Study on the Performance of Upstream Obstacles Under Different Exit Loads

Abstract

Obstacles “upstream” of the exit significantly impact evacuation efficiency and deserve attention. Based on the discrete cellular automaton model, this paper studies the impact of different obstacle settings on evacuation efficiency in different emergency levels under different exit loads. Through simulation, we found that at low emergency levels, the appearance of obstacles has little impact on evacuation efficiency, while at high emergency levels, the changes in evacuation efficiency vary greatly under different obstacle settings: when the exit is relatively wide (evacuation pressure is low) and has the “faster is faster” effect, obstacles upstream of the exit reduce the evacuation efficiency, and setting obstacles directly opposite of the safety exit has the most obvious impact on the evacuation efficiency; while when the exit is narrow (evacuation pressure is high) and has the “faster is slower” effect, appropriately setting obstacles can slightly improve the evacuation efficiency. Our findings help to understand the impact of obstacles on evacuation efficiency under different exit loads to set upstream obstacles reasonably.

1. Introduction

The rapid development of urbanization (over 110 construction projects over 200 m high were completed each year in the past 10 years [1]) and the sharp increase in population (more than 8 billion by mid-2024 [2]) have made evacuation increasingly important and have also attracted extensive research, including experiments (e.g., “faster is slower” effect [3], pedestrian merging process [4,5], and evacuation under different visibility conditions [6]) and simulations (e.g., time pressure-based CA model [7], impatience-based CA model [8], natural step length fine CA model [9], and cumulative prospect theory CA model [10]). Half a century ago, researchers had already studied pedestrian traffic [11,12], but at that time, researchers mainly focused on pedestrian facilities. After years of development, the research on pedestrian evacuation has become very diverse, e.g., human behavior in fires [13], and the main purpose is to reduce pedestrian risks and ensure pedestrian safety. Among them, improving the efficiency of pedestrian evacuation is a very important direction because, in an emergency, every second is crucial to the safety of life and property [14].

Although the best way to understand evacuation dynamics and thus improve evacuation efficiency is to conduct actual evacuation experiments to guide the evacuation process and set up evacuation facilities, it is limited by ethics, safety, and funding. Fortunately, with the development of computer technology, evacuation simulation, which is not restricted by factors that limit real evacuation experiments, has become the main means to understand evacuation dynamics, conduct accident analysis, and formulate evacuation strategies [15,16,17]. Evacuation simulation models are divided into macroscopic models [18,19] and microscopic models [20,21]. Compared with the macroscopic pedestrian dynamics models that focus on overall characteristics (such as the pedestrian Macroscopic Fundamental Diagram [18]), the microscopic models focus on individual characteristics and can more accurately characterize the movement of crowds and analyze the rationality of facilities and evacuation rules in different environments, thereby reducing or even avoiding casualties caused by crowd activities. The cellular automaton (CA) model [22,23,24,25] and the social force model (SFM) [26,27] are representative discrete and continuous models in microscopic models, respectively. The CA model requires relatively less calculation than the SFM model and can also give sufficient accurate predictions [28,29,30,31]. Due to its advantages, such as high computational efficiency and strong scalability, the CA model is widely used to study the dynamics of pedestrian evacuation [32,33,34,35,36,37,38].

The CA model, which does not require the establishment or solution of complex differential equations and is very suitable for describing the evolution of simulated crowd evacuation [39], is a dynamic system with discrete time, space, and state. The discrete time is called the time step, and the discrete space is called the cell or grid. According to the cell size, the CA model can be divided into a fine grid size model [40,41,42] and an ordinary grid size model [43,44,45]. Correspondingly, it is also divided into a multi-grid model [46,47] and a single-grid model [33] according to the number of cells occupied by one person. Pedestrians move from one cell to another according to the neighborhood rule within the time step and change the states of related cells. The movement rule specifying the grids that a pedestrian may move to at the next moment is called the neighborhood rule, which mainly includes two types: von Neumann’s and Moore’s neighborhood rules. Von Neumann’s neighborhood rule stipulates that pedestrians can move up, down, left, and right in four directions (as in Figure 1a). In contrast, Moore’s neighborhood rule stipulates that pedestrians can move to the adjacent eight cells (as in Figure 1b). Moore’s neighborhood rule is considered more reasonable than von Neumann’s rule because pedestrians have a certain probability of detouring and are more likely to have eight direct neighbors than four [48]. Therefore, this paper uses the synchronously updated CA model, stipulating that pedestrians evacuate according to Moore’s neighborhood rule.

In addition, due to the diversity and heterogeneity of pedestrians, the synchronous update method is more in line with the actual evacuation process and can better reflect the competition between pedestrians during the evacuation process [36,37,49,50,51]. Moreover, the CA model is based on the discreteness of time and space and simple motion rules, and its description of the environment, pedestrian position, and behavior is not accurate enough. Therefore, many studies focus on improving the classical CA model. For example, to better describe the evacuation dynamics, some researchers have introduced psychological theories into the pedestrian evacuation process (e.g., the pedestrian aggressiveness [51], the psychological impatience theory [52]), some researchers have added pedestrians’ exploration of the environment and their interactions with each other into the model [53,54], some researchers have used different field rules in the model (e.g., the lattice gas model [22], the floor field model [50,55], and other field-based model [56,57,58]), and some researchers have made more detailed subdivisions of the time and space of the CA model [9,40,41,42]. Similar to previous studies [36,37,51], this paper uses optimized aggressiveness [37] to more accurately describe the moving dynamics.

