Determining an influencing area affecting walking speed on footpath: A case study of a footpath in CBD Bangkok, Thailand

Physica A 391 (2012) 5453–5464

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Determining an influencing area affecting walking speed on footpath: A case study of a footpath in CBD Bangkok, Thailand Chalat Tipakornkiat a,∗ , Thirayoot Limanond a , Hyunmyung Kim b a

Asian Institute of Technology, Thailand

b

Myong Ji University, Republic of Korea

article

info

Article history: Received 29 June 2011 Received in revised form 19 April 2012 Available online 19 June 2012 Keywords: Influencing area Pedestrian Walking speed Density Bi-directional flow

abstract Intuitively, the crowd density in front of a pedestrian will affect his walking speed along a footpath. Nevertheless, the size of the influencing area affecting walking speed has rarely been scrutinized in the past. This study attempts to determine the distance in front of pedestrians that principally affects their walking speed under normal conditions, using a case study of a footpath in Bangkok. We recorded pedestrian activities along a test section of 20 m, with an effective walking width of 2.45 m in the morning and at noon. The morning dataset was extracted for analyzing various influencing distances, ranging from 1 to 20 m in front of the pedestrian. The bi-directional walking speed–pedestrian density models were developed, for each tested distance, using linear regression analysis. It was found that an influencing length in the range of 5–8 m yields the highest correlation coefficients. In the case of high density conditions, the walking speed of the equally-split flow (50:50) was found to be higher than other proportional flow analyzed. The finding has useful implications on the improvement of the walking simulations in mesoscopic models. © 2012 Elsevier B.V. All rights reserved.

1. Introduction Walking is a common and major travel mode for short-distance trips. Understanding of walking behavior is crucial information for designing buildings and walkway facilities under normal as well as disaster situations. Existing studies under normal situations are related to urban planning [1–3], tourist behavior [4], and traffic operations [5], while studies under disaster situations are important for human safety [6] under critical periods, such as, fire and tsunami evacuation. The knowledge of pedestrian flow is vital information needed for more efficient planning and safer design in accordance to the observed pedestrian behavior rather than relying on the rules set to accommodate people’s travel and lifestyle. The pedestrian models are common tools utilized to evaluate the connectivity of the pedestrian facilities [7]. In current practices, pedestrian models can be classified into three major classes including microscopic, mesoscopic, and macroscopic, as shown in Fig. 1. For microscopic models, individual characteristics are considered as an agent, a cell, and a molecule. For example, a discrete time Cellular Automata model (CA) presents a regular grid. The current state of a specific cell is determined by the states of its neighboring cells at the last time step [8]. The social force model consists of a term describing the acceleration towards the desired velocity of motion, a certain distance to other pedestrians and borders [9]. Lattice gas model is the discrete-time fine network made up of a series of grid cells. Each pedestrian occupies one point of the grid and is able to move in the forward, left and right directions [10,11]. In the agent-based model, the difference of pedestrian characteristics is represented to form the escaping skill probabilities and behaviors of each individual [12,13]. Based on the

∗ Correspondence to: Field of Study Transportation Engineering, School of Engineering and Technology, Asian Institute of Technology, P.O. Box 4, Klong Luang, Pathumthani, 12120, Thailand. Tel.: +66 86 732 6727; fax: +66 86 693 6537. E-mail address: [email protected] (C. Tipakornkiat). 0378-4371/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.physa.2012.06.001

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Fig. 1. Schematic of pedestrian studies.

