Experimental study on the movement strategies of individuals in multidirectional flows

Accepted Manuscript Experimental study on the movement strategies of individuals in multidirectional flows Yanghui Hu, Jun Zhang, Weiguo Song

PII: DOI: Article number: Reference:

S0378-4371(19)31184-7 https://doi.org/10.1016/j.physa.2019.122046 122046 PHYSA 122046

To appear in:

Physica A

Received date : 24 January 2019 Revised date : 8 June 2019 Please cite this article as: Y. Hu, J. Zhang and W. Song, Experimental study on the movement strategies of individuals in multidirectional flows, Physica A (2019), https://doi.org/10.1016/j.physa.2019.122046 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Highlights： 

The experiment on multidirectional flows with more than four directions was carried out.



Some typical pedestrian behaviors under multidirectional flows were observed.



More than 72% of pedestrians select the straight strategy to reach their destinations.



2% - 15% pedestrians choose the detour strategy to reach their destinations.



In most cases, detour strategy is the most efficiency strategy to reach destination quickly.

*Manuscript Click here to view linked References

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Experimental study on the movement strategies of individuals in multidirectional flows Yanghui Hu, Jun Zhang*, Weiguo Song* State Key Laboratory of Fire Science, University of Science and Technology of China, Hefei 230027, China Abstract Multidirectional flows are common phenomena in reality but have been little investigated before. To investigate pedestrian behaviors and movement strategies in multidirectional flows, a series of experiments were carried out under different densities and typical pedestrian behaviors like detour, acceleration, following, etc. were observed. A linear relation between the length of walk path and the number of pedestrians was obtained. Three strategies were classified to describe pedestrian movement: straight (least effort) strategy, straight to detour (non-least strategy) strategy and detour (non-least strategy) strategy. From the experiment, more than 72% of pedestrians selected the straight strategy to reach their destinations. 8% - 17% pedestrians changed their initial straight strategy to detour strategy, which is related to the waiting time and the flow rate in the central area. Three strategies were compared with movement time and the length of walk path. These findings can be used to provide basics for simulation rules and parameters in multidirectional flows simulations and make evacuation plans according to different focuses in normal and emergency conditions. Keywords: pedestrian evacuation; pedestrian behaviors; multidirectional flows; walk path; strategy 1. Introduction Human safety has attracted more and more attention in recent years. A large number of simulation and experimental researches have been carried out to investigate pedestrian dynamics. The results can be basics for designing of the facility capacity, making evacuation plans and modifying transportation handbooks. Due to the controllable variables and convenience of the scenario, laboratory experiments were adopted to collect empirical data recently. Experiments such as single-file movement, unidirectional flow and multidirectional flows experiments were conducted to investigate pedestrian flow characteristics. These empirical data are significant for calibrating model and extracting simulation parameters. To reduce the influence from the environment and other pedestrians, single-file movement experiment was used to investigate the pedestrian inherent characteristics. Seyfried et al. carried out a single-file pedestrian movement experiment and found a linear relation between the velocity and the inverse of the density. Lateral interference has negligible influence on the velocity–density relation in certain conditions [1]. Ziemer et al. obtained the fundamental diagram of single-file movement and transformed data into a quasi-one-dimensional straight line to analysis the Stop-and-Go wave [2]. Lv et al. investigated the velocity-headway relation of single-file movement and applied it to simulating pedestrian following behavior [3]. In addition, Zeng et al. obtained the relation between step length and frequency under different headways [4], Song et al. investigated the relation betweem velocity and distance headway [5]. Crowd component can also influence pedestrian characteristics in single-file movement. Cao et al. investigated pedestrian movement properties of crowd with different age compositions. They found the composition of crowd has significant influence on fundamental diagrams [6, 7]. They also compared the relations of velocity-step width, velocity-step length and 1

