Experimental study of luggage-laden pedestrian flow in walking and running conditions

Zhigang Shi; Jun Zhang; Weiguo Song; Xiangxia Ren; Ma Weibin

doi:10.1088/1742-5468/ab8554

1. Introduction

Luggage-laden pedestrians are typical groups in transport hubs such as railway stations and airport terminals. Luggage not only enlarges pedestrians' dimensions but also decreases their average walking step lengths [1]. In real traffic evacuation, luggage-laden pedestrians might take more short breaks while walking [2] and would increase blockage, and discarded luggage would become obstacles to other pedestrians, posing a great threat to evacuation. Understanding the movement characteristics of luggage-laden pedestrians can be helpful for the design of infrastructures and modeling of luggage-laden pedestrian movements in these places.

Field observation is an efficient and commonly used way to study luggage-laden pedestrian flow. It is indicated that luggage can affect the flow of pedestrian traffic, and pedestrians with bags or trunks walk more slowly than other pedestrians whether at airports [3] or on escalators [4], stairways [5] or city streets [6]. According to an observation at a walkway section in an airport terminal, Davis and Braaksma [7] suggested that the walking speed and the time headway of luggage-laden pedestrians are the variables that should be studied. Moreover, Ye et al [8] reported that the size of luggage influences the pedestrian walking behavior significantly, and the trolley case should be distinguished from other large luggage types when analyzing speed. However, the observation data were disturbed by many other factors, which is not conducive to reaching conclusions specifically for luggage-laden pedestrians.

In order to eliminate uncontrollable factors in observational experiments, controlled experiments have been conducted for luggage-laden pedestrians in recent years. Huang et al [9] considered that luggage has less influence on pedestrian walking speed than subjective control, but the average distance headway between pedestrians was obviously enlarged. Also, it is reported [10] that when luggage-laden pedestrian moved in a narrow seat aisle, the hindrance of the seat configuration obviously affected the randomness of pedestrian behavior. Gao et al [11] showed that the individual velocity can be significantly affected by trolleys in a corridor with a high pedestrian density. In contrast, in low densities a trolley has almost no effect on the velocity. However, the data are mainly on walking speeds but less attention has been paid to running speed, which is equally important especially in emergencies. Even if a faster-is-slower phenomenon is found from animal experiments [12] and model simulation [13], it does not seem applicable to pedestrians from the experiment in [14], where three desired speed levels (walking, jogging and running) were set. Still fewer studies have focused on the running of luggage-laden pedestrians.

Luggage carried by a pedestrian occupies a certain space around them and influences other nearby pedestrians differently. The spatial distribution of pedestrians is an important issue that needs to be noticed. To avoid the need to continuously adjust their speed to that of their neighbors, pedestrians try to keep a given distance but follow the person in front of them, as well as accepting and observing pedestrians to their sides [15]. There are symptoms of strong correlations [18] between the positions of closely located pedestrians. Zeng et al [16] found that step length and step frequency would first increase with increasing headway and then remain constant. Webb and Weber [17] indicated that vision, hearing and mobility play important roles in the interpersonal distance of the elderly. Besides, it is shown that walking speed had a significant effect on personal space when one subject moved toward an oncoming pedestrian [18]. The size of the personal space at high speed is significantly different from that under static conditions. By investigating the pedestrian inflow process in a room with a separate entrance and exit, Liu et al [19] suggested that the proxemics and attraction from the exit both affect pedestrians' spatial distribution. However, all of the aforementioned studies focus on pedestrians without any luggage. There is still a lack of quantitative description of the spatial distribution of luggage-laden pedestrians whether walking or running.

Consequently, in this work we focus on the speed and spatial distribution of luggage-laden pedestrians both walking and running in straight corridors. The trajectories of luggage-laden pedestrians are critically analyzed with a well-developed method [20–23]. The nearest neighbors, boundary distance and distance headway are adopted to quantify the spatial distribution. The findings provide quantitative parameters for modeling of luggage-laden pedestrian evacuation and give a constructive opinion on architectural design in traffic hubs.