previous experiments on animals, mice escaped from a water pool to a dry plate similar to the results of CA modeling [14]. The key point of the microscopic model is the detailed interaction between pedestrian and environment in a short period, which depends on the perception level of each individual. Macroscopic models, on the other hand, primarily analyze the sequential crowd density in a particular section of walking facilities. Continuum flow is evaluated by using fundamental diagrams, which involve speed, flow and density. Older [15] and Fruin [16] had analyzed the relationships among speed, density and flow of pedestrians in England and United States. Similar studies were conducted in Singapore [1], Hong Kong [2], India [3] and in Beijing [17], and the maximum walking speed was found in India. For analytical models, Helbing et al. [18] noticed that pedestrian continuum flow under medium and high crowd densities is similar to streamlining of fluids. In general, details of walking behavior, such as an interaction and maneuver, are neglected in the macroscopic analysis; nevertheless, macroscopic analysis is useful to analyze the service rate of facilities, which allows us to understand the overview of the walking conditions of interest. For mesoscopic models, a group of individuals is modeled as separate objects allocated to one of a number of delineate tracts. Time progression is typically modeled using discrete time, where in the time update it is decided how the distribution of people changes by transferring people from one region to another one [19]. Groups of pedestrians can be divided into facilities such as a block, a stair [20,21], which are moved through the network [22]. Groups can also be classified by a physical group and a logical group which has the same direction such as an arrival group and a departure group [23]. Teknomo and Gerilla [24] called a group of similar pedestrians as a multi-agent. Mesoscopic models require the speed–density lookup functions specific to each walking facility type to estimate pedestrian movement over one time unit. Different modeling classes have their own merit for various applications. The macroscopic models are beneficial in terms of a short calculation time, and are commonly applied in crowded footpaths such as markets or evacuations. The microscopic model, having the highest calculation load, is applied for bottleneck analysis to determine gate width, number of gateway of buildings, under normal and emergency conditions. Finally, the mesoscopic models can be applied for the public transport facilities such as transfer areas in a train station. Zainuddin and Shuaib [25] argued that the effect of local density in microscopic scale could change the speed of an individual, while those outside the influencing area have less impact on the individual walking speed. They mentioned that the local density of repulsive force exerted by other on an individual has an inverse relationship with the pedestrian’s awareness area. In contrast with Ref. [26], pedestrians normally adapt their walking speed to the pedestrian in front. However, they do not only consider the person immediately ahead but also the further pedestrian ahead is regarded. Both distances influenced by others on the speed–density relationship in Refs. [25,26] implied that there is a different point of view. The pedestrian in our awareness area would influence us in a microscopic view because of social attributes and limitation of a required step and a further ahead person still influences us in a mesoscopic view because of the remote action. Above mentioned, the current pedestrian’ behavior is influenced by that of others formed ahead of them. The major assumption of the present study is that there is a certain influencing area ahead of the pedestrian which most influences the pedestrian walking speed. This can be illustrated by Fig. 2. A pedestrian footpath is separated in finite regions. The figure

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Fig. 2. The effect of fluctuation density on a footpath.

(a) Angular dependence shape.

(b) Rectangular shape.

Fig. 3. Examples shape of perception area of pedestrian in microscopic view.