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velocity-stepping time of different ages [8]. Zhang et al. carried out bicycle single-file movement experiment and compared the results with pedestrian single-file movement. A universal fundamental diagram which was adjusted properly of space and time was used to describe dynamics of cars, bicycles and pedestrians [9]. Cao et al. carried out single-file movement under different visibility and investigated the headway–velocity relation, the time-space diagram and fundamental diagrams under different visibility [10]. Huang et al. studied the walking speed, headway distance and fundamental diagram under different aisle widths in single-file movement. They found that walking speed of pedestrian increases fast exponentially to an asymptotic value as aisle width increases [11]. Other researchers also found culture difference has impact on pedestrian dynamics in single-file movement [5, 12, 13]. Many researches on unidirectional flow have been carried out. Hoogendoorn et al. conducted a series of experiments to investigate pedestrian behavior at bottlenecks and found the “zipper” effect in experiment [14, 15]. Seyfried et al. studied the unidirectional pedestrian flow through bottlenecks under laboratory conditions. The individual speed, density and individual time gaps in bottleneck with different widths were investigated [16]. Some researchers also investigated the effect of bottleneck on pedestrian dynamics [17-20]. Zhang et al. found that the fundamental diagrams of three different widths unidirectional flow agreed well, which indicates that the specific flow is independent of the width for the same facility [21]. Dias et al. studied the effect of corridor turning angle on pedestrian dynamics in unidirectional flow [22]. Ren et al. carried out experiment on elderly pedestrian movement in straight corridor. The border distance, the nearest neighbors and spatial distribution areas were compared with elderly and young student [23]. In our daily life, multidirectional pedestrian flows are common in shopping malls, train stations, subway stations, campuses and etc. Multidirectional flows experiments have been conducted to investigate the interaction between pedestrians and the effect of movement directions. Isobe et al. carried out experiment on pedestrian counter flows to investigate the arrival time, the pattern formation and jamming transition. They found that the arrival time increases and the mean velocity decreases with the increase of density [24]. Hoogendoorn et al. carried out several experiments on pedestrian flow and observed some typical phenomena such as lane formation in bi-directional pedestrian flows and strip formation in crossing flows [25]. Kretz et al. investigated passing time, walking speed, flux and lane formation in different counter flow ratios [26]. Zhang et al. investigated different ordering forms in bidirectional streams and found that no large difference among density–flow relationships of different ordering forms in the observed density range [27]. Zhang et al carried out intersecting flows experiments with two different intersecting angles (90° and 180°) and found no apparent difference in fundamental diagram [28]. Guo et al. investigated the effect of version on unidirectional flow and bidirectional flows. They found that in both unidirectional flow and bidirectional flows the flow rate decreases in view-limited condition compared to the normal condition [29]. Saberi et al. investigated the spatial fluctuations of pedestrian velocities in bidirectional streams and found that the self-organization phenomenon has great influence on pedestrian velocities varying over time and space [30]. Lian et al. carried out experiment on four-directional intersecting pedestrian flows. The density and velocity were studied under four-directional flows [31, 32], Daamen et al. carried out 10 experiments to study microscopic and macroscopic pedestrian flows characteristics [33]. Cao et al. compared the fundamental diagrams of uni-, bi- and multidirectional flows [34, 35]. Due to different types of pedestrian flow, many differences were found between unidirectional 2