The rest of the paper is organized as follows. The setup of the experiment is described in section 2. Then we investigate the effect of luggage-laden pedestrians walking and running based on their way of carrying luggage, speed and spatial distribution in section 3. Finally, section 4 summarizes the paper and makes a conclusion.

2. Experimental setup

The experiments were carried out in the campus of University of Science and Technology of China in March 2019. Given that the composition of the crowd may influence the result, it is necessary to provide more detailed information on the participants in our experiment. In this study, we recruited 70 university students (40 males and 30 females) with an average age of 24 and average body height of 1.695 m to participate in the experiments in a manmade straight corridor. Although the composition has certain differences from the crowd in transportation hubs in reality due to its approximate homogeneity, it allows one to focus on the movement styles and luggage and to eliminate the influence of age, physical ability and education level.

Figure 1 provides an illustration and a screenshot of the experimental scenario. The length and width of the straight corridor are 10 m and 3 m respectively. The sizes of the luggage range from 20 inches to 26 inches (51–66 cm), which are the most common sizes in traffic hubs. Extra 5 kg books were added uniformly to each item of luggage. Although the weight is obviously less than that of the typical suitcase in airports and large train stations, it is close to the 5 kg weight limit of most flight management regulations on carry-on baggage. To make the situation simple we will not consider the real weight distribution of luggage in this study, since a heavier suitcase would lead to large physical disparities of pedestrians in different runs of the experiment. The participants were told to carry their luggage in a comfortable way and either pushing or dragging was allowed. Before the formal experiment, each participant walked and ran once in the corridor alone to measure their free movement speeds. To mimic the pedestrian movement and evacuation, the formal experiments were composed of two movement conditions: quick walking (W) and emergency running (R). A total of three different ratios of luggage in the crowd are considered in the experiments to study the influence of luggage on speed and spatial distribution. In the quick walking condition, the participants were instructed to walk through the corridor as quickly as possible. During the emergency running, participants were asked to imagine themselves escaping from a disaster. Before passing through the corridor, all the pedestrians stood within the 'waiting area', which was 4.2 m away from the entrance to provide adequate longitudinal space for acceleration. At the beginning of the experiment, the luggage-laden pedestrians were uniformly distributed to guarantee the same initial experimental condition and to determine the influence of different luggage ratios. It is worth mentioning that we did not ask the participants to move in parade formation as the initial state. The arrangements of luggage for different ratios are shown in figure 2 and detailed information on the setup of each scenario can be found in table 1. Each scenario is performed once.

**Figure 2.** The arrangement of luggage in different scenarios. Considering the space occupied by luggage, the number of pedestrians in each row is different. A red circle represents a luggage-laden pedestrian, and a blue circle one without luggage. (a) 0% luggage-laden pedestrians and six pedestrians in each row. (b) Five pedestrians with 20% luggage in each row. (c) Four pedestrians with 50% luggage in each row.
Download figure:
Standard image High-resolution image

Table 1. Details of our experiment in each run.

Index	Conditions	N_peds	N_luggage (proportion)	Total pedestrians
W1	Walking	6	0 (0%)	72
W2	Walking	5	15 (20%)	72
W3	Walking	4	35 (50%)	70
R1	Running	6	0 (0%)	72
R2	Running	5	15 (20%)	72
R3	Running	4	35 (50%)	70

Two HD video cameras (1920 × 1080 pixel resolution and 50 fps) were mounted on the top of a building so that the whole experiment could be recorded and further analyzed. To ease the automatic extraction of trajectories, pedestrians were asked to wear colored hats. Pedestrian trajectories were tracked by using the open-source software PeTrack [24] with a maximum error of 0.05 m.

By means of digital image processing, the pedestrian trajectories in different scenarios were obtained. As shown in figure 3, each trajectory starts from the waiting area and the instantaneous speed is marked with colors. Lane formation can be clearly observed in each scenario and it is more distinct for running than walking. Also, with increasing amount of luggage, the distance from each wall increases; this means that luggage greatly affects the spatial distribution, and this will be discussed in more detail in the following section. Based on these trajectories, movement characteristics such as speed and spatial distribution at any time and position can be calculated.