shows the effect of different crowd density in front of a white-head pedestrian on a footpath, section a shows less density and section b shows high density. Teknomo et al. [27] argued that the pedestrian simulation models require calibration and validation to best replicate actual pedestrian walking patterns. However, the data collection for pedestrian dynamics is very difficult. Even though, GPS, a radar gun and image processing are useful data collection tools in traffic engineering for observing vehicle flow characteristics, the usefulness of them to collect pedestrian flow is still questionable. It is unfriendly to stand in front of or on the side of our example pedestrians and shoot a radar gun at them in a city. In case of GPS, there is an applicable method for a probe pedestrian, but the continuous movement of large data collection will be cost-demanding to acquire sufficient number of GPS equipment. Image processing is difficult to track the foot position of the same pedestrian in a crowd. Most pedestrian flow simulations assumed that walking behavior is affected by the neighborhood area, which can take different shapes in different methods. Cellular automata (CA) and lattice gas models often utilize neighborhood rectangular cells, while social force models often apply a half circle shape of influencing area, as shown in Fig. 3. The arrow represents the direction of walking. The gray area means a perception area or an influencing area in a micro level, each of which has been influenced by neighborhoods on his/her walking speed and direction in a microscopic model. Past studies regarding the influencing area on walking speed estimation is limited on microscopic. Perception area of a pedestrian in the microscopic point of view is the body and buffer area that other pedestrians or objects in the perception area have an influence on a pedestrian. In contrast with a mesoscopic point of view, the region should be larger; however that area is influenced by others similarly to the microscopic concept which is called the influencing area. One reason for the knowledge gap in the field of the pedestrian characteristics study may be the lack of in-depth data collection, which allows investigating the influencing area on pedestrian behavior. The objective of this study is to determine a suitable influencing area in order to improve the determination of walking speed along footpaths. The walking speed–density models were developed, for each tested distance, using linear regression analysis. Coefficient of determinations between speed and density were used to assess the influencing level of each tested distance. The developed models were further cross-checked for their prediction accuracy using pedestrian activities during noontime. 2. Methodology The study was conducted on a footpath along Silom Road in the central business district of Bangkok, Thailand under the non-transient of congestion. Temperature was 26.9 °C in the morning and 30.5 °C at noon. Speed of wind was zero knots. The surface of the footpath was paved with concrete. We observed that pedestrians who use this footpath usually walk for work-related trips. The footpath has no side influence, or in other words, pedestrians do not interact with any fixed object disruptions except interaction with other pedestrians [28]. It means that there are no windows or street shopping nor non-motorized vehicles parked on the footpath, which could generate disruption of pedestrian flow. Fig. 4 shows the location of the study site and the schematic map of the studied footpath. L represents a longitudinal length of the test section, 25.0 m, a represents the effective width of 2.45 m and b represents a footpath’s furniture width of 1.40 m. (According to Ref. [28], effective width is the portion of a walkway that pedestrians can use effectively for movement with no presence of any physical objects such as light poles, telephone booths.)

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Fig. 4. Layout of the study area and the section of the footpath.

(a) The first camera installation point.

(b) The second camera installation point. Fig. 5. The camera installation points.

Two video cameras were mounted on elevated structures to capture walking activities of the test section, as shown in Fig. 5. The exploration of the site found no single location to install video camera that can track the pedestrian flow in the whole test segment, thus, two cameras were used and later synchronized in the laboratory for data extraction. We recorded walking activities along the test section for two hours; one hour in the morning (7:30–8:30) and one hour at noon (12:00–13:00). The morning data was later analyzed to develop the speed–density models, while the noon data was later used to verify the developed models. In this study, we only included those pedestrians who walked through the test section and did not stop walking when they passed the study area. A total number of 719 pedestrians were analyzed and used for the walking speed model development. Every 100–125 frames of video (4–5 s) a sample pedestrian was randomly chosen out of the population, and the instant of onset density and travel time was measured in the laboratory. Video files were observed in the laboratory to analyze walking speed and pedestrian density, in a similar fashion to the previous study [29–31]. The recordings were analyzed frame by frame with a rate of 25 frames per second (accuracy = 0.04 s) in order to minimize the errors for extracting walking time data. The error of position measurement can be estimated by an

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(a) Example of illustration of influencing length 5 m.

(b) Example of illustration of influencing length 10 m. Fig. 6. Examples of measurement.

accuracy of walking time multiplied with walking speed, for example, in our case, the average walking speed was 1.23 m/s, thus the position error is approximately 0.05 m. A sample pedestrian’s identification number is denoted by (i). Influencing areas (s) in front of1 sampled pedestrians were  observed with various influencing distances (ls ) and an effective width (w). An influencing area Ai,s of sample pedestrians

  (i) is w × ls . The number of pedestrians in the influencing area is denoted as Ni,s . Thus, pedestrian density in the influencing       area can be estimated by dividing the number of pedestrians Ni,s by the size of the influencing area Ai,s , denoted as kinst i,s .  in   out 

