A comparative study of funnel shape bottlenecks in subway stations

Transportation Research Part A 98 (2017) 14–27

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Transportation Research Part A journal homepage: www.elsevier.com/locate/tra

A comparative study of funnel shape bottlenecks in subway stations Lishan Sun a, Wei Luo a, Liya Yao b, Shi Qiu a,⇑, Jian Rong a a b

Beijing Key Laboratory of Traffic Engineering, Beijing University of Technology, Beijing 100124, China School of Mechanical and Vehicular Engineering, Beijing Institute of Technology, Beijing 100081, China

a r t i c l e

i n f o

Article history: Received 8 December 2015 Received in revised form 21 December 2016 Accepted 23 January 2017

Keywords: Subway bottleneck Funnel shape Pedestrian flow Pedestrian characteristic

a b s t r a c t A bottleneck typically denotes a narrowed area that reduces the flow through a channel. Congestion is expected to form at bottlenecks such as escalator and staircase entrances with high rate of passenger flow, which could decrease walking efficiency and passenger comfort. Currently, no special treatment is adopted in most of the conventional bottlenecks in subway stations. This study conducts a series of pedestrian experiments to investigate the effectiveness of adding a funnel shape buffer zone in front of the bottleneck entrance. Different angles of funnel bottleneck are experimented under different pedestrian volumes. By analyzing factors including walking speed, individual passing time, total passing time, and time gap, it is found that funnel shape would overall improve the traffic effectiveness of the bottlenecks, especially when the flow rate is high. The recommendation of setting funnel angle depends on passenger flow level, the optimal of which should be between 46° and 65°. This study provides a rationale for agencies to improve the current pedestrian traffic efficiency at bottlenecks. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction With the acceleration of urbanization and the expansion of subway network, the average daily passenger traffic of Beijing subway has exceeded 11 million since 2014 (Beijing Municipal Commission of Transport, 2015). Crowding, a common phenomenon in subway, which is usually defined by the low level of average space per person (i.e., less than 0.93 m2/ped), has attracted substantial researchers’ attentions in recent years (Lam et al., 1999; Cox et al., 2006). Crowding can influence people’ path choice (Kim et al., 2015), generate stress and feelings of exhaustion (Mahudin et al., 2012), and even lead to crushing incidents (Still, 2000, 2014). In addition, crowding could increase pedestrians’ swings, and often form congestion at the bottleneck. Overcrowding and crushing incidents have occurred around the world occasionally (Still, 2000). In the subway stations, congestion is frequently formed at bottlenecks such as escalator and staircase entrances when the passenger flow is high, which could decrease walking efficiency and passenger comfort, as shown in Fig. 1. Combined with other factors, the congestion formed at the bottleneck could be hazardous to passengers. Therefore, how to make the passengers walk through bottleneck in a fast and efficient manner has become an emergent task for subway operational management, particularly for the subway stations with constantly high volumes at peaks. Improving bottleneck condition is a challenge to researchers and subway managers. Many studies on pedestrian bottleneck have been conducted in the past two decades. Through computer simulations, Helbing and Molnar (1998) found that ⇑ Corresponding author. E-mail address: [email protected] (S. Qiu). http://dx.doi.org/10.1016/j.tra.2017.01.021 0965-8564/Ó 2017 Elsevier Ltd. All rights reserved.

L. Sun et al. / Transportation Research Part A 98 (2017) 14–27

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Fig. 1. Pedestrian flow at Bottleneck in Beijing Subway.