3. Analysis and result

In this section, the way of carrying luggage is analyzed. Then the speed is calculated to quantify the impact of different ratios of luggage. The spatial distribution influenced by luggage is mainly analyzed, since the luggage influences pedestrian movement directly as an external feature.

3.1. The way of carrying luggage

In this section, we analyze the way pedestrians carry their luggage in different scenarios. In free movement, nearly all pedestrians push their luggage on the left or right side when walking but drag it behind while running. In the formal experiment, 30 pedestrians pushed their luggage and only five dragged it in W3 scenario, which indicates that pedestrians prefer to push luggage when walking. However, the way pedestrians carry luggage in R3 scenario is noticeably different from the result in the free running condition, in which all the pedestrians drag the luggage. As shown in figure 5(a), 22 pedestrians (17 males and 5 females) drag the luggage and 13 (3 males and 10 females) push their luggage. This shows that males prefer to drag luggage while running whereas females prefer to push. Furthermore, it was observed that pedestrians changed their ways of carrying luggage during the movement. In R3 scenario a female firstly dragged her luggage then began to push it while running in a steady condition.

Besides, it is observed that the pedestrians in the corridor can be regarded as two groups. Those along the walls at the both sides moved in single-file, while those in the middle of the corridor were in an alternate pattern, as depicted in figure 4. Based on this consideration, we divide the corridor into three regions (left (y ∈ [0 m, 0.8 m]), right (y ∈ [2.2 m, 3 m]) and middle (y ∈ [0.8 m, 2.2 m])) to quantitatively analyze the influence of the way pedestrians carry luggage in different positions. From figure 5(b), the numbers of pedestrians who push and drag luggage in the middle region are nearly the same. By contrast, nearly all the pedestrians in the left and right regions drag their luggage.

**Figure 4.** Sketch of the three regions. In the corridor, we observed that pedestrians on the both sides are likely to move in signal-file and the ranges are y ∈ [0 m, 0.8 m] on the left and y ∈ [2.2 m, 3 m] on the right; the movement in the middle is a staggered distribution and the range is y ∈ [0.8 m, 2.2 m]. Hence, we divided the corridor into three regions in the analysis of the way of carrying luggage, boundary distance and distance headway.
Download figure:
Standard image High-resolution image

**Figure 5.** The way pedestrians carry luggage in R3: (a) division between male and female; (b) division between different regeions.
Download figure:
Standard image High-resolution image

We conclude that gender influences the way pedestrians carry luggage: more males prefer to drag luggage while running than females (in R3 scenario, 17 males and 5 females drag the luggage, while 3 males and 10 females push).

The pedestrian's position in the corridor also influences the way they carry luggage. Pedestrians near the walls prefer to drag luggage (14 dragging and 4 pushing), while the numbers of pedestrians who push or drag luggage in the middle of the corridor are nearly the same in R3 scenario.

As for the speed, it is observed that all pedestrians pushed luggage while walking and dragged luggage while running in free movement. When pedestrians ran, they dragged the luggage and kept a larger distance away from it. This helps an individual to swing their body so as to accelerate.

Overall, it can be concluded that gender, position and speed of movement all affect the way in which luggage is carried. Hence, when modeling luggage-laden pedestrians to optimize traffic hubs, the way in which luggage is carried should be considered under different conditions. The characteristics between pushing and dragging luggage are a key point that is worth analyzing deeply.

3.2. Influence of luggage on speed

3.2.1. Speed analysis in free movement

In free movement, the individual speed across the entire corridor was calculated. In order to exclude individual differences, we compare the walking and running speeds for each pedestrian both with and without luggage. To minimize the error, we only consider the data in a steady state by eliminating the initial and final transients, and select the region x ∈ [7 m, 11 m] as the measurement area to calculate the free speed. As shown in figure 6(a), the average free walking speed is 1.80 ± 0.15 m s⁻¹ for common pedestrians and 1.82 ± 0.13 m s⁻¹ for luggage-laden pedestrians. In order to further investigate whether carrying luggage has a significant impact on free walking speed, we tested hypotheses with a T-test. We formulated the null hypothesis and alternative hypothesis as