The arrival time ti,s and the departure time ti,s of sample pedestrians were recorded and used to estimate the individual walking speed vi,s =  outls in  . Fig. 6 shows examples of measurement for the influencing downstream distances ti,s −ti,s

of 5 and 10 m. The arrival time of each sample pedestrian started from the same beginning line of the section. The proportion of crowd who walk in an opposite direction seems to affect the walking speed of a pedestrian. On-coming pedestrians would occupy some walking space available, and create the resistance to a pedestrian in a different way from the pedestrians who head in the same direction. To account for this effect, this study incorporates the concept of proportional flow in the speed–density relationship. Here the proportional flow is denoted by 2 numbers in parenthesis as (AA:BB). The former number (AA) represents the percentage of pedestrians in the influencing area walking in the same direction as the pedestrian of interest, while the latter (BB) represents the percentage of pedestrians walking in the opposite direction. The two numbers combined to total 100%. For example, the proportional flow (70:30) refers to the situation that 70% of pedestrians in the influencing area walk in the direction of interest, while 30% of pedestrians in the influencing area walk in the opposite direction. In our analysis, we focus on four different levels of proportional flow: (100:0), (70:30), (50:50) and (30:70). The following steps were used to extract the pedestrian walking speed from the video files. (1) Select the influencing length (ls ) and determine the rectangular shape of the influencing area Ai,s , (2) Randomly select a sample (i),  pedestrian  (3) Record the arrival time tiin,s of a sample pedestrian (i),





1 Under normal walking condition, we assume no pushing force behind the pedestrian, thus we only consider the influencing area in front of the pedestrian; however, in case of evacuation studies, this force should be included.

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(4) When the sample pedestrian’s  is on the beginning line, the video file was paused  foot (5) The number of pedestrians Ni,s in the influencing area were counted and separated in two directions to determine the bi-directional flow category (AA:BB).   (6) Dividing the number of pedestrians by an influencing area Ai,s to calculate the crowd density kinst i ,s . (7) Record the departure time tiout ,s of sample pedestrian (i),    in  (8) The walking time of sample pedestrian (i) in the influencing length is tiout ,s subtracted from ti,s .





in  (9) The influencing length (ls ) was divided by the walking time tiout ,s − ti,s to obtain the walking speed vi,s =





ls in tiout ,s −ti,s



of

the sample individual. (10) Repeat the process until the required sample size is obtained. In this study, the relationship between the walking speed and the crowd density for various influencing distances was plotted, and analyzed with linear regression analysis. The crowd densities were plotted on the X -axis, and the walking speeds were plotted on the Y -axis. The coefficient of determination (R2 ) was used to measure how well the linear relationship fits. As the coefficient of determination is higher and approaches 1.0, an estimated regression fits better. The coefficient of determination between the density (Ks ) and walking speed of the pedestrian (Vs ) can be estimated using the following equation. R2s =

 √

Cov (Ks , Vs )

2 (1)

Var(Ks ) · Var(Vs )

where Ks = k1,s , k2,s , k3,s , . . . , kn,s and Vs = v1,s , v2,s , v3,s , . . . , vn,s . Cov (Ks , Vs ) is covariance of Ks and Vs . In addition, Var(Ks ) and Var(Vs ) are variance of Ks and Vs , respectively. To determine the most appropriate influencing distance for estimating walking speed, we analyzed the relationship between the walking speed and the pedestrian density for various influencing distances. An initial series of the 6 influencing distances are tested in this study including 1, 3, 5, 10, 15, and 20 m. We later found that the optimal influencing distance was likely being between 5 and 9 m, thus, we further analyzed the influencing distances in this range in more detail at 6, 7, 8 and 9 m. The results of 10 tested distances are shown and discussed in the next section. Note that, for each of the influencing distances, we analyze 4 levels of bi-directional flow: 30:70, 50:50, 70:30 and 100:0.



