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Experimental investigation of alleged influences of social diversity on single file pedestrian fundamentals derived from comparative analyses

In pedestrian dynamics, density and speed are related to each other and can be analyzed quantitatively. Even the simplest systems, such as pedestrian streams in corridors, still have some deficiencies in the detailed understanding of this fundamental relationship. There are significant differences between textbook specifications and measurements taken under different experimental conditions, as evidenced by literature reviews. This contribution aims to explore alleged social diversities influences on speed-density relation, speed-headway, and flow-density relation corridors as possible causes of deviations. Consequently, it is the simplest system because it has the fewest degrees of freedom. A closed boundary condition is involved in this system, where pedestrians walk along a line. Chinese test subjects' speed is less affected by density than Ghanaians’ test subjects' speed. Surprisingly, the data analyzed indicated that the Chinese make more progress than Ghanaians due to their more random behaviour. Their different organizational styles may be the reason. It is not possible to tell if there is any difference without comparing statistical measures. This hypothesis test indicates quantitatively that there is a difference in pedestrian fundamentals, indicating the alleged social diversity influences walkers.


Introduction
Analyzing pedestrian dynamics and their impact on human safety has been studied in several studies(1)(2)(3)(4) (5). To maximize crowd control and plan facilities, a complete understanding of pedestrian dynamics is essential, In general, most crowds of people are composed of people who share a common interest and are gathered for cultural or recreational reasons. Despite a lack of much interest in studies on cultural groups' impact on pedestrian dynamics, some have studied how individual difference affects pedestrian dynamics(2)(6) (7).
Culture refers to the way of doing life and it involves the knowledge and characteristics of people including customs, arts, beliefs, societal habits, and laws. People obtain cultural patterns through a learning procedure of socialization and enculturation which is portrayed by the difference of cultures across the diverse communities; because cultural differences don't bring separation in the society, but instead, cultural diversity creates collective power which could benefit all humanity (8). A cultural norm dictates acceptable behavior in the society; it provides a guideline for conduct, language, dress code, and character in a particular situation which creates a code of expectations in a certain social group. When a particular group of people accepts a monoculture only, it's very risky; the same way a certain species withers and fades when faced with climatic changes, due to a lack of operational response to that change (9).
The way fundamental diagrams (FDs) are originally conceived is to define the link between three factors: the density (unit of persons m -2 ), the speed (ms -2 ), and flow (10)(11) (12) (13) (14). The FDs were initially developed to define the link between three factors. In (15), it is explained that FDs are useful for describing pedestrian flows and densities and are related to numerous self-organising occurrences in crowds, including pedestrian alleys and congestion, where people can be observed to stop moving in the crowd when the density of people is high enough. FDs have been discussed from a cultural perspective before. Divergent cultures and populations can also affect the flow, density, and speed of people (7)(16)(17)(18) (19).
In this study, (20) (21). The present study examined Hofstede's dimensions of culture (22) and proposed a method for analyzing videos according to the dimensions of Hofstede's theory of cognitive dimensions (20) and a method for analyzing crowd culture by applying the five-factor model to video collections. Use of pedestrian tracking (20) (21). The geometric representation of geometric features such as speed, angular variation, and distance allows them to be related to dimensions (23).
By comparing the results of FDs among two countries, China and Ghana, we hope to investigate the alleged cultural differences in people that can affect crowds. In order to simulate crowds, we will use this information based on differences across cultures. The FD is chosen based on the fact that the populations undergo the same task in the same controlled environment with the same number of individuals. Currently, a difference in social beliefs is evident in the diverse mindsets between the old and the young, as well as rural and urban dwellers. The older population and people in rural areas tend to uphold, value, and preserve traditional culture; while on the other hand, people in the city and Chinese youths tend to be more enthusiastic and open to progressive ideologies.
Civilization begins with walking, one of man's most valuable skills (7). The most common way humanity has moved throughout history has been by walking. For thousands of years, walking was the only mode of transportation. Researchers continue to conduct large-scale studies on the development of faster and safer modes of transportation, like walking.
Concerning the cultural aspect, the speed-density relationship (or fundamental diagram) illustrations are very enthusiastic. Different shapes have been obtained for the fundamental diagram by researchers doing experiments in different cultures (17). People of different cultures walk differently, as this observation indicates. Across all pedestrian groups, (24) (2). Pedestrian speeds in Asian 3 countries are slower than in western countries. According to(4), Singaporeans' walking speeds are slower than Americans' but their flow rates are higher than those in western nations. (4)(5) points out the importance of reforming pedestrian design standards and integrating Western standards into this process. The pedestrian flow characteristics in Hong Kong are different depending on the type of walking facility, according to (25). According to (17) (26), the behavior of Indians may be considered more like that of Middle Easterners. Having studied pedestrian movement across cultures (German and Indian), (26) concluded that density had less of an effect on the speed of Indian test subjects than that of German test subjects. Remarkably, Indians are more disorganized than Germans. According to (19), pedestrian flow in different cultures differs significantly from the fundamental diagram.
The main purpose of this work is to investigate the impact of putative social diversity in pedestrian movement in a single-file fundamental between the two countires, namely China and Ghana, using video recordings to automatically and manually extract the data, we have studied how pedestrian composition affects their movement characteristics, which are based on factors such as density, speed, path distance, taking into account gender, culture, and age. The results of our experiments with mixed-gender grous in Ghana were compared with similar conducted elsewhere particularly in China using single-file movement experiments (27). As part of our plan, we intend to use the quantities of pedestrian movement, like speed changes and headway changes at different density levels (17) India(7)(2), China(28) (29), and Palestine(6)By analyzing these data, one can determine whether these parameters differ between cultures, such as flow, speed, and headway.