$\begin{equation}\begin{gathered}{c}{H}_{0}:{p}_{1}={p}_{2}\\ {H}_{1}:{p}_{1}\ne {p}_{2}\end{gathered}\end{equation} \tag{ 1 }$

where p₁ is the proportion of walking speeds of luggage-free pedestrians and p₂ is the proportion of walking speeds of luggage-laden pedestrians. We get p = 0.058, so we fail to reject the null hypothesis, which means that luggage makes no significant difference to a pedestrian's free walking speed in terms of statistics. This result is consistent with the findings of Huang et al [9]. In addition, whether carrying luggage or not, the speed of females is slightly lower than that of males. The speed of females is 1.76 m s⁻¹ with luggage and 1.73 m s⁻¹ without; that of males is 1.83 m s⁻¹ with and 1.85 m s⁻¹ without; also gender makes no difference in carrying luggage or not, with p = 0.64 for females and p = 0.61 for males where p is the probability that the difference between samples is due to the sampling error and p < 0.05 represents a statistically significant difference. Overall, luggage makes no difference to the free walking movement of pedestrians.

The speeds in the running case are exhibited in figure 6(b). The average speed of free running luggage-laden pedestrians is 3.83 ± 0.68 m s⁻¹, while it is 3.48 ± 0.54 m s⁻¹ for pedestrians without luggage. In order to further investigate whether carrying luggage has a significant impact on free running speed, we conducted a T-test. We formulated the null hypothesis and alternative hypothesis as formula (1), where p₁ is the proportion of running speeds of luggage-free pedestrians and p₂ is the proportion of running speeds of luggage-laden pedestrians. We get p = 0.000, so we reject the null hypothesis. It is indicated that luggage enhances a pedestrian's running speed and plays a positive role when a pedestrian runs alone. This sounds like the so-called 'no pressure, no power'. We speculate that the luggage-laden pedestrians tried to finish the experiment as soon as possible to get rid of the resistance of the luggage, which stimulated them to move faster and then led to a larger personal space. We also conclude that luggage seems to have little impact on individual walking speed with 1.82 m s⁻¹ and 1.80 m s⁻¹ for pedestrians with and without luggage respectively, whereas carrying luggage could increase the running speed in some cases.

3.2.2. Speed analysis in the formal experiment

The speeds of six scenarios (table 1) in the 10 m corridor are analyzed. The measurement area x ∈ [7 m, 11 m] is selected for all of the six runs for the following analysis to minimize the fluctuation in speed. Moreover, we only consider the data in a steady state, eliminating the initial and final transients.

From figure 7, the speed is 1.61 m s⁻¹ in W1 and 3.41 m s⁻¹ in R1 (ratio of luggage, r_L = 0), which is consistent with the free movement speed. Also, the speeds in W2 (r_L = 20%) for pedestrians with and without luggage are both 1.69 m s⁻¹, and those in R2 (r_L = 20%) are 3.49 m s⁻¹ and 3.46 m s⁻¹ for pedestrians with and without luggage respectively. It is indicated that r_L = 20% makes no difference to the speed of luggage-laden pedestrians. The speeds in W3 (r_L = 50%) are 1.75 m s⁻¹ and 1.78 m s⁻¹ respectively, while they are 3.26 m s⁻¹ and 3.32 m s⁻¹ in R3 (r_L = 50%) for pedestrians with and without luggage respectively. Overall, in the same scenario, the speed is similar whether carrying luggage or not.

However, we notice that the speed in walking scenarios increases with increasing amount of luggage; the speed in running scenarios first increases and then falls with the increasing amount of luggage. In order to figure out what contributes to the difference, evacuation time and density are calculated. Here, the evacuation time is defined as the time from the first person through the exit to the last one. In figure 8, we show the time series of density in the measurement area y ∈ [7 m, 11 m] based on the Voronoi method [25]. Luggage occupies space, so luggage is regarded as one pedestrian when calculating the density.

**Figure 8.** Time series of density in six scenarios.
Download figure:
Standard image High-resolution image

As can be seen from the table 2, the evacuation time grows and the density decreases in W1, W2 and W3 with increasing speed. It can be suggested that luggage contributes to a larger gap between pedestrians, which results in a lower density, greater speed and longer evacuation time. When running, the average density of R3 is 1.20 (pedestrians/m²), which is larger than those of R1 and R2. Therefore, the speeds of R1 and R2 are similar while that of R3 is less. Besides, the evacuation times of R1, R2 and R3 increase with increasing amount of luggage. We can conclude that, when running, the existence of luggage increases the evacuation time.