Furthermore, it is widely accepted that ensuring unobstructed evacuation routes is a fundamental requirement for efficient evacuation. However, some researchers [59] argue that strategically placing obstacles on the “upstream” side of safety exits can enhance evacuation efficiency and increase the chances of a successful escape. They propose that in emergencies with high crowd density and limited evacuation time, pedestrians tend to become impatient, increasing expected movement speed and competitive pushing behaviors. By placing obstacles at the exit, the physical pressure exerted by the dense crowd can be absorbed, preventing congestion near the exit and improving overall evacuation efficiency. Subsequent actual evacuation experiments [60,61,62] and simulation studies [63,64,65,66,67] have explored the impact of obstacles near safety exits on evacuation efficiency. However, ongoing debate remains regarding the effectiveness of such obstacles [68]. In our previous study [69], based on actual experiments with the “faster is slower” effect, we simulated the impact of obstacles upstream of the exit on evacuation efficiency and found that under narrow exit conditions, some settings can improve evacuation efficiency. In this paper, we consider the pedestrian aggressiveness and the friction between pedestrians, which can more accurately describe the psychological dynamics of pedestrians and deal with the competition that occurs during the movement of pedestrians [37], verify the model based on actual experiments with the “faster is faster” effect, and study the performance of obstacles with different forms at the exit under different exit loads.

The paper is structured as follows: Section 2 introduces the related parameters, Section 3 conducts the model validation and analysis, and Section 4 provides a summary, discussion, and future work.

2. Model

This section will detail the relevant parameters and update rules of the synchronous update CA model considering pedestrian aggressiveness, including static floor field, pedestrian aggression, friction coefficient, moving speed, update rules and conflicts.

2.1. The Static Floor Field and the Probability of Selecting the Target Cell

The cellular automaton model divides the space into individual grids, each of which can be empty, occupied by pedestrians, or obstructed by obstacles. Only one pedestrian can occupy a grid at a time. Based on the location and characteristics of these grids, different potential field values are assigned. These values include static floor field values, which are determined by the physical environment of the evacuation space and generally remain constant over time. The potential field values guide pedestrians towards areas with higher safety levels, such as safe exits, based on the environmental conditions. The complete potential energy field with a specific static floor value is referred to as the static floor field. To obtain the static floor field, this study employs a dual-track iterative weighting method, similar to the previous research [36,37]. The weight formula for calculating the final floor field value of a cell $\left(i, j\right)$ is as follows:

$$S_{i,j}=ϵV_{i,j}+\left(1-ϵ\right)M_{i,j} \left(0\le ϵ\le 1\right)$$

(1)

The figures illustrate the basic static floor field values $V_{i,j}$ (shown in Figure 2a) and $M_{i,j}$ (shown in Figure 2b), obtained using von Neumann’s neighborhood rule and Moore’s neighborhood rule, respectively. The weight parameter $ϵ$ determines the influence of $V_{i,j}$ in the final static floor field. In Figure 2, green cells represent safe exits, blue cells represent obstacles, and the number in each cell represents the static floor field value. The value “Inf” represents infinity, indicating that pedestrians cannot occupy those cells due to the presence of obstacles. In this study, we assign equal weight ($ϵ=0.5$) to both $V_{i,j}$ and $M_{i,j}$, resulting in the final static floor field shown in Figure 2c.

During an evacuation, pedestrians typically aim to reach the safe exit as quickly as possible, maximizing their benefit at each step. This principle aligns with the cellular automaton (CA) model, where pedestrians are more inclined to select cells with lower static floor field values as their target cells at each step. The probability of a pedestrian choosing cell $\left(i, j\right)$ as their target cell can be determined using the following equation [36,37]:

$$P_{i,j}=N·\mathrm{e}\mathrm{x}\mathrm{p}\left[{-K}_S·\left(S_{i,j}-S_{min}\right)\right]·\left(1-{\delta }_{i,j}\right)·{\lambda }_{i,j}$$

(2)

where $N$ is a normalization factor, $K_S$ represents the sensitivity of pedestrians to the static floor field, and $S_{i,j}$ denotes the static floor field value of cell $\left(i, j\right)$. $S_{min}$ corresponds to the minimum static floor field value of the cell that the pedestrian can move to in the next time step. ${\delta }_{i,j}$ and ${\lambda }_{i,j}$ indicate whether cell $\left(i, j\right)$ is occupied by another pedestrian or obstacle. If the cell is occupied by another pedestrian,${\delta }_{i,j}$ is set to 1, and if it is occupied by an obstacle, ${\lambda }_{i,j}$ is set to 0.