Designed Experiment
An experiment involving a senior high school in the upper west region of Ghana was conducted in 2021. Figure 1 The scenario and the experiment are illustrated in the following image. The closedloop corridor has a principal circumference of 25.7 meters made up of two straight 5m sections and two semicircles. (28) (27) (29). To prevent overtaking during movement, the corridor was determined to be 0.8 meters wide. About 140 volunteers from Wa senior high school (ages between 17-and 24 years old) and 20 teachers from the school (ages between35-and 45years old) participated in the test. Findings from the study are illustrated in table 1. A total of 24 runs were conducted with the different types and numbers of participants (6 runs with male volunteer groups; 6 runs with female volunteer groups, 6 runs with mixed groups of males and females volunteers, 2 runs with teachers, and 4 runs teachers and volunteers mixed) in the corridor. The ratio of volunteers in the mixed group was 1:1 in each run, with the volunteers being alternated with the teachers in the corridor. All participants received the same instruction throughout each run. To collect more data, especially under steady-state, and ensure that the results are repeatable and meaningful, they were asked to walk for at least 3 minutes in a normal manner without overtaking. Taking into account the different numbers N of pedestrians in each run, the global densities = ⁄ , 0.39 to 2.28m -1 were the ranges for volunteers and the same thing applied to the teachers and the mixed group because all the setup was the same number of pedestrians N = 10, 20,30, 40, 50 and 60. During the experiment, we occasional stop to allow volunteers and teachers to rest for safety reasons.

Fig. 1. Snapshots of the experiment (i) and (ii) representing Chinese and Ghanaians respectively
The experimental setup and measurement method for the Chinese study is identical to the one for the Ghanaians study; the only difference is the composition of the participants. manual and automatic extraction of the data (7), were used for both experiments. The adult ages were between 35 to 45, but that of the young ones was identical (28). There were 152 to 180cm in height across the participants, with the most average height at 165cm.