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flow and multidirectional flows. Helbing et al. carried out several experiments in a corridor with bottlenecks to compare the effect of pedestrian counter flows and unidirectional flow. They found that counter flows are significantly more efficient than unidirectional flows [36]. In the contrary, Zhang et al. found that the fundamental diagrams of uni- and bi-directional flows show clear differences in the experiment for ρ > 1.0 m−2. The maximum flow value of unidirectional flow is significantly larger than that of bidirectional flows [27, 37]. Lam et al. found that the bidirectional flows reduced the pedestrian velocity compared to unidirectional flow [38]. Zhang et al. found that due to the change of the geometry and the merging of the streams, the fundamental diagram of the ‘right’ and ‘left’ parts of T-junction are significantly lower than that of the ‘front’ part [21]. Cao et al. compared the shape of fundamental diagram of unidirectional flow, bidirectional counter flows, bidirectional cross flows and four-directional cross flows. They found that there is no difference in the fundamental diagrams in low density, but the difference becomes obvious with increasing density [35]. Xiao et al. investigated the pedestrian dynamics in circle antipode experiments and obtained the distribution law of route length, route potential, travel time and speed [39]. However, little research has been done on more than four directional flows. Meanwhile, it is common that there are multiple-exits and entrances in modern buildings. In emergency, pedestrians and salvagers from different directions form complicated multidirectional flows which would be much more complex than four-directional flows. Faced with such issues, it is necessary to understand the characteristics of multidirectional flows and have a deep comprehension on the pedestrians’ decision-making behaviors like path selection, detouring etc. In this study, a series of experiments was carried out within a circle area to achieve the multidirectional flows. Pedestrians can select their desired way to reach their destinations according to different experimental setups. The structure of the paper is as follows: In section 2, the experiment setup is introduced. Trajectories, typical pedestrian behaviors, walk path, and strategies are discussed in Section 3. The conclusions are summarized in Section 4. 2. Experiment setup The experiment was carried out in November 2017 in the University of Science and Technology of China, Anhui, China. Fig.1 is the sketch of the experiment scenario and a snapshot of the experiment. In total, 72 participants took part in the experiment. They are all university students with the ages between 18 and 24 years old. Since gender has influence on pedestrian dynamics such as walking speed [40, 41] and waiting time at intersections [42], we only consider a special condition that the ratio of male to female is close to 1. All of them are mentally and physically healthy. At the beginning of each run, participants stood evenly on the border of the circle with a radius of 5 m. To create multidirectional flows, the destination of each pedestrian was the opposite side of the circle. So the moving direction of each one was different. The number of flow in each experiment is equal to pedestrian number. When the start instruction emitted, all participants began to move simultaneously. Thus, the multidirectional flows formed. As the experiment went on, congestion appeared in the central of the circle. During the movement, they can freely choose their preferred manner to avoid collisions with others to reach their destinations (went straight, made a detour, made an acceleration or waited for others). Pedestrians were asked to reach their destinations as quickly as possible in each run with the same instruction. Six runs were performed with different number of participants (13, 24, 36, 48, 60 and 72). The details of each experiment run are shown in Table 1. 3

127

128 129 130 131 132

133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151

(a)

(b)

Fig. 1 (a) Schematic illustration of the scenario and (b) a snapshot of the experiment. Table 1. Details of each experiment run Run index

Pedestrian numbers

Global density (ped/m)

1

13

0.41

2

24

0.76

3

36

1.15

4

48

1.53

5

60

1.91

6

72

2.29

The global density is calculated by equation (1): ,

(1)

where N is the pedestrian number which is equal to 13, 24, 36, 48, 60 and 72 in the experiment. L is the circumference of the circle (31.4 m = 2 * 3.14 * 5). Two cameras were fixed on the 5th floor of a nearby building to record the experiment. Pedestrians were asked to wear yellow or red hats to extract their trajectories. The frame rate of the trajectories data corresponds to 25 fps. 3. Results and discussions 3.1 Trajectory To obtain the trajectory of the pedestrian's head, the software PeTrack is used based on its high precise tracking [43]. Due to the bipedal movement of pedestrian, the trajectory of the head shows a periodic swing with steps. As mentioned in [44], a time series method considering the step frequency was used to smooth the trajectory of pedestrian. It is reported that the step frequency of pedestrians is 2 Hz [13]. That is to say, the time interval of stepping for the same leg is 1 second. As a result, 1 second is used as time window to smooth the trajectory in this study (the average of the x and y coordinates of the pedestrian in 1 s) based on the equation (2). In this way, the periodic swing of head can be eliminated. The instantaneous velocity is calculated by equation (3). The trajectory of pedestrians in different 4

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experiments are shown in Fig. 2. The color of trajectory is used to demonstrate the instantaneous velocity of each pedestrian during whole experiment. The smooth equation of trajectories is defined as: , where

and

are original coordinates,

and

are the mean value of 25 fps original

coordinates. The frame rate of the trajectories data corresponds to 25 fps. “i + 12” means 12 fps after i. “i - 12” means 12 fps before i. The instantaneous velocity

is defined as:

160 161 162 163

(2)

(3) where

and

are the x and y coordinates of pedestrian i at time t and

this paper.