 

 









 

 







3. Findings Table 1 summarizes the walking characteristics under various influencing lengths, both in the morning and at noon. The total number of samples is 719 in the morning, and 250 at noon. The test section of the footpath was generally more crowded in the morning (the overall average density was 0.52 person/m2 ) than at noon (0.46 person/m2 ). There is a decreasing trend of the average density as the influencing length gets longer for both time periods. For example, in the morning, the average density of the 5 m influencing length was 0.54 person/m2 , while that of the 20 m influencing length was 0.22 person/m2 . The overall average speeds in the morning and at noon were 1.23 m/s and 1.22 m/s, respectively. These are comparable to the average speed found in the previous study (1.22 m/s) of Thailand [32]. Mean walking speeds in the morning vary in the range of 1.11–1.31 m/s depending on the influencing lengths of interest, and they are comparable to mean walking speeds at noon. Fig. 7(a)–(j) shows the estimated curves of the walking speed against the pedestrian density of the observed data for 10 various influencing lengths. For each influencing length, there are four proportion flow patterns as 100:0, 70:30, 50:50 and 30:70 in intervals of 5%. As shown, for all plots, speed tends to decrease with increasing density, which is intuitively correct. When there are more pedestrians ahead, a pedestrian is likely to walk with a slower speed. Looking at individual directional flows one by one, we found the following. For the proportion flows of (30:70), pedestrians in the minor flow direction (30) can adapt their actual walking speed to the preferred walking speed during low density conditions. However, walking speed in the minor flow direction tends to receive much resistance from the opposing flow, thus the walking speed tends to reduce with a higher decreasing rate when density increases. Therefore, the proportional flow of (30:70) tends to have the steepest slope in almost all plots. Conversely, the proportion of bi-directional flows of (70:30), pedestrians in a major flow direction (70) can walk faster than the pedestrians in a minor flow direction (30) because the effect of following the majority crowd. When compared to each other, pedestrians in the major flow direction tend to be able to walk at a higher speed than the minor opposing flow. It was found that the equally-split flow of (50:50) has a relatively flat slope for almost all influencing lengths. This means that, under crowd conditions, pedestrians under the equally-split flow of (50:50) can still walk with relatively high speeds compared with other proportional flows, even faster than the unidirectional case. One plausible explanation is that pedestrians in both directions have more balanced face-to-face exchange positions which means that both pedestrians on each side have balanced opportunities for a detour, slip past, or bump for smooth exchange of place if necessary. So they have more opportunity to finally organize themselves to minimize conflict and waiting. Furthermore, they also may pay attention to follow the crowd in front (due to the pressure from the opposing stream) more than the unidirectional flow (100:0) condition. The interesting findings confirm the previous simulation results of Refs. [33–35].

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Table 1 Pedestrian characteristics in tested influencing lengths. Characteristics

Influencing length (m)

Morning (data collection) Average density (person/m2 ) Mean walking speed (m/s) S.D. walking speed (m/s) Range maximum speed (m/s) Minimum speed (m/s) Sample size of proportion (30:70) (50:50) (70:30) (100:0) Total sample size (719) Noon (validation) Average density (person/m2 ) Mean observed speed (m/s) S.D. observed speed (m/s) Range maximum speed (m/s) Minimum speed (m/s) Sample size (250)