Data Gathering
On the 3rd floor of a building, digital video cameras were mounted to collect pedestrian trajectories for the experiment. The video data were used to obtain information about time, speed, and density. We automatically and manually extracted pedestrian trajectories from the video recording (7). In addition, the trajectory data were corrected manually for the entire experiment. Twenty-five frames per second (25fps) were used to collect the trajectory data. In the observation section, the speed of individuals is determined in the following way as referring (7): Where p is the observation section, is the points speed of the individual, is time out and is the time in. Now, average density, but we have to find the density in a frame . Which is also global density that is equation (1). = ⁄ , We know to be pedestrians number in the frame, denotes length of the observation section.
Now to find from it will be: In the equation is total frames number (25) (7), is the density that exhibits a smooth distribution while , due to the classical definition, shows strong fluctuations. As for both the Ghanaian (left) and Chinese (right) cases, there are three distinct segments: the initial segment, the fixed segment, and the finish segment, when participants complete the process.
The procedure consists of three segments: the initial, the fixed segment, and the finish segment. In the initial segment, the pedestrian starts walking and both the velocity value and the variation of the velocity differ from the fixed segment. While the Chinese data fluctuate less than the Ghanaians data in the fixed segment, the Ghanaians data fluctuate more, indicating a more disordered movement. After the corridor is opened and people leave the corridor, the finish segment begins, characterized by higher velocities. We focus our analysis on the fixed segment.

Pre-processing of the data
Global density is used to calculate = ⁄

The speed-density relation across gender
The physiological and physiological characteristics of males and females differ in terms of size behavior, and behaviourally reactions (32).      Table 3 shows density-velocity relation statistics Headway space personal space personal space Figure 7 shows a sketch of pedestrian keeping specific distance from the other pedestrians.

Figure 6 Illustrating Density-velocity relation comparison between female group (FG) and Mixed group (FMG) experiments and male group (MG) with a mixed group (FMG)experiments at different densities
We also studied the 'Headway' movement characteristic here. A sketch in figure 7 shows a pedestrian keeps a specific distance from other pedestrians while walking to ensure that he or she can move forward. This movement is analysis in Figure 8.  (a) Density-headway (b) Velocity-headway Figures 8 (a) and (b) show headway density relation and velocity and headway relation with different gender groups Chinese while in Ghanaians the range is 0.51 to 0.62ms −1 . The density ranges for N = 40 in Chinese are 0.26 to 0.32m -1 , while in Ghanaians they are 0.21 to 0.28m -1 . Hence, the differences. Although the Chinese composition of subjects is more homogeneous than that of Ghanaians, the ratio between individual passage times and distances to neighbouring subjects is higher in the Chinese. According to the video recordings, this is the case. Ghanaians also appear to have a faster change in velocity with density changes (between 1 and 2m -1 ) than the Chinese when densities are medium to high. It should also be noted that neither in Chinese nor in Ghanaians is the relationship between density and velocity linear, as shown in Figure 10. In contrast, the density-velocity relationship (h) and velocity (v) shown in Figure 9 is more likely to be linear. To better understand this phenomenon, the h-v data for the two countries (China and Ghana) were obtained using linear fitting relationships and numerous hypotheses about the projected coefficients were tested.