164

165

5

is used in

166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189

Fig. 2 Trajectory of pedestrians in different experiments (The small black arrow represents the direction of each pedestrian in the original position. The black dot-dashed line is the central area. The central area is a circle with the radius of 3 m in the central of the scenario, in which congestion appeared and the trajectories of pedestrians crossed seriously) As shown in Fig. 2, the trajectories become complicated as the pedestrian number increases. The trajectories outside the central area are smooth, and the trajectories in the central area are messy. It means that congestion and stop phenomena happened in high-density conditions and central area, where the dark blue trajectories represent pedestrians whose velocity is equal to 0 m/s. Some pedestrians detoured to keep away from the high-density area and to avoid conflicts with other pedestrians. As the experiment progressed, pedestrians reached the central area gradually. Due to the gathering of pedestrians from multiple directions, the density of the central area increased resulting in congestion. Pedestrians had to reduce their velocities to avoid the collisions with pedestrians. From Fig. 2, it can be seen that the area of the central dark blue region increases as the number of pedestrian increases, which indicates the increase of the congestion area (0, 0, 3.99, 7.8, 6.24 and 10.6 m 2 for the six experiments respectively). The congestion area here is defined as the area occupied by stop pedestrians whose velocities are lower than 0.1 m/s [6]. 3.2 Typical pedestrian behaviors Fig. 3 shows some typical pedestrian behaviors observed in the experiment. The blue and black dots represent the pedestrians with typical behaviors and the red dots represent other pedestrians. The direction of the arrow represents pedestrian movement direction, and the length of the arrow is related to pedestrian velocity. These typical phenomena are beneficial for understanding pedestrian behaviors and strategies under multidirectional flows and the building pedestrian simulation models.

6

190 191

192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217

(a)

(b)

(d)

(c)

(e) Fig. 3 Typical pedestrian behaviors

3.2.1 Lane formation Pedestrians with the same moving direction form a lane automatically to reduce the conflicts with other pedestrians in different directions and maintain a faster velocity. In the experiment, lane formation appeared in central high-density area due to the tacit understanding between pedestrians. As shown in Fig. 3 (a), black arrows represent pedestrians who move from the bottom left to the top right. Blue arrows represent pedestrians who move from the top right to the bottom left. Pedestrians in the lane can maintain a relative higher speed and cross central area continuously. In bidirectional flows, the movement direction of pedestrians in the same lane is the same. However, in multidirectional flows, the direction of pedestrians in the same lane can be different. Pedestrians with similar directions changed their original direction temporarily and walked in the same lane. They separated with each other according to their initial directions after getting through the crowd area. The formation of lanes is beneficial to the movement of the whole experiment. In emergency conditions, pedestrians with different directions move in different areas can create different lanes which can improve movement efficiency. In bidirectional flows, lane formation can increase the movement efficiency and reduce of the collision between pedestrians. In multidirectional flows, lane formation is beneficial for pedestrians in the central area to get through the crowd area quickly. It is shown that the lane formation is conducive to reducing the conflicts with different direction pedestrians and keeping moving in high density, which agrees well with the previous studies [45, 46]. 3.2.2 Detour behavior Pedestrians select the shortest path to their destinations in most cases [47]. However, detour can reduce the frequency of deceleration, stopping and avoidance maneuvers considerably and improve the average efficiency under congestion condition [46]. By changing the moving directions and not always 7

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moving towards the destinations, the length of walk path is longer than the straight distance to the destination. Fig. 3 (b) shows the trajectory of one detour pedestrian in experiment. The blue line is the movement trajectory of the detour pedestrian during the experiment. The black arrows is moving directions of the detour pedestrian in different positions. It can be seen that the detour pedestrian can reach destination smoothly. In the experiment, 2% - 15% pedestrians moved at the boundary of the crowd and kept away from the congested area, the detour direction is based on the length of the detour path and the density of both sides. In unidirectional flow, the detour behavior is caused by speed difference. In bidirectional flows, the detour behavior is caused by speed difference or directional difference (the opposite direction). In multidirectional flows, the detour behavior is similar to that of bidirectional flows, but the number of different moving directions (the opposite direction, the vertical direction, and etc.) is more than that of bidirectional flows. 3.2.3 Follow behavior Following others’ ideas and behaviors are traits of personality and to avoid conflict with others [48, 49]. Fig. 3 (c) shows a follow behavior in our experiment. The lines represent the trajectories of first one and the followers in the past. When congestion occurred in central area, the blue dot made a detour to avoid conflicts firstly. During the detour process, the black dots followed the blue one to change their moving directions to make a detour too. The detour flow outside the central area occurred. Follow behavior can also produce lane formation in the central area, pedestrians continuously followed the former to get through the central area. The follow behavior in multidirectional flows is the same as unidirectional flow and bidirectional flows, which may lead to lane formation and avoid collisions. Follow behavior can reduce the decision time and produce lane formation to improve efficiency. 3.2.4 Waiting behavior The effort-saving and effective way to avoid collisions is waiting behavior in movement. As shown in Fig. 3 (d), the red dots represent the pedestrians in moving lane, they kept a relative fast speed to cross the central area. The moving directions of the blue dots are perpendicularity to that of red dots. The blue dots reduced their speed and even stopped to avoid collisions with the red dots. The waiting behavior prevents the overcrowding phenomena and collisions between pedestrians. Waiting behavior often occurs in multidirectional flows. When there are others with different direction ahead the 。