Average

1

3

5

6

7

8

9

10

15

20

1.20 1.31 0.36 2.78 0.53

0.55 1.3 0.22 1.8 0.72

0.54 1.17 0.21 1.72 0.72

0.61 1.23 0.23 1.76 0.76

0.47 1.26 0.21 1.69 0.83

0.48 1.11 0.15 1.46 0.79

0.46 1.19 0.18 1.55 0.83

0.37 1.25 0.20 1.69 0.85

0.29 1.24 0.19 1.72 0.79

0.22 1.26 0.15 1.58 0.95

0.52 1.23 0.21 1.78 0.78

30 25 23 33 111

15 11 22 35 83

10 13 20 27 70

9 13 6 25 53

13 15 16 15 59

14 14 23 22 73

6 18 10 19 53

9 15 13 20 57

15 21 12 45 93

11 14 15 27 67

– – – –

– – – – – –

– – – – – –

0.61 1.13 0.21 1.70 0.69 50

0.51 1.21 0.15 1.55 0.83 50

0.43 1.28 0.18 1.77 0.96 50

0.40 1.24 0.16 1.74 1.01 50

0.41 1.22 0.17 1.57 0.92 50

0.38 1.26 0.15 1.58 1.03 50

– – – – – –

– – – – – –

0.46 1.22 0.17 1.65 0.91

(a) Influencing length 1 m.

(b) Influencing length 3 m.

(c) Influencing length 5 m.

(d) Influencing length 6 m.

Fig. 7. Pedestrian speed–density-influencing length relationship on a footpath in Bangkok.

Table 2 summarizes the speed–density function and resulting coefficients of determination (R2 ) for various influencing lengths and proportional flows. As shown, the R2 vary in a wide range from 0.12 to 0.80. These represent from fair to good fits to the data. (A better fit is obtained the closer R2 is to 1.) This implies that there is a certain distance ahead for each proportional flow of the pedestrian that most influences on the pedestrian average walking speed with a linear relationship. It can be described into four directional splits, the influencing lengths between 8 and 9 m have an R2 0.67, 0.69 and 0.78 for

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(e) Influencing length 7 m.

(f) Influencing length 8 m.

(g) Influencing length 9 m.

(h) Influencing length 10 m.

(i) Influencing length 15 m.

(j) Influencing length 20 m. Fig. 7. (continued)

proportional flows at 30:70, 70:30 and 100:0 respectively. The influencing length of 5 m gives the highest R2 at 0.80 for a proportional flow at 50:50. Lastly, the influencing length of 10 m and longer, yields an R2 lower than 0.48. The results indicate that the pedestrian density in the area of 8 m in front is the most effective in determining walking speed of a pedestrian when proportional flows are 30:70 and 70:30. The pedestrian density in the area 5 m in front are the most effective in determining walking speed of a pedestrian when a proportional flow is 50:50 and the pedestrian density in the area 9 m in front are the most effective in determining walking speed of a pedestrian when a proportional flow is 100:0. 4. Verification In this study, we verified the study results by testing the walking speed models determined from the previous section with the data collected during the noon time. Four influencing lengths for proportional flows at 30:70, 50:50, 70:30 and

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Table 2 Influencing lengths and coefficient of determination R2 relationship. Proportional flow