self-organization effects can be utilized for an optimization of pedestrian flows. Then, Bolay (1998) pointed that the flow at bottlenecks could be improved by a funnel-shaped construction based on simulations. Helbing et al. (2000) also studied the pedestrian flow at bottlenecks under the panic. Helbing et al. (2001) pointed four simple instances on how to partially improve standard elements of pedestrian facilities without data verification, including that the flow at bottlenecks could be improved by expanding a funnel-shaped space in the bottleneck construction. Pedestrian experiments were used by Daamen and Hoogendoorn (2003a, 2003b) to study the characteristics of pedestrian flow passing a bottleneck. They considered four experimental variables, which are free speed, walking direction, density, and the effect of bottlenecks. Hoogendoorn and Daamen (2005) also used pedestrian experiment to identify the zipper effect, which described the overlapping phenomenon of layers at bottleneck. Based on the zipper effect, it was identified that the capacity of the bottleneck was increased in a stepwise fashion with the increasing width of the bottleneck which was less than 3 m wide. Kretz et al. (2006) conducted pedestrian experiments to find that there was difference between narrow (one person at a time) and wide bottlenecks (two persons at a time) in the distribution of time gaps. By considering the effect of a psychological phenomenon, Kretz et al. (2008) also identified the relationship between flow and bottleneck width. Seyfried et al. (2009a, 2009b) compared the findings of bottleneck pedestrian experiments from different researchers. They believed that the congestion would occur even if the incoming flow is less than the capacity. Daamen and Hoogendoorn (2010) found factors such as width of the bottleneck and population could affect the capacity of evacuation door. Guo (2014) proposed a revised social force model to simulate the pedestrian counter flow through a bottleneck. This model could reproduce these self-organizing movement patterns of pedestrians, such as oscillatory flow and three classes of lane formations. Based on pedestrian experiments, Seriani et al. (2016) studied the types of queues, formation of lanes, density by layer, and distance between passengers about the platform edge doors. Liao et al. (2016) proposed a modified version of the cumulative sum control chart algorithm, which could robustly detect steady states from density and speed time series of bottleneck experiments. From above literature review it can be seen that bottleneck width has been highlighted in previous studies. Some recognized that a funnel shape bottleneck may help ease the congestion; however, only theoretical analyses were carried out without field validation (Bolay, 1998; Helbing et al., 2001). In addition, the optimal funnel angle for subway stations is rarely explored. In this study, controlled pedestrian experiments were conducted to investigate the impact of funnel shape bottleneck on pedestrian behaviors. It is very meaningful to develop theoretical basis and practical reference for subway station designers and managers through this research. This paper is organized as follows: the first section introduces background and current research about pedestrian flows at bottleneck. Section 2 analyzes real-world pedestrian characteristic at bottleneck from a video footage taken at Beijing subway stations. Section 3 describes the controlled pedestrian experiment in detail. Section 4 lists all the analytical results of pedestrian flow characteristics at different angles of funnel shape bottlenecks. Finally, Section 5 concludes this study and proposes future research recommendations.

2. Analysis of pedestrian charateristic at bottleneck A field survey is first conducted on pedestrian walking characteristic at bottleneck in a weekday morning rush hour (7:00–8:00 am). To analyze the pedestrian behavior in an automated fashion, a digital camera was attached in the ceiling. SIMI Motion, which is a commercial software application using novel algorithms to process video footage, is used for motion capture in this study. Video footage at a unidirectional flow bottleneck in Guomao subway station was extracted and analyzed. Fig. 2 shows the gradient of instant speed at the bottleneck. First, it is observed that the pedestrian speed is decreased when approaching the influx and a slight bouncing back occurs after entering the bottleneck. Pedestrians who are far away

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Speed (m/s) Z (speed (m/s) )

Y (m)

X (m) Fig. 2. Speed distribution at a Bottleneck in Beijing Subway. Pedestrians walk from Left (x = 0 m) to Right (x = 10 m).

Table 1 Descriptive statistics of speed. Observation region

Mean (m/s)

Medium (m/s)

Max (m/s)

Min (m/s)

Standard deviation (m/s)

Before the Bottleneck (0 m < x < 6 m) Bottleneck Corridor (6 m < x < 10 m)