Table 2. Evacuation time and flow in each run.

	Walking			Running
	W1	W2	W3	R1	R2	R3
Speed (m s⁻¹)	1.61	1.69	1.77	3.41	3.47	3.29
Evacuation time (s)	10.34	12.04	14.10	7.98	8.96	10.64
Density (pedestrians/m²)	1.87	1.68	1.53	1.12	1.16	1.20

In this section, we compare the speed of luggage-laden pedestrians and those without luggage in free movement and the formal experiment. It is found that luggage has little impact on individual walking speed, which is comparable to the findings in previous studies [10]. In addition, the speed is similar in the same scenario whether carrying luggage or not. In other words, luggage influences not only pedestrians who are carrying it but also those who are not, which needs to be considered when simulating the movement pedestrians with luggage. Interestingly, it is found that luggage increases pedestrian running speed in free movement, which may be due to high motivation and needs to be further studied.

3.3. The influence of luggage on the spatial distribution

In this section, the spatial distribution is analyzed in terms of nearest neighbors, boundary distance and distance headway.

3.3.1. The distance and location of nearest neighbors

Pedestrians influence others around them during the movement, especially their nearest neighbors [26]. Therefore, in this part, the nearest neighbor distance between pedestrians in six scenarios is analyzed. By using the method of calculating the nearest neighbor distance between pedestrians in [27], the influence of luggage is discussed and presented with the quantitative ellipse parameters.

The distance and position distribution of the nearest neighbors in a steady state in the measurement area x ∈ [4.2 m, 14.2 m] are depicted in figure 9. Here, we defined the first nearest neighbor as the first person at the shortest distance, so the nth nearest neighbor stands for the nth shortest distance. We only calculate the 1st–4th nearest neighbors in this analysis. As can be seen in figure 9 the distance to the nth nearest neighbor increases and the shape becomes more circular with increasing n, especially for the fourth nearest neighbor, where the shape is close to a real circle. The first nearest neighbors are mainly to the side of the pedestrian with few in front, which indicates that the pedestrian would prefer to keep their distance from the person in front and be closer to those either side. With increasing n there are more pedestrians in front and the number to each side decreases. The running scenarios experience a more chaotic distribution and larger distances than the walking scenarios. Also, the distance for the nth nearest neighbor increases as well, and the distance between pedestrians becomes greater with an increasing amount of luggage. For first and second nearest neighbors, luggage increases the distance significantly, while for third and fourth nearest the impact becomes weak and the sphere of influence caused by luggage can be quantified by an ellipse. Here the least-squares algorithm is used to fit an elliptic curve for each condition and the result is shown in table 3.

Table 3. The parameters of the fitted elliptic curve in different conditions.

	Semi-major	Semi-minor	Area		Semi-major	Semi-minor	Area
Name	axis (m)	axis (m)	(m²)	Name	axis (m)	axis (m)	(m²)
W1-1st	0.5263	0.4154	0.6865	R1-1st	0.6459	0.5545	1.1246
W1-2nd	0.7997	0.6388	1.6041	R1-2nd	0.8550	0.8169	2.1931
W1-3rd	0.8641	0.7646	2.0746	R1-3rd	1.1068	0.9848	3.4225
W1-4th	0.9132	0.9102	2.6100	R1-4th	1.2161	1.1524	4.4005
W2-1st	0.5912	0.5609	1.0412	R2-1st	0.7163	0.6515	1.4653
W2-2nd	0.9408	0.7757	2.2915	R2-2nd	0.9887	0.8943	2.7764
W2-3rd	1.0012	0.9395	2.9536	R2-3rd	1.1421	1.1420	4.0954
W2-4th	1.0951	1.0593	3.6425	R2-4th	1.3423	1.2352	5.2061
W3-1st	0.7500	0.6873	1.6186	R3-1st	0.7809	0.7397	1.8138
W3-2nd	1.0373	0.9259	3.0158	R3-2nd	1.1098	1.0997	3.8322
W3-3rd	1.1912	1.0897	4.0759	R3-3rd	1.3448	1.2679	5.3539
W3-4th	1.3048	1.2395	5.0783	R3-4th	1.5292	1.3691	6.5740