Speed–density function

R2

1

30:70 50:50 70:30 100:0

v v v v

= −0.39 × k + 1.75 = −0.17 × k + 1.54 = −0.50 × k + 2.02 = −0.38 × k + 1.70

0.14 0.13 0.20 0.16

3

30:70 50:50 70:30 100:0

v v v v

= −0.95 × k + 1.76 = −0.16 × k + 1.39 = −0.56 × k + 1.63 = −0.33 × k + 1.50

0.33 0.16 0.26 0.24

5

30:70 50:50 70:30 100:0

v v v v

= −0.58 × k + 1.57 = −0.45 × k + 1.45 = −0.38 × k + 1.43 = −0.36 × k + 1.28

0.35 0.80 0.43 0.42

6

30:70 50:50 70:30 100:0

v v v v

= −1.04 × k + 1.76 = −0.50 × k + 1.53 = −0.29 × k + 1.39 = −0.38 × k + 1.46

0.59 0.66 0.54 0.45

7

30:70 50:50 70:30 100:0

v v v v

= −0.79 × k + 1.67 = −0.58 × k + 1.54 = −0.71 × k + 1.60 = −0.78 × k + 1.59

0.64 0.62 0.69 0.47

8

30:70 50:50 70:30 100:0

v v v v

= −0.40 × k + 1.32 = −0.53 × k + 1.36 = −0.53 × k + 1.37 = −0.67 × k + 1.41

0.67 0.59 0.69 0.49

9

30:70 50:50 70:30 100:0

v v v v

= −1.02 × k + 1.71 = −0.37 × k + 1.36 = −0.53 × k + 1.41 = −0.70 × k + 1.51

0.52 0.48 0.42 0.78

10

30:70 50:50 70:30 100:0

v v v v

= −0.77 × k + 1.61 = −0.50 × k + 1.45 = −0.43 × k + 1.33 = −0.72 × k + 1.47

0.40 0.44 0.31 0.48

15

30:70 50:50 70:30 100:0

v v v v

= −0.65 × k + 1.36 = −0.66 × k + 1.38 = −1.01 × k + 1.49 = −0.74 × k + 1.51

0.26 0.30 0.21 0.42

20

30:70 50:50 70:30 100:0

v v v v

= −0.97 × k + 1.47 = −0.55 × k + 1.39 = −0.86 × k + 1.46 = −0.33 × k + 1.31

0.22 0.15 0.19 0.12

Influencing length (m)

100:0 were extracted for verifications, since they are in the range that yields a strong correlation between walking speed and crowd density. The walking speed was computed from the models, and compared against the actual walking speed of pedestrian. The concept of the mean absolute percentage error (MAPE) was used to verify the models of various influencing distances. MAPE can present the precision of the estimated walking speed to the observed speed, calculated using equation (2). In addition, the concept of Pair-test also was presented in Table 3. MAPE =

n 1   vobs (i) − vest (i) 

n i =1

  

vobs (i)

  

(2)

where

vobs (i) is observed speed of pedestrian (i) and vest (i) is estimated speed of pedestrian (i). Fig. 8(a)–(d) show diagonal plots between estimated speed and observed speed on the tested influencing lengths. Table 3 summarizes the associated mean absolute percentage error (%) for various influencing distances. As shown, the related data of proportional flow are extracted to present the influencing distances. For the proportions of bi-directional flow (30:70) and (70:30), the influencing length 8 m yields a good prediction of walking speed. The unidirectional flow (100:0), influencing length 9 m yields a good prediction of walking speed and the proportion of bi-directional flow (50:50) at influencing length 5 m also presents a good estimation of walking speed because of lowest MAPE. In addition, the Paired sample tests of both average speeds in the morning and at noon for the different of proportion

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(a) Proportional flow: 30–70.

(b) Proportional flow: 50–50.

(c) Proportional flow: 70–30.

(d) Proportional flow: 100–0.

Fig. 8. Diagonal plots between estimated speed and observed speed on influencing length. Table 3 Mean absolute percentage error (%) and pair sample test. Proportional flow

Influencing length (m)

Sample

MAPE (%)

Average observed speed (m/s) (S.D.)

Average estimated speed (m/s) (S.D.)

Pair samples test Sig. (2-tailed) α = 0.05

30:70 50:50 70:30 100:0

8 5 8 9

7 11 14 34

0.08 0.12 0.09 0.08

1.20 (0.14) 1.19 (0.21) 1.20 (0.12) 1.12 (0.14)

1.13 (0.08) 1.20 (0.11) 1.16 (0.07) 1.13 (0.12)