pedestrians (when the angle of different directions is larger than 30 ，the waiting behavior occurred in our experiment), pedestrians may stop to avoid collision with the ahead pedestrian. Waiting behavior in unidirectional flow or bidirectional flows appeared in the congestion. 3.2.5 Acceleration behavior Acceleration is a non-least effort to avoid collisions in the experiment. Very few pedestrian increased speed get through the central area before others. As shown in Fig. 3 (e), the blue dots represent the current and the past positions of the acceleration pedestrian. It indicates that the speed of the acceleration pedestrian can reach two to three times as much as that of other pedestrians. Acceleration behavior exists in unidirectional flow and multidirectional flows. Few pedestrian takes acceleration strategy to get through the experiment scenario quickly. When others in the experiment scenario, the acceleration behavior would be hindered. Acceleration behavior is a learned behavior in our experiment. At the beginning of the experiment, pedestrians walked at normal speed in low density. With the increases of density, someone made an acceleration and others found it can reduce movement time. In high density, many pedestrians attempted to make an acceleration to reach their destinations. There are 8

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two types of acceleration behavior: successful pedestrian with acceleration and failed pedestrian with acceleration. In our experiment, only one pedestrian reach his destination with acceleration successfully, and his movement time is 5.68 s which is 2.3 times faster than the average movement time in the same experiment (that is, the speed of the acceleration pedestrian is 2.3 times higher than average speed). To decrease the wait time and obey the experiment instruction, many pedestrians adopted the acceleration behavior to walk faster under high density conditions. However, when many acceleration pedestrians ran into the central area, they had to decrease the speed to avoidance collisions between others. And they failed to reach their destinations by acceleration behavior. 3.2.6 Other behaviors Some other behaviors were observed in our experiment due to high density and multi-direction in central area. Unlike particle system, pedestrians in our experiment weren’t locked in the central area. Pushing behavior was observed. Some aggressiveness participants pushed others to break the congestion and opened up a lane to get through the congestion area. Some passiveness participants rotated their shoulders to compress their personal space and gave way to the aggressiveness participants. These behaviors can be found in high density or emergency conditions. These behaviors may lead to trample accident and should be investigated deeply in the future. 3.3 Length of walk path Since the destination of each pedestrian was not clearly defined in the experiment, the displacement of each pedestrian was different. Table 2 shows the displacement of different experiments. It can be seen that the difference of displacements can be neglect caused by undefined destinations. Besides, to avoid the effect of undefined destinations, normalized processing method was used to analyse pedestrian displacement. The length of walk path is divided by the displacement to characterize the length of specific walk path. Formula (4) is used to calculate the walk path of pedestrians and formula (5) is used to calculate the displacement of pedestrians. To eliminate the impact of obvious individual difference, the trajectories data of 80% of pedestrian who have accomplished the experiment first are used for analysis. The reason for ignoring the bottom 20% of trajectories is that the pedestrians who have completed the experiment have influence on the pedestrian who haven’t completed the experiment at the destination especially under high densities, which caused the abnormal increasing of trajectories in the destination. In addition, due to the individual difference and half-heartedness attitude of the experiment some pedestrians wandered around in the scenario causing the abnormal increase of the trajectories. Table 2 Displacement of different experiments Run index Displacement (m) (M(SD))

294 295 296 297

1

2

3

4

5

6

9.82(0.09)

9.86(0.21)

9.87(0.16)

9.88(0.19)

9.79(0.22)

9.85(0.23)

, where

and

are the start and end time of pedestrian,

pedestrian at time i,

and

and

(4)

are the x and y coordinates of

are the coordinates of pedestrian at time i+1. “i + 1” means 1 fps 9

298 299 300 301 302 303 304 305 306 307 308 309

after time i. , where

and

are the coordinates of pedestrian at the destination,

(5)

and

are the coordinates

of pedestrian at origin. In Fig. 4, the specific walk path increases as the number of the pedestrian increases. The fitting line of pedestrian number and the specific walk path is:

.