0.63 0.84

0.37 0.18

1.59 1.47

0.58 0.88

0.30 0.09

from the bottleneck possess a relatively higher speed. In addition, pedestrian speed varies greatly before entering the bottleneck. After entering the bottleneck, the speed change is less than before. Quantitative analysis is made in Table 1. The pedestrian average speed in the bottleneck is about 33% faster that approaching the bottleneck, which can be partially explained by psychological effects (Gérinlajoie et al., 2005; Fujiyama, 2005; Curtis and Manocha, 2012). Meanwhile, the swaying amplitude and the walking speed turned out to be negatively correlated between each other in the normal situation (Hoogendoorn and Daamen, 2005). To illustrate the individual pedestrian characteristics at the formation stage of congestion at bottleneck, walking trajectory for the first passengers entering the video-taped area is shown in Fig. 3. Pedestrians usually sway when walking. Hence, each individual passenger requires space not merely in the longitudinal direction but also in the lateral direction. As shown in Fig. 3, overall, the pedestrian walking trajectory exhibits a ‘‘Z” shape pattern at approaching and departing the bottleneck (See the highlighted illustration in Fig. 3d). With the decreased space availability, pedestrian speed slows down and congestion is observed. At the same time, the increment of pedestrians’ swing is greater, meaning fluctuation of the individual moving path is increased, which requires more lateral space. This also concurs with the finding of other researchers (Daamen and Hoogendoorn, 2003a,b; Hoogendoorn and Daamen, 2005). It is possible to reduce the transverse interference and increase walking efficiency by using a funnel shape bottleneck design (Bolay, 1998; Helbing et al., 2001). This paper investigates the impact of different funnel shapes on pedestrians. Furthermore, the efficiency of the funnel with different angles is analyzed. 3. Setup of pedestrian experiment It is preferred to collect field data to analyze the pedestrian traffic at bottlenecks in the subway. However, it is considerably difficult to directly take and analyze the field data video given the complex environment such as uncontrollable traffic volume, uncontrollable funnel shape and low ceilings at the subway station. The controlled pedestrian experiment has appeared in many pedestrian studies (Helbing et al., 2001; Daamen and Hoogendoorn, 2003a, 2003b; Hoogendoorn et al., 2003b; Daamen and Hoogendoorn, 2003a,b; Hoogendoorn and Daamen, 2005; Kretz et al., 2006, 2008; Seyfried et al., 2009a,b; Guo, 2014; Fernández et al., 2015). Controlled pedestrian experiment has some drawbacks, for example, circumstance is not exactly the same as real scenario, which may have impact on pedestrian movement. Or pedestrians have specific trip purposes in actual subway station whereas not in the pedestrian experiments. However, it possesses more merits: (1) Controllable circumstances; (2) Strong purpose-oriented; (3) Need-based flexible experiment setup. Therefore, controlled pedestrian experiments are conducted to analyze the funnel shape bottleneck in subway. 3.1. Fundamentals of the experiment The pedestrian experiment was conducted in Beijing University of Technology on April, 17, 2015, a sunny day with little wind. As shown in Fig. 4, the experiment was carried out at the field in front of the teaching building. The space is adequate

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(a) Pedestrians 1-10

(b) Pedestrians 11-20

(c) Pedestrians 21-30

(d) Pedestrians 31-40

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Fig. 3. Trajectories of Pedestrians at a Bottleneck.

for conducting the experiment and provides wide vision for placing the camera. The experimental site is flat without any grade. Comparing to the calm wind, stable light and comfortable temperature in Beijing subway stations (BMCUP, 2013), the ambient conditions are favorable (reasonably constant light intensity, few shadows, smooth surface) for the experiment. A pixel camera with a resolution of 1920⁄1080 is set up vertically (20 m above the ground), which is adequate for analyzing the speed and position change of pedestrians (Sun et al., 2014). Through Euclidean transformation and other algorithm, Simi Motion was used to capture motion (Bader, 2011). Besides, the extraction motion data were validated to be accurate by Becker as well as other researchers (Becker and Russ, 2015; Muehling et al., 2015). 3.2. Geometrical layout of the experiment field The design of experimental scene references from Hoogendoorn and Daamen (2005), Seyfried et al. (2009a,b), and Yang et al. (2014). The normal corridor width is set as 5 m, which is the maximum width of one-way channel in Beijing subway station. Moreover, previous studies suggested that the at least 4 m width is needed for bottleneck analysis (Hoogendoorn and Daamen, 2005; Seyfried et al., 2009a,b). The section width at bottleneck is set as 1 m, which conforms to the existing bottleneck width in Beijing subway. The entire corridor is enclosed with an artificial wall with a height of 2 m, which is far higher than participants in the highest height 181 cm. The coordinates and experimental scene are marked in Fig. 5a and b, respectively. The pedestrian walking direction is the direction of X. The experimental scene is divided into two parts: analysis region and preparation region. The analysis region is 6 m ⁄ 5 m (Region 1) and 4 m ⁄ 1 m (Region 2), as shown in Fig. 5d, which represents the experimental data collection and analysis area, respectively. The preparation region is set according to Seyfried et al. (2009a,b) and Yang et al. (2014), which is 5 m ⁄ 2 m, ensuring that participants are random and in natural state for each trial. The distance from preparation region to the entrance of the bottleneck is 6 m, which has adequate longitudinal space to analyze pedestrian movement for the traffic volume and width in this study,

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Fig. 4. An illustration of the experiment field.