Considering the elliptic equation

$\begin{equation}A{x}^{2}+Bxy+C{y}^{2}+Dx+Ey+F=0\end{equation} \tag{ 2 }$

the geometric center is given by

$\begin{equation}{X}_{\mathrm{c}}=\frac{BE-2CD}{4AC-{B}^{2}}\end{equation} \tag{ 3 }$

$\begin{equation}{Y}_{\mathrm{c}}=\frac{BD-2AE}{4AC-{B}^{2}}\end{equation} \tag{ 4 }$

the semi-major axis of the ellipse by

$\begin{equation}{A}^{2}=\frac{2\left(A{X}_{\mathrm{c}}^{2}+C{Y}_{\mathrm{c}}^{2}+B{X}_{\mathrm{c}}{Y}_{\mathrm{c}}-F\right)}{A+C+\sqrt{{\left(A-C\right)}^{2}+{B}^{2}}}\end{equation} \tag{ 5 }$

and the semi-minor axis by

$\begin{equation}{B}^{2}=\frac{2\left(A{X}_{\mathrm{c}}^{2}+C{Y}_{\mathrm{c}}^{2}+B{X}_{\mathrm{c}}{Y}_{\mathrm{c}}-F\right)}{A+C-\sqrt{{\left(A-C\right)}^{2}+{B}^{2}}}\end{equation} \tag{ 6 }$

Hence, it can be concluded that with an increasing amount of luggage, the distance to the nth nearest neighbor increases. For first and second nearest neighbors, luggage causes an obvious increase in distance, while for third and fourth nearest, its impact weakens. With the quantitative ellipse parameters, the nearest neighbor of a pedestrian influenced by luggage can be quantified and used as a model input to simulate the characteristics of luggage-laden pedestrians.

3.3.2. Boundary distance

Pedestrians usually keep a distance from walls when walking and running. By using the method [28] of calculating the distance to the wall, the spatial distributions of pedestrians near the left and right walls are discussed. Luggage-laden pedestrians in the experiment carried their luggage in their right hand, and as a result they are closer to the left wall while the luggage is closer to the right wall. Based on this consideration, we analyze the left and right boundary distances separately and define d_pw as the distance from the head of each pedestrian to his nearest wall in the left and right, as shown in figure 4.

d_pw of pedestrians was calculated in a steady state in the measurement area x ∈ [4.2 m, 14.2 m] as plotted in figure 10. As depicted in figure 10(a), d_pw of W1 (r_L = 0) for the left and right is similar for p = 0.4545 in the T-test, where p is the probability that the difference between samples is due to the sampling error and p < 0.05 represents a statistically significant difference. This indicates no significant difference between this pair. In other words, there is no distinction in d_pw between left and right when undisturbed by luggage. Compared with the W1 scenario, the fluctuation of d_pw in R1 (r_L = 0) is more obvious for p = 0.0006 through the T-test, which reveals a significant difference of d_pw between left and right in R1. It can be suggested that d_pw of pedestrians on the left and right in W1 are identical while those in R1 differ.

Considering that luggage does affect d_pw on both sides, d_pw of W2, W3, R2 and R3 on the left and right are plotted in figure 11. As depicted in figure 11(a), d_pw of luggage-laden pedestrians is slightly larger than that of those without luggage in W2 scenario (r_L = 20%) on both left and right, so the effect of luggage is apparent in walking with r_L = 20%. In comparison, figure 11(c) shows that d_pw of R2 (r_L = 20%) for luggage-laden pedestrians is larger than for luggage-free pedestrians on the left, and vice versa on the right.