The increase of pedestrian number leads to longer walk path for unit displacement. The congestion caused by high density resulting in more stopping and detour phenomena, leading to an increase in the walk path. Besides, high density affects pedestrians not only by reducing their speed, but also by increasing their length of the walk path, which leads to the consumption of longer time in high density. That is, the walking utility of pedestrian decreases with the increase of environment density.

Length of walk path / Displacement

1.2

y = 0.995 + 0.001x R2 = 0.95

1.1

1.0

0.9 10

20

30

40

50

60

70

80

Pedestrian number

310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325

Fig. 4 Length of walk path/Displacement in different experiments To analyze the pedestrian movement state in detail, the length of walk path with time is shown in Fig. 5. Formula (6) is used to calculate the initial displacement of each pedestrian. In Fig. 5 the blue lines represent that the pedestrian stopped and their velocities are smaller than 0.1 m/s, and the black lines represent that the normal speed of pedestrians and their velocities are between 0.1 and 1.5m/s, and red lines represent that the rapid speed of pedestrian and their velocities are larger than 1.5 m/s. Since the experimental scene is a circle, the start point of each pedestrian is different. An initial position according to their number is used to observe the change of the walk path at the same time (the real time displacement). The initial displacement is calculated by equation (6): ,

(6)

where N is the total number of pedestrians in each experiment (13, 24, 36, 48, 60, 72), and P is the serial number of each pedestrian. The real time displacement is calculated by equation (7): (7) where

and

are the x and y coordinates of pedestrian at time i,

coordinates of pedestrian at time i+1. “i + 1” means 1 fps after time i.

10

and

are the

326

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Fig. 5 Real time displacement in different experiments From Fig. 5 we can know that the movement time of the pedestrian increases with the number of pedestrian. Moreover, the difference (the difference between maximum and minimum movement time of the six experiments are 4.6, 5.48, 11.92, 16.92, 16.48, 16.68 s, respectively) in movement time increases as the pedestrian number increases. It shows that under different strategies movement time varies greatly. The frequency of overtake behavior in walk path increases in the experiment with high density. The rapid movement appeared in the beginning of the experiment and the end of the experiment. At this time, there was adequate space in front of pedestrians allowing the rapid movement. Stop phenomena appeared in the experiment with high density. The stop time also increases with the pedestrian number. It can also be seen that the stop phenomena appeared almost at the same point and longer stop time appeared under high density. Fig. 6 shows the time and ratio of stop and rapid pedestrian in different experiments. Pedestrians with the speed below 0.1 m/s are regarded as stopped. The stop time is the duration of the stop. The speed above 1.5 m/s are regarded as rapid speed. And the rapid time is the duration of the rapid speed. The value of stop time and rapid time is the sum of that of each pedestrian in the same experiment. And the ratio of stop and rapid is the proportion of the number of stop and rapid pedestrians to the total number of participants in each experiment.

11

Ratio

1.0

Stop Rapid

0.5

0.0

Time (s)