0.148 0.811 0.217 0.654

flows were conducted and presented in Table 3. It confirms that the estimated model can predict well, as the predicted numbers are not statistically different from the observed numbers. 5. Conclusions and discussions In this study, we analyzed the relationship between walking speed and pedestrian density for various downstream distances. We validated the spectacle and concluded that there is a required distance of the influencing area for the speed and density relationship. The project site is a walkway along a major arterial in the central business district of Bangkok. The walkway has an effective width of 2.45 m with an average walking speed of 1.23 m per second. In this study, we utilized a linear regression analysis to represent the walking speed and the crowd density relationship. It is reasonable to assume that pedestrians select their walking speed based on the crowd density in front of them. The group of pedestrians ahead in the influencing area is the key determination of walking speed rather than a few people immediately in front or pedestrians further away. Influencing distance range for mesoscopic modeling is 5–9 m with high R2 . In addition, our results conform to simulation results of Ref. [26] that the downstream distances of 17.3, 20.0 and 50.0 m have no notable influence on the speed–density relationship. Our study finds out that the downstream distance of 15 and 20 m yields the highest R2 of only 0.42 and 0.22, respectively. The results are realistic that pedestrians have higher walking speeds at low crowd density for all proportions of bi-directional flow. That is because they have more opportunities to use their desired speeds. Our results conform to the simulation results by Refs. [33–35] that almost relationships at a balanced flow (50:50) is that the performance of flow increasing at the higher density than other proportional flows studied because of flow balance and smooth exchanges of position. The proportions of bi-directional flows are tested under different influencing lengths. Almost influencing lengths have similar proportional patterns, but the coefficients of determination between the density and average walking speeds are different for each influencing length. The proportion of bi-directional flow at (50:50) allows pedestrians to adapt their preferred walking speeds to actual speeds which are higher than unidirectional flows, (30:70), and (70:30). That is because

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they have more opportunities of face-to-face to change their position. The balance flow of an influencing length 5 m shows the strongest R2 . The proportions of bi-directional flows (30:70) and (70:30) shows the effect of majority that the major density direction has the negative impact on the minor density direction. The proportion of bi-directional flow at (30:70) and (70:30) of an influencing length 8 m shows the strongest R2 . The unidirectional flow shows the jam situation effect which created by slow moving ahead person because the limitation of exchange positions. The unidirectional flow at an influencing length 9 m indicates the strongest R2 . The finding of this research has useful implications for mesoscopic simulation models. The footpath in the mesoscopic point of view divides the system into sub-regions that are connected together. One of the problems with mesoscopic models is that the optimum lengths of the regions are answered, so the setting of these parameters in the simulation plays the role of the outcome of system series. For example, consider a study site near the gate of a subway. Mesoscopic simulation has an advantage on the time calculation. It can be used to predict the early-warning time for facility management in case of crowd on the footpath coming on subway station. The upstream and downstream pedestrian volume on a footpath will be detected for travel demand generation. Travel route choices are limited to inflow and outflow of a subway gate. Person groups will be defined by suitably influencing an area which is determined by the proportion flow-density—influencing length lookup function. The travel delay and level of service will be predicted for facility management. These findings are not only useful for model simulation, but it will be a useful guide for data collection also. In addition, from the comparison of proportional flow performance, it can be implied that if pedestrians can organize them into balance flow, then the performance could be improved. So, lane providing on a footpath by color marking could be a helpful guide for self-organizing of pedestrians. Although the conventional speed–density function is well fitted with dataset, our research – unfortunately considered as a rare study – does not have sufficient amount of data to conduct reliable analysis for non-linear relations such as S-curves and multi-regimes. The non-linear relationship is an interesting issue and worth to be explored in future researches. In addition, a decaying function with distance is another interesting approach to present the impacts of a front crowd on pedestrian walking speed. Temperature in the morning and at noon was 26.9 °C and 30.5 °C respectively, and surface pavement of the footpath was concrete. We found a small difference in an average speed between morning and noon: that the average speed in the morning (1.23 m/s) is slightly faster than the average speed at noon (1.22 m/s). However, two temperature check points are not sufficient enough for model estimation. In future research, we would have to expand the scope of research to cover more locations, to make the results that can be better generalized to more cases. This research focuses on a normal walking situation and uninterrupted flow on a footpath in a central business area of Bangkok, Thailand. It does not represent a very crowded situation nor a walking situation in Europe, the North American continent and Japan where citizens usually walk faster than other Asian pedestrians. In addition, future research studies could be focused on walking behavior of pedestrians in other continents as well as walking behavior of proportions of bi-directional during critical/capacity situations. 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