The effect caused by luggage can be noticeably observed in W3 and R3 scenarios (r_L = 50%). On the left, d_pw of luggage-laden pedestrian is slightly larger than d_pw without luggage in both W3 and R3. In comparison, on the right, d_pw of luggage-laden pedestrians is significantly larger than that of those without luggage in both scenarios, which is reasonable because a pedestrian carries luggage in their right hand and the luggage is closer to the right wall, so d_pw on the right increases with a high ratio (r_L = 50%) of luggage. Additionally, the mean d_pw in all scenarios on both left and right are represented in table 4 and p-values are calculated. Based on the ORIGIN platform a T-test is applied to test the significance of the difference and p < 0.05 represents that there is a statistically significant difference between the samples. The detailed results of the p-values are listed in table 4.

Table 4. The mean boundary distance d_pw and p-value.

Name	Mean d_pw (m)	p-value	Name	Mean d_pw (m)	p-value
W1-left	0.4978	0.4545	R1-left	0.5220	0.0006
W1-right	0.5014	0.4545		R1-right	0.0006	0.4999
W2-left-luggage	0.4535	0	R2-left-luggage	0.5969	0
W2-left-none	0.4236	0		R2-left-none	0	0.4681
W2-right-luggage	0.5122	0	R2-right-luggage	0.4521	0
W2-right-none	0.4789	0		R2-right-none	0	0.5965
W3-left-luggage	0.5013	0	R3-left-luggage	0.5252	0
W3-left-none	0.4729	0		R3-left-none	0	0.5022
W3-right-luggage	0.6330	0	R3-right-luggage	0.5735	0
W3-right-none	0.5035	0		R3-right-none	0	0.4970

In this section, we analyze the relation between luggage-laden pedestrians and the wall. For a uniform distribution of luggage in the crowd, the movement of luggage-free pedestrians affected that of luggage-laden pedestrians, and the results in R2 scenario do not seem to be consistent. In the experiment, we found that luggage does increase the right boundary distance for luggage-laden pedestrians, because those in the experiment carried their luggage in their right hand; as a result, their right boundary distance increases, which would provide a useful suggestion for engineers designing a structure related to luggage-laden pedestrians and a wall. For example, do not place objects such as trash cans on the right side of the aisle of a traffic hub.

3.3.3. Distance headway

Distance headway is a characteristic of the spatial distribution of pedestrians that is relevant in an evacuation, especially for luggage-laden pedestrians. Previous studies found that carrying luggage could significantly increase the distance headway of pedestrians [10]. In the corridor, we observed that pedestrians on both sides prefer to move in signal-file, and the ranges are y ∈ [0 m, 0.8 m] on the left and y ∈ [2.2 m, 3 m] on the right, while the movement in the middle is a staggered distribution with the range y ∈ [0.8 m, 2.2 m]. So the distance headway of pedestrians on both sides can be calculated. it is then compared between pedestrians with and without luggage, and the result is consistent with previous studies [10]. Here, the distance headway is defined as the distance between one individual and the pedestrian in front of them. Considering the scattered distribution of pedestrians shown in figure 12, we calculate the distance headway of the measurement area x ∈ [4.2 m, 14.2 m] at the left and right boundaries and ignore the middle area; detail about the division of the three regions is shown in figure 4. The distance headway in a steady state is analyzed in figure 13. The average distance headway in the walking group increases from 1.04 m to 1.29 m as the amount of luggage increases, which is identical to previous studies. The average distance headway in R1 is 1.55 m, while those in R2 and R3 scenarios are 1.63 m and 1.59 m respectively, only a slight increase. Comparing walking and running scenarios, the distance headway in the running group increases significantly as depicted in figure 14. The distance headway rises 49.0% and 45.5% in the scenarios without luggage and with 20% luggage respectively. However, in the scenario with 50% luggage the distance headway only increases 23.3%, which shows that luggage weaken the increase in distance headway when pedestrians with a large amount of luggage run to evacuate the corridor. The reason is that, when running, the distance in R1 is large enough that the distance headway does not increase much with an increasing amount of luggage. In other words, luggage plays a key role in the distance headway of walking pedestrians, while the distance headway is an inconspicuous characteristic for running luggage-laden pedestrians.