3 0

10

20

30

40

50

60

70

80

Stop Rapid

2

1

0 0

345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376

10

20

30

40

50

60

70

80

Pedestrian number

Fig. 6 Time and ratio of stop and rapid pedestrian in different experiments It can be seen from Fig. 6 that the proportion of stop increases with pedestrian number (except for experiment 5), and the stop time increases with the pedestrian number. This is because that as the number of pedestrian increases, density in central area increases resulting in the congestion. The congestion leads to the increase of stop ratio and time. The rapid pedestrian ratio decreases with pedestrian number increasing and the rapid time of each experiment is almost the same. This is because that as the number of people increases, the space occupied by each pedestrian is reduced, and only a small part of pedestrians can maintain rapid movement, resulting in a decrease in proportion. The location of rapid movement is relatively fixed: at the beginning of experiment and the ending of experiment. So the rapid time changed little. The reason of the lower stop ratio and smaller stop time of experiment 5 is that more pedestrian choose detour to reach their destination, which will be explained in 3.4. 3.4 Strategies Usually, pedestrians choose the shortest path (least effort) to reach their destinations and reduce unnecessary detour. But sometimes pedestrians take a detour strategy to reach their destinations to avoid conflicts with other pedestrians. Three strategies were classified in the experiment: Strategy A: pedestrians moved in straight ways, Strategy B: pedestrians took a detour to their destinations directly, Strategy C: pedestrians selected straight strategy to reach their destination at first, and with congestion occurred the waiting time increased, some pedestrians changed their directions and made a detour to reach their destinations. Deviation distance is introduced to represent the degree of detour. The deviation distance is the maximum distance from the pedestrian trajectory to the line of the starting point and the ending point. Combined with experimental video, the deviation distance longer than 1 m is defined as detour. The detour pedestrians are manually verified and the incorrect data are removed. The detour point is the point where the angle between pedestrian movement direction and pedestrian destination direction is larger than 45°and pedestrian keep moving at the same time (To prevent the error caused by pedestrian stopping behavior). In the experiment, the deviation distance smaller than 1 m is defined as strategy A, the deviation distance longer than 1 m and the detour point before congestion is defined as strategy B (no stopping behavior in the movement), the deviation distance longer than 1 m and the detour point after congestion is defined as strategy C (stopping behavior appeared in the movement). To observe the 12

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evolution of trajectory in different strategies, the trajectory of pedestrian is rotated by equation (7). The purpose of rotation trajectories is to observe the trajectories under different strategies at the same originate, such as the large deviation distance of the detour pedestrian, the trajectory of the straight pedestrian is near the center, etc. Fig. 7 shows the trajectory of the pedestrians after rotation. It can be seen that different strategies were adopted at different locations and the change of speed and trajectory in the whole experiment. The original trajectory was rotated around the center of the circle. The initial position of original trajectory is rotated to the left of the circle and the destination position of the original trajectory is rotated to the right of the circle. The rotated trajectory is calculated by equation (7): , where

and

are the rotated coordinate of pedestrian at time t,

coordinates of pedestrian at time t,

and

and

(7)

are the original

are the coordinates of centre of the circle,

is the

anticlockwise angle between the rotated starting point (the left of the circle), the current original point and the centre of the circle.

392

393 394 395 396 397 398 399 400 401 402

Fig. 7 Rotated trajectory of pedestrians Due to that the specific end point of each pedestrian is not appointed, the rotated end points of the pedestrians are different. Some difference of strategies can be found. For strategy A, trajectories are close to central line and longer blue trajectory (lower walking speed) can be found. For strategy B, relatively higher speed can be found, no stopping behavior appeared and the deviation distance to the center is larger. For strategy C, pedestrians speed is close to 0 m/s in central area, then pedestrians detour out of the congestion and their speed increase. It can be found that the deviation distance 13

403 404 405 406 407

increases with pedestrian number. It can be seen that most of detour points are at the central area. Few detour points are at the beginning of the experiment. Table 3 is the ratio of different strategies in different experiments. Table 3 Strategy ratio of different experiments Experiment index

408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434

Least effort

Non-least effort

Straight (A)

Detour (B)

Straight-Detour (C)

Total

1

92%

8%

0

8%

2

87%

13%

0

13%

3

72%

14%

14%

28%

4

90%

2%

8%

10%

5

73%

15%

12%

27%

6

75%

8%

17%

25%

As can be seen from table 3, most pedestrians choose strategy A. Even though there are many conflicts, they are not willing to lengthen their walk path, and they choose to reduce their speed to avoid conflicts. In the experiment, more than 85% (strategy A and strategy C) of pedestrians choose straight way to their destinations at first. The congestion area which can be seen in Fig. 2 increases with pedestrian number resulting in the increase of waiting time. 8% - 17% pedestrians change their initial strategy (straight strategy) to make a detour to reach their destinations. But more than 72% of pedestrians insist on their original strategy (A), even if this ratio gradually decreases with the pedestrian number increases. In the experiment, 2% - 15% pedestrians choose the non-least effort strategy (B) to avoid the conflicts with others at first. In experiment 4, the reason of the higher percentage of strategy A is that a stable lane formation appeared in central area which enables pedestrians to pass the central area directly and quickly, so fewer pedestrians selected strategy B and changed their initial strategy (strategy C). The movement time and walk path under different strategies are calculated to represent the characteristics of different strategies. The movement time can represent the average pedestrian speed in experiment. The Length of walk path / Displacement can represent the energy consumption of pedestrian at a certain extent. Seneviratne found pedestrians select the shortest distance in movement, since walking requires physical effort [50]. Fig. 8 (a) shows the average movement time of pedestrians of three strategies in different experiments. The movement time shows an upward trend with the increase of pedestrian number. In each experiment, the movement time of strategy C is the shortest. The movement time of strategy B is the longest. Under strategy C, pedestrians are away from high-density areas, and the speed of pedestrians is less affected by other pedestrians. Pedestrians can maintain relative higher speed to reach their destinations. The reason why the movement time of strategy B is longer is the longer walk path and longer detour decision time in strategy B. It can be found that detour strategy is an efficiency way to reduce the movement time especially in high density. The decision time can significantly influence pedestrian movement time.