2.2. Aggressiveness and Conflict Resolution

Pedestrian aggressiveness represents the manifestation of pedestrians’ inclination to secure limited resources, such as evacuation space, during the evacuation process, influenced by internal and external factors. The level of aggressiveness tends to increase in more urgent situations. In this study, we adopt an optimized approach to determine pedestrian aggressiveness, taking into account the specific circumstances of the pedestrians [68,69,70]. The formula for calculating the optimized aggressiveness is as follows [36,37]:

$${\dot{r}}_{l }={{\delta }_l}^{{\displaystyle \frac{1}{\lambda }}}{·P}_{i,j},$$

(3)

The perception of the surrounding environment and other pedestrians by pedestrian $l$ is denoted by ${\delta }_l$, which ranges from 0 to 1. A higher emergency level corresponds to a larger value of ${\delta }_l.$ The parameter $\lambda$ adjusts the growth rate of aggressiveness, and $\lambda >0$. $P_{i,j}$ represents the normalized value of the probability that pedestrian $l$ selects cell $\left(i,j\right)$ based on Equation (2). Following the approach proposed by Hu et al. [51], the pedestrian’s speed is influenced by the emergency level, which is controlled by the perception of the environment $\delta$. The formula for speed change is as follows:

$$v_l=v_0+R\ast {\delta }_l\ast v_0,$$

(4)

where $v_0$ and $v_l$ represent the normal speed and competitive speed of pedestrians, respectively. In our study, we set the normal velocity to 1 m/s (as in previous research [36,51]) and the competitive velocity to 2.62 m/s (representing slow-running velocity [60]). The velocity increase ratio, denoted as $R$, is calculated as 1.62 ($\left(2.62-1\right)=1.62$) in this case.

Pedestrians exhibit diversity and heterogeneity, and the synchronous update method aligns better with the real evacuation process. It accurately reflects the competition among pedestrians during evacuation and is widely employed in CA models [36,37,49,50,51]. However, conflicts arise when multiple pedestrians select the same target in models that use synchronous updates. To address this issue, we utilize an optimized aggressiveness approach based on the “friction” concept introduced by Kirchner et al. [70] and the friction function equation proposed by Hu et al. [51]. This allows us to determine whether conflicts can be successfully resolved, as outlined below:

$${\varphi }_{\mu }={\left({\displaystyle \frac{{\sum }_{l=1}^k{\dot{r}}_l}{r_{max}}}\right)}^{\mu }$$

(5)

where $\mu$ representing the allowable conflict coefficient, is the parameter opposite to friction that determines the likelihood of resolving conflicts during the evacuation process. A larger value of $\mu$ indicates a higher probability of successfully resolving conflicts and, consequently, a smoother evacuation process. Parameter $k$ represents the number of pedestrians involved in a single conflict, and $r_{max}$ denotes the maximum possible aggressiveness, which is set to 5 in this study. Although, based on Moore’s neighborhood rule, up to eight pedestrians can potentially move to an unoccupied grid, the probability of more than five pedestrians selecting the same grid as their target is almost negligible.

The resolution of conflicts occurs with a probability of ${1-\varphi }_{\mu }$, where ${\varphi }_{\mu }$ is the probability of unsuccessful conflict resolution. If conflicts are not successfully resolved, none of the pedestrians involved can reach their target cell. Equation (6) (as defined in previous research [36,37]) is used to determine the winning pedestrian after conflict resolution. The selection is based on the optimized aggressiveness of all pedestrians involved in the conflict, with a higher aggressiveness corresponding to a greater probability of movement, as follows:

$$p_l={\displaystyle \frac{{\dot{r}}_l}{{\sum }_{j=1}^k{\dot{r}}_j}}$$

(6)

3. Simulation and Analysis

The model’s parameters are determined through simulation and comparison with actual evacuation experiment results. We compared the simulation results without obstacles with the experimental results without obstacles in the experiment conducted by Shi et al. [60] and adjusted the model parameters.

As shown in Figure 3, the actual experimental evacuation scene is a square room with a side length of 8 m, including a two-meter waiting area and a safety exit width of 1.2 m. Fifty students from different grades and colleges were recruited to participate in the experiment. Their average shoulder width was 42 cm, ranging from 32 to 58. The average speeds of normal walking and slow running were 1.31 and 2.62, respectively, ranging from 1.09 to 1.78 and 2.02 to 3.22, respectively, and the average time to evacuate from the safety exit was about 16 s and 12.5 s, respectively.

The model’s cell size is 500 mm (the shoulder width is 42 cm). After 50 pedestrians are added to the model, the scenario is shown in Figure 4, in which green cells represent the safety exit, blue cells represent the walls, and red circles represent pedestrians who will evacuate from the waiting area and leave the room through the safety exit. The net space size is 8 m × 8 m (16 × 16 cells), including a waiting area of 8 m × 6 m (16 × 12 cells) and a blank area of 8 m × 2 m (16 × 4 cells), which corresponds to the actual evacuation experiment.

Then, we conduct evacuation simulations and adjust the coefficient $\mu$, the weight parameters $K_S$ of the static floor field, and the coefficient of the aggressiveness $\lambda$ based on the actual experimental results. Through repeated simulations, the coefficient $1/\lambda$ (the larger $1/\lambda$ is