(a) Analysis Region

(b) Preparation Region

(c) Setting of Funnel Shape of Bottleneck (d) Setting of Experiments Region for Speed Fig. 5. Settings of the pedestrian experiment field.

meanwhile is longer than 3 m (Seyfried et al., 2009a,b) and 5 m (Hoogendoorn and Daamen, 2005) in previous bottleneck studies. The scheme of funnel angle change is based on advice from subway managers, practical application, and the number of experiments, the angle of funnel shape is 0°, 30°, 45°, 60°, and 90° (90° is a common scenario in Beijing subway station,

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which is essentially equivalent to an extension of the guardrail). The setting of different funnel shape bottlenecks is as shown in Fig. 5c. 3.3. Experiment participants and training The authenticity and availability of the experimental scene are critical to the controlled pedestrian experiment. Therefore, the experiment pedestrian flow and the actual pedestrian subway flow are compared. A pre-experiment was conducted according to the extracted volume and number of pedestrians from the subway videos. Two sets of data are compared through the one-way analysis of variance (ANOVA), which each including 4902 speed and acceleration data entries, respectively. The significance test reveals that there is no significant effect of the investigation method (the actual pedestrian subway flow and pre-experiment pedestrian flow) on speed (F(2, 4902) = 1.9023, p = 0.15) and acceleration (F(2, 4902) = 0.1169, p = 0.88) (p < 0.05 represents significant difference; p > 0.05 represents no significant difference). This finding demonstrates that the pedestrian experiment could mimic bottleneck scenario in subway station. Formal experiment was conducted after the reliability of pedestrian experiments was validated. The participants of formal experiment consist of 50 healthy undergraduate students, including 27 males and 23 females. To minimize the acquaintance among students, which might influence the results, students were selected from different classes and departments. The age is between 18 to 25 years old and stature between 160 cm to 181 cm. The average age and average stature is 22 years old and 169.38 cm, respectively. The deviation of age and stature is 2.05 cm and 6.82 cm, respectively. Participants are asked to wear colorful hats, in order to detect and tracking of pedestrians better in the post video data processing. Before the experiment, experimental instruction (including rules and purposes and so on) was emphasized for participants to walk according to the actual situation in the subway station and they need to assume themselves walking in subway scenario with some purposes such as going to class, and going to work. Before each trial, all participants were randomly queuing in line. The starting positions of the participants are randomized in front of the yellow start line for each trial. This randomization would also prevent participants to learning behavior during the trials. When experimental instruction given the sign, the participants were starting walking. Therewith, participants become random and natural state for each walk in prepare region. Moreover, experiment participants do not need to stop at the end of the corridor, which ensures a normal flow. 3.4. Experiment scenarios Considering the funnel shape bottleneck influence could vary under different volumes, three levels of the pedestrian volumes are chosen by the following aspects: When the average spatial per person is less than 0.93 m2/ped, it can be seen crowding (Lam et al., 1999). According to Highway Capacity Manual (HCM), when the average spatial per person is less than 0.93 m2/ped, the level of service is E or F. Hence 2940 per/h/m and above capacities are considered. According to the definition in TRB’s Transit Cooperative Research Program (TCRP) Report 100: Transit Capacity and Quality of Service Manual, the standard one direction passageway capacity is 5000 person/h/m (TCRP, 2003). Hence 5000 per/h/m and above capacities are considered. The cumulative 85% percentage of the rush hour volume is 4200 person/h/m at the Guomao subway station. Hence 4200 person/h/m and above capacities are considered. Taking the above three aspects into consideration, three levels of the pedestrian volumes are experimented in this research: 4000 person/h/m, 5000 person/h/m, 6000 person/h/m. In total, 15 scenarios are set up for analysis, as listed in Table 2. Table 2 Experiments scenario setting. Scenario Scenario Scenario Scenario Scenario Scenario Scenario Scenario Scenario Scenario Scenario Scenario Scenario Scenario Scenario Scenario

1a 1b 1c 2a 2b 2c 3a 3b 3c 4a 4b 4c 5a 5b 5c

Angle of funnel

Volume (p/h/m)