A comparison of the speed-density relationship across cultures
The individual mean density and velocity for Ghanaians and Chinese pedestrians were calculated.
According to mixed group (FMG) experiments, Ghanaians walk more slowly than Chinese pedestrians as shown in Figure 8, with an average speed of 0.781ms -1 to 0.963ms -1 when there is low dense and 0.134ms -1 to 0.202ms -1 with high dense, as compare to the Chineses of 0.99ms -1 to 1.035ms -1 and 0.187ms -1 to 0.233ms -1 respectivly. The analysis revealed that Ghanaian pedestrians walk in low densities faster than Chinese pedestrians, the Chinese however walk in high densities in mixed groups faster than the Ghanaians. Based on our assumptions, these differences were caused by the alleged social diversity influence and social conventions that determined pedestrian comfort zones. A comparison of groups of different ages from different cultures, (28)According to this study, people's walking movement is influenced not only by their age but also by social diversity factors. Figure 10 illustrates the headway-velocity relationship for different age compositions. In comparison to Ghanaians pedestrians and Chinese pedestrians, when the velocity increases, walk with more visible headway(28)(6). Further, we can observe that the Ghanaians and Chinese walk at the same speed at a density equal to 1.3m -1 , and that when velocity is less than 0.7ms -1 , they walk at the same speed. Ghanaians pedestrians have a shorter headway than the Chinese pedestrians when walking at speeds above 0.5ms -1 . Therefore, younger pedestrians walk with shorter headways and this varies depending on the alleged social diversity in the area.   h=0.31+1.14*v h=0.29+1.04*v Figure 10.

Illustration of density-velocity distance relations and velocity-headway and their statistics analysis between Chinese and Ghanaians in table 8 below with details linear fitting and linear relation for headway-velocity ℎ = +
where ℎ is the headway, is the intercept, . is the slope and is the velocity.

Speed-distance headway relation across culture
An analysis of the Chinese and Ghanaians data is carried out using this equation ℎ = + which is fitted for analysis (7). Table 4 shows the values of and for the Chinese and Ghanaians data and Statistics are also provided. Lines fitted to the data are also displayed, along with other statistics shown in figure 10. According to t-statistics values and 2 values are displayed in where is the critical value, and represent Chinese and Ghanaian respectively, and and are the standard error for the data from Chinese and Ghanaians in China. As a result, the jam density in China seems higher than that of Ghana. Figure 11. illustrate the walking pattern with pedestrians under different situation.
It is necessary to have some space in front of you when walking. It is the space in front of the path that determines the speed of the voyage, and it is also the space that determines the number of pedestrians that can pass a place in a given time.

Effect on the corridor length
This graph displays headway distance (h) and speed (v) in Ghana's closed corridors of different distances = 25.7m and 34.5m in Figure 11. The double-length corridor needs to be constructed at comparable densities, we selected N = 10, 20, 30, 40, 50, and 60 test subjects for the fitted relation table 6 shows values for , , and 2 . Hypotheses tests comparing intercepts and slope terms between the short and long length sections did not show significant differences. Therefore, the distance of the corridor has no significant influence on headway-velocity relations.  Table 6 shows the statistical analyses of the relationship in different lengths of the corridor.

Conclusion
Specifically, we examined the composition and dynamics of pedestrian crowds in this study. Both genders were considered in this study. To understand the correlation between different pedestrian characteristics, we manually calculated speed, density, and headway in each experiment and analysis the data using originPro21 software (linear fitting) and statistics (t-test and z-test). The gender, culture, and age differences in single-file movement experiments between Chinese and Ghanaians were examined, Our study found that gender doesn't affect pedestrian movement when both men and women are present (average velocity is 0.45±0.1ms −1 ) But when mixed groups are included, the velocity changes. When mixed-gender pedestrians walked together, their velocities began to slow because of social conventions. Furthermore, mobility is different in different cultures. With a density of 0.623 ±, 0.02m -1 Ghanaians walk slower with a velocity of 0.926± 0.1ms -1 for the same density as Chinese pedestrians, and their personal space needs are smaller. Additionally, we also discovered that the age factor can influence pedestrian dynamics. Elderly individuals walked slower when densities differed. Comparable older Chinese pedestrians were faster than younger Ghanaians in densely populated areas. There are several interesting and important facts that these results have revealed about how gender influences pedestrian movement: it is generally believed that female pedestrians move differently than male pedestrians because of socio-cultural influences. This assumption cannot be confirmed by our study, as female and male participants exhibit the same macroscopic features. The need for more experimental data is expected in the future for work on lower and higher densities for both males and females in different age compositions and different countries especially in Africa where we have different cultural beliefs.