individuals around them. Using numerical simulations, we verify that the model has the ability to formulate the effect of seats on the capacity of aisles, where they are situated, and to formulate following behavior among pedestrians during evacuation. The model can be used to qualitatively and quantitatively reproduce the evacuation process of pedestrians in these experiments. The results of simulations imply that the velocity of pedestrians under condition of zero visibility is about half that of pedestrians under condition of good visibility, and evacuation exercises are helpful for improving the efficiency of pedestrian evacuation under

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