/ / / 30° 30° 30° 45° 45° 45° 60° 60° 60° 90° 90° 90°

4000 5000 6000 4000 5000 6000 4000 5000 6000 4000 5000 6000 4000 5000 6000

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Manual controls are imposed to implement the desirable flow. The equivalent volume of 4000, 5000, and 6000 person/h/ m corresponds to 6, 7, and 8 participants entering the preparation region per second, respectively. Hence, the volume is adjusted by controlling the entrance rate. 4. Analysis of experiment results 4.1. Evaluation parameters Microscopic parameters are extracted from the video footages to analyze pedestrian under different shapes funnel bottleneck. The evaluation parameters for traffic efficiency analysis of pedestrian through bottleneck, such as travel speed are defined. The statistics of the evaluation parameters are used to analysis pedestrian characteristics under different funnel shapes of bottlenecks. Due to characteristics such as space limitation, strong purposes, and so on in subway, bottleneck pedestrians often demonstrate velocity jump, path selection diversification on individual characteristics, which can be expressed through individual speed, individual passing time, and trajectory and so on. Individual speed and individual passing time are frequently used to describe the individual characteristics (Steffen and Seyfried, 2010; Ma et al., 2010; Daamen and Hoogendoorn, 2003a). Due to subway’s operating feature, bottleneck pedestrians often demonstrate vulnerable to environmental impact and periodic law with passenger’s arrival and departure, which can be expressed through total passing time, time gap, and density and so on. Total passing time and time gap are frequently used to describe the group characteristics (Tian et al., 2012; Kretz et al., 2006). Therefore in this paper, two sets of parameters (each set containing two parameters) are used to analyze the traffic efficiency of the bottleneck. (1) Individual parameters Speed: it is a basic parameter describing pedestrian flow, which is the walking distance over a unit of time. According to the different characteristics of pedestrian walking in different regions, two regions are divided for analysis, as shown in Fig. 5d. In this study Region 1 is focused. Individual Passing Time: it is defined as the time from a pedestrian entering the analysis region to the departing of the analysis region. (2) Group parameters Total Passing Time: it is defined as the time from the first pedestrian entering the analysis region to the last pedestrian departing of the analysis region. Time Gap: In this study, the time interval between the two consecutive pedestrians passing through Section W 2 is defined as time gap. It is the headway in pedestrian study. 4.2. Individual parameters 4.2.1. Speed In Fig. 6, x and y represent the coordinate of the speed, and different color represent different speeds. In Region 1, as shown in Fig. 6a, a box is used to describe the extent of low speed (low speed is defined as less than 0.5 m/s), which is represented by red1 color. And the percentage of low speed in Region 1 is demonstrated in Table 3. The extent of the low speed is reduced with the increase of the angle under 4000 p/m/h. At 45° funnel, the extent of the low speed is the smallest, accounting 48.73% of Region 1, and the extent of the low speed is enlarged with the increase of the angle. It is shown from Fig. 6b that under 5000 p/m/h, with the increase of the angle, the extent of pedestrians at low speed has been reduced. As shown in Fig. 6c, under 6000 p/m/h, the extent of the low speed is reduced with the increase of the angle. However, in the case of 90° funnel, the extent of the low speed is smaller than others, which could be related to the fact that the 90° funnel is extending the bottleneck length, while the speed in bottleneck is generally higher than before bottleneck. By examining the series maps shown in Fig. 6, there are little speed fluctuations in the Region 2 with the different angles of the funnel is arranged. The speed is concentrated in 0.9 m/s. Moreover, no matter which kind of funnel is set up, the mean of speed in Region 2 is generally higher than that in Region 1. In order to further quantitatively analyze the pedestrian speed in Region 1, the descriptive statistics of pedestrians speed is summarized in Table 4. The mean speed of the pedestrian in the experimental Region 1 is about 0.6 m/s. With the difference of funnel angle, the mean speed shows some fluctuations. With the increase of the funnel angle, the mean speed is increased at first and then decreased under 5000 p/m/h and 6000 p/m/h. The mean speed of 45° funnel is the maximum (3.91%, 3.59% higher than no-funnel scenario under 5000 p/m/h and 6000 p/m/h, respectively) (see Fig. 7). However, this is different from the mean speed under 4000 p/m/h. With the increase of the funnel angle, the mean speed is increased at first, then decreased and increased at last under 4000 p/m/h. This implies that the improvement of traffic efficiency depend on the volume when the funnel is 90°. With the increase of the funnel angle, the standard deviation of speed is increased at 1

For interpretation of color in Fig. 6, the reader is referred to the web version of this article.