**Figure 12.** Screenshot of pedestrian movement in a 10 m corridor. Single-file movement can be observed at the left and right boundaries and a scattered distribution in the middle.
Download figure:
Standard image High-resolution image

**Figure 13.** Distribution of distance headway in the boundary: (a) walking; (b) running.
Download figure:
Standard image High-resolution image

**Figure 14.** The distance headway in each scenario.
Download figure:
Standard image High-resolution image

Hence, it can be concluded that with an increasing amount of luggage, distance headway would increase in the walking condition. In running movement, the distance headway of R1 (r_L = 0%) is large enough that an increasing amount of luggage has little impact on it. The differing influence of luggage on distance headway should be considered when modeling luggage-laden pedestrian movement in walking and running conditions.

4. Summary

In this paper, an experiment was performed with pedestrians carrying different amounts of luggage walking and running in a straight corridor under controlled conditions. The trajectories of each pedestrian are extracted by the software PeTrack.

It is observed that all the pedestrians pushed luggage while walking and dragged it while running in free movement. Their position in the corridor, gender and speed of movement are all factors that influence the way they carry luggage. From this point of view, the influence of different factors on the way of carrying luggage should be considered when modeling luggage-laden pedestrians or optimizing traffic hubs. Meanwhile, the characteristics between pushing and dragging luggage are worth deeper analysis in the future.

As a fundamental variable in pedestrian dynamics, the speed is analyzed in this paper. By analyzing the free speed and the speeds in six runs, the detailed process of the experiment was presented clearly. Then, the reasons that contribute to the differences in speeds were discussed in terms of density and behavior. The free walking speed of pedestrians is 1.80 ± 0.15 m s⁻¹ with luggage and 1.82 ± 0.13 m s⁻¹ without, which demonstrates no obvious impact of luggage on pedestrian walking speed. The speeds of females are 1.76 m s⁻¹ with luggage and 1.73 m s⁻¹ without, while those of males are 1.83 m s⁻¹ and 1.85 m s⁻¹ respectively. It is concluded that gender makes no difference to walking when carrying luggage or not (with p = 0.64 for females and p = 0.61 for males). The average free running speed of a pedestrian is 3.83 ± 0.68 m s⁻¹ when carrying luggage and 3.48 ± 0.54 m s⁻¹ without luggage. A significant difference can be observed between running pedestrians with and without luggage (p = 0.000 through a T-test).

From the analysis of the spatial distribution of the nth nearest neighbors, it is found that the first nearest neighbor is mainly concentrated on either side and the distance to the first nearest neighbor increases with a growing amount of luggage. The distance to the nth nearest neighbor increases with an increasing amount of luggage. Luggage causes an obvious increase in distance for the first and second nearest neighbors, and less so for the third and fourth nearest.

Pedestrians unconsciously keep a certain distance from walls when walking and running. With a high ratio of luggage (r_L = 50%), the distances to the wall for luggage-laden pedestrians are larger on the right and increase slightly on the left due to the preference to carry luggage in the right hand. When modeling the movement of luggage-laden pedestrians or designing public facilities, the effect of boundary distance for luggage-laden and luggage-free pedestrians should be considered.

Quantitative values of distance headway with different ratios of luggage are provided. Besides, we found that the distance headway would increase when walking with an increasing ratio of luggage, while luggage has little impact on distance headway when running.

The results obtained from the experiments can serve as a database for model validation and calibration in pedestrian evacuation with luggage scenarios, such as at subway stations, railway stations and airport terminals. As a limitation, it should be noted that each experimental scenario was performed once by us and only three ratios of luggage are considered. It would be better to design more ratios of luggage and repeat the experiment more often for each run to get more robust results in further research. Further studies should pay more attention to completely distinguishing luggage-laden and luggage-free pedestrians to get more specific results for the former group.

Acknowledgments

The authors acknowledge the foundation support from the National Natural Science Foundation of China (Grant No. 71704168, U1933105), from Anhui Provincial Natural Science Foundation (Grant No.1808085MG217), the Fundamental Research Funds for the Central Universities (Grant No. WK2320000040, WK2320000043), Fund of China Academy of Railway Sciences Corporation Limited (2019YJ194).

Experimental study of luggage-laden pedestrian flow in walking and running conditions

Article metrics

Permissions

Author e-mails

Author affiliations

Author notes

Dates

Abstract

1. Introduction

2. Experimental setup