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Fig. 9 Grade of three strategies under (a) 80% (b) 50% (c) 20% movement time weight Under 80% and 50% movement time weights, the grade of strategy C is the highest. However, under 80% length of walk path weight, the grade of strategy A is larger than strategy C in high density. The grade of strategy B is the lowest all the time. To reach the destination quickly, detour strategy is the most effective strategy. As the length of walk path weight increases, detour strategy is no longer the most effective way to reach destination. The length of walk path of strategy C is far longer than that of strategy A in high density. When the dominant factor is length of walk path, smaller length of walk path is crucial. What’s more, longer walk path and longer detour decision time of strategy B leads to the lowest grade of strategy B. Movement time, length of walk path and detour decision time are the key factors which influence the grade in our experiment. Utilizing detour strategy reasonably and reducing decision time are good for improving evacuation efficiency. It is vital to make different evacuation plans or guide strategies according to different concerns. 4 Summary and discussion Multidirectional flows experiments under different densities were carried out to study pedestrian behaviors and strategies in movement. A circle experiment scene was used to create the multidirectional flows and ensure the same environment of each pedestrian. The trajectory and typical pedestrian phenomena are discussed. The length of walk path and different strategies are analyzed. The trajectories crossed seriously and low speed appeared in the central area which indicated that congestion and stopping behavior appeared in this area. Some typical pedestrian behaviors such as lane formation, detour behavior, follow behavior, waiting behavior, acceleration behavior, pushing behavior and rotating shoulder behavior were observed in our experiment. The Length of walk path / Displacement is proportional to pedestrian number. The walking utility of pedestrian decreases with the increase of environment density. Stop phenomena appeared in high density, and the stop time increases with the pedestrian number. Trajectories of pedestrian are rotated to investigate the evolution of pedestrian speed and strategies in the whole experiment. Three strategies are investigated in this study. More than 85% pedestrians selected the least effort strategy at first. More than 72% pedestrians insisted the least effort strategy during the whole experiment (Strategy A). As waiting time increases, 8% - 17% pedestrians who selected least effort strategy at first changed their moving directions to make a detour to their destinations (Strategy B). 2% - 15% pedestrians chose the non-least effort at first (Strategy C). Strategies are graded with different dominant influence factors. In most cases, detour strategy is the most efficiency strategy to reach destination quickly. When focusing on length of walk path, detour strategy is no longer the most efficiency strategy due to the far longer walk path compared to that of strategy A under high density. Movement time, length of walk path and detour decision time are the key factors which influence the grade in our experiment. The findings can provide a deeper understanding of pedestrian behaviors and their strategies in multidirectional flows. These characteristics can be used to provide basics for simulation rules and parameters of multidirectional flow. Utilizing detour strategy reasonably is good for improving evacuation efficiency. It is necessary to make evacuation plans and pedestrian guide strategies according to density and concerns. The experiment setting such as gender of participant, the accuracy destination, experiment instruction and some learned behaviors may have influence experiment results. 16

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In our experiment, the participants were asked to reach their destinations quickly, which may lead to the acceleration of pedestrians. If they were asked to walk at normal speed, the acceleration behavior may not appear. In the future, we will take more considerations into account to carry out accurate experiment. The mechanism of avoidance and the influence of pedestrian component will be investigated in the future. Acknowledgements The authors acknowledge the foundation support from the National Natural Science Foundation of China [Grant No. 71704168], from Anhui Provincial Natural Science Foundation [Grant No. 1808085MG217] and the Fundamental Research Funds for the Central Universities [Grant No. WK2320000040]. References

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