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Fig. 6. Pedestrian trajectories and speed under different volumes.

Table 3 The percentage of low speed (less than 0.5 m/s) in Region 1. Volume (p/h/m)

Funnel angle (°)

4000 5000 6000

0

30

45

60

90

56.02% 56.74% 57.47%

49.94% 56.45% 56.68%

48.73% 50.33% 56.47%

55.52% 51.29% 54.58%

44.81% 47.24% 49.04%

Table 4 Descriptive statistics of speed under different volumes in Region 1. Volume (p/h/m)

Funnel angle (°)

Mean (m/s)

Medium (m/s)

Max (m/s)

Min (m/s)

Standard deviation (m/s)

4000

None 30 45 60 90

0.60 0.60 0.62 0.60 0.62

0.66 0.50 0.51 0.46 0.54

1.63 1.85 1.85 1.99 2.21

0.00 0.01 0.04 0.02 0.02

0.33 0.35 0.38 0.37 0.35

5000

None 30 45 60 90

0.60 0.61 0.62 0.60 0.59

0.45 0.42 0.50 0.49 0.52

1.68 1.95 1.89 1.91 2.67

0.09 0.01 0.00 0.01 0.02

0.35 0.36 0.36 0.35 0.36

6000

None 30 45 60 90

0.58 0.59 0.60 0.60 0.56

0.46 0.45 0.45 0.47 0.51

1.90 1.81 1.87 2.49 2.24

0.03 0.03 0.03 0.02 0.02

0.35 0.37 0.39 0.40 0.32

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Fig. 7. The increase rate of speed under different funnel angles in Region 1.

first and then decreased. And the standard deviation of speed of 45° funnel is the maximum (12.6%, 2.3% and 13.5% higher than no-funnel scenario under 4000 p/m/h, 5000 p/m/h and 6000 p/m/h, respectively). Overall, the above analysis demonstrates that funnel design could improve walking speed. And 45° funnel design seems more obvious. 4.2.2. Individual passing time Fig. 8 and Table 5 show the relation between funnel angle and individual passing time. Quadratic fitting is conducted to observe the trend. For individual passing time, adjusted R2 of over 0.9 are achieved except the volume of 6000 p/m/h. It clearly shows that regardless of what kind of passenger traffic, with the increase of funnel angle, individual passing time presents decreased first and then increased trend. However, the trend is not obvious in a small pedestrian flow. The individual passing time reaches the lowest at 45° or 60° funnel. For the fitted situation, the optimal individual passing times are 57°, 45°, and 49° under 4000 p/m/h, 5000 p/m/h and 6000 p/m/h, respectively.

Fig. 8. Relation between funnel angle and individual passing time.

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L. Sun et al. / Transportation Research Part A 98 (2017) 14–27 Table 5 Relationship of funnel angle and individual passing time. Volume (p/h/m)

Relationship of speed (y) and Angle (x)

R2

Extreme value (°, s)

4000 5000 6000

y ¼ 15:39225  0:02395x þ 0:00021x2 y ¼ 160:0691  0:04997x þ 0:00051x2 y ¼ 15:40847  0:02757x þ 0:00031x2

0.96 0.99 0.74

(57.35, 14.71) (49.01, 14.84) (45.01, 14.79)

Table 6 Descriptive statistics of individual passing time under different volumes. Volume (p/h/m)

Funnel angle (°)

Mean (s)

Medium (s)

Max (s)

Min (s)

Standard deviation (s)

4000

None 30 45 60 90

15.38 14.92 14.68 14.71 14.93

15.50 15.30 14.20 14.80 16.00

24.80 22.80 25.70 24.20 21.50

7.10 6.10 5.90 5.80 5.30

5.18 5.16 5.43 5.34 4.96

5000

None 30 45 60 90

16.07 15.04 14.81 14.95 15.69

14.80 16.00 15.20 15.80 15.20

23.50 25.80 23.50 24.90 23.70

6.30 5.80 5.80 5.60 5.00

5.28 5.87 5.15 5.15 5.71

6000

None 30 45 60 90

15.35 15.02 14.78 14.70 15.46

14.90 15.20 15.20 14.50 16.60

25.20 24.00 24.00 24.50 22.90

5.60 5.70 5.70 4.60 4.70

5.80 5.54 5.47 5.78 5.35

The descriptive statistics of individual passing time under different volumes is summarized in Table 6. It shows that, with the increase of funnel angle, the mean of individual passing time is decreased at first and then increased, standard deviation is significantly increased and then decreased trend. But the optimized angle is different under different volume. The minimum mean of individual passing time are 45° funnel (2.15% lower than no-funnel scenario), 45° funnel (7.87% lower than nofunnel scenario), and 60° funnel (4.28% lower than no-funnel scenario) under 4000 p/m/h, 5000 p/m/h and 6000 p/m/h, respectively. However, with the increase of funnel angle, standard deviation of individual passing time is increased first and then decrease. Overall, the above analysis demonstrates that setting funnel can decrease the individual passing time, with the 45° angle the most significant. For the above three passenger volume levels, the angles between 45° and 60° show a relatively lower individual passing time. The larger flow scenarios show a more significant pattern.

4.3. Group parameters 4.3.1. Total passing time Fig. 9 and Table 7 show the relation between funnel angle and total passing time. Quadratic fitting is conducted to observe the trend. For total passing time, adjusted R2 of over 0.9 are achieved except the volume of 4000 p/m/h. It clearly shows that regardless of what kind of volume, with the increase of funnel angle, total passing time presents decreased first and then increased trend. However, the trend is not obvious in a small pedestrian flow. In addition, the total passing time reaches the lowest point at 45° funnel. For the fitted situation, the optimal total passing times are 48°, 41°, and 42° under 4000 p/ m/h, 5000 p/m/h, and 6000 p/m/h, respectively. The total passing time of 45° funnel is 2.15%, 5.18%, and 6.59% lower than no-funnel scenario under 4000 p/m/h, 5000 p/m/h and 6000 p/m/h, respectively. With the increase of passengers flow, the increase rate of total passing time is increased. Overall, the above analysis demonstrates that funnel can decrease the total passing time, and 45° funnel is more obvious. For the angle between 45° and 60°, three passengers flow shows a minimum total passing time. It is more significant on larger flow scenarios.

4.3.2. Time gaps Time gaps reflect the efficiency of exit. As shown in Fig. 10, the mean of time gap concentration in 0.6 s, the maximum concentration in 1.2 s, and the minimum is close to zero. The mean and peaks of time gap are different with the setting of the funnel. The time gap of no-funnel concentrates at one peak (about 0.7 s). With the increase of funnel angle, time gap concentrates at two peaks (0.25 s and 0.7 s). Then the time gap of 90 ° funnel concentrates at one peak again (0.7 s). Meanwhile, the mean of time gap did not change significantly under 4000 and 5000 p/m/h. However, the mean of time gap of 60° funnel to no-funnel is reduced by 24% under 6000 p/m/h. It indicates that 60° funnel can effectively improve the

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Fig. 9. Relation between funnel angle and total passing time.

Table 7 Relationship of funnel angle and total passing time. Volume (p/h/m)

Relationship of speed (y) and Angle (x)

R2

Extreme value (°, s)

4000 5000 6000

y ¼ 32:63476  0:02405x þ 0:00025x y ¼ 32:65524  0:07962x þ 0:00097x2 y ¼ 33:43619  0:1191x þ 0:00142x2

0.68 0.92 0.98

(48.36, 32.05) (40.89, 31.03) (41.94, 30.94)

2

efficiency of exit under large flow. The change of time gaps shows that the angle of the funnel is significant to the efficiency of exit, especially under large flow. 4.4. Summary In summary, the pedestrian’s walking characteristics and comprehensive assessment with equal-weighted under different funnel shape is summarized in Table 8. Equal-weighted has been proposed to yield an efficient solution for multi-index programming problems, which is intuitively simple, easy to calculate, and ensuring accuracy. Comprehensive assessment is implemented through normalization and equal-weighted, the scale of which is 0-to-1, with 0 indicating the worst traffic effectiveness scenario and 1 meaning the best traffic effectiveness scenario. Note that it is a relative measure instead of an absolute measure. Through comprehensive assessment values and curve fitting, the optimal funnel angle related to the level of passenger flow is obtained, as shown in Table 9.  The funnel shape can effectively improve the traffic efficiency at bottleneck. It is more significant in larger flow scenarios. After conducting funnel transformation at bottleneck, the pedestrian mean speed in Region 1 and Region 2 increased, the total pass time, mean of individual pass time and mean of time gap reduced.  When the funnel angle is between 30°and 60°, passengers walk more efficiently. The efficiency is different with different angle funnel shape of bottleneck. Overall, with the increase of the angle, the efficiency is increases firstly and then decreases.  Under different passenger volume conditions, the maximum efficiency of funnel shape is different. 45° funnel has the best performance under 4000 and 5000 p/m/h, where comprehensive assessment values are 0.83 and 0.86, respectively. However under 6000 p/m/h, Region 1 of 45° funnel has the highest mean speed; Region 2 of 90° funnel has the highest mean speed; 45° funnel has the least total passing time; 60° funnel has the least individual passing time; and 30° funnel has the least mean of time gap. This means that pedestrian characteristics are more complex in large passenger flow. Meanwhile, the 60° funnel has the best comprehensive assessment value, 0.786.  The optimal angles are 61°, 65°, and 46° under 4000 p/m/h, 5000 p/m/h, and 6000 p/m/h, respectively.

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L. Sun et al. / Transportation Research Part A 98 (2017) 14–27

(a) Frequency Histogram of Time Gap in 4000 Volume

(b) Frequency Histogram of Time Gap in 5000 Volume

(c) Frequency Histogram of Time Gap in 6000 Volume Fig. 10. Frequency histogram of time gap in different volume.

Table 8 Walking characteristics under different funnel angles. Volume (p/h/m)

Angle of funnel (°)

Mean speed in Region 1 (m/s)

Mean speed in Region 2 (m/s)

Total passing Time (s)

Mean of passing Time (s)

Mean of time gap (s)

Comprehensive assessment

4000

None 30 45 60 90

0.60 0.60 0.62 0.60 0.62

0.87 0.95 0.94 0.88 0.96

32.60 32.30 31.90 32.10 32.50

15.38 14.92 14.68 14.71 14.93

0.63 0.60 0.59 0.60 0.62

0.45 0.71 0.83 0.65 0.74

5000

None 30 45 60 90

0.60 0.61 0.62 0.60 0.59

0.92 0.83 0.88 0.81 0.95

32.70 31.10 30.80 31.70 33.30

16.07 15.04 14.81 14.95 15.69

0.62 0.57 0.57 0.59 0.64

0.43 0.68 0.86 0.58 0.45

6000

None 30 45 60 90

0.58 0.59 0.60 0.60 0.56

0.91 0.91 0.87 0.93 0.96

33.40 31.20 31.10 31.20 34.30

15.35 15.02 14.78 14.70 15.46

0.62 0.56 0.56 0.59 0.67

0.44 0.76 0.78 0.79 0.28

The significance of bold values represent the maximum comprehensive assessment under different volumes.

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L. Sun et al. / Transportation Research Part A 98 (2017) 14–27

Table 9 Relationship of funnel angle and score of comprehensive assessment. Volume (p/h/m)

Relationship of comprehensive assessment

R2

Extreme value (°, s)

4000 5000 6000

y ¼ 0:4658 þ 0:0097x  0:00008x2 y ¼ 0:4421 þ 0:0129x  0:0001x2 y ¼ 0:4256 þ 0:0185x  0:0002x2

0.73 0.74 0.98

(60.63, 0.76) (64.50, 0.86) (46.25, 0.85)

5. Conclusions and recommendations Pedestrian congestion is a commonly seen phenomon at bottlenecks in Beijing subway corridors. To reduce the conflict and improve pedestrian traffic efficiency, this study explores adding funnel shape at bottlenecks. Different angles at different volumes are investigated with pedestrian experiments, which have controllable circumstances, strong purpose-oriented and can change different optimization measures easily. It is identified from this research that funnel shape can bring traffic effectiveness to bottleneck, which provides a simple and feasible control means for subway management. The recommended angle should depend on passenger flow level. Overall, the optimal funnel angle is between 46° and 65° under all flows, which is recommended at bottleneck. The findings of this study is conducive for rail transit designer administration to optimize inevitable bottleneck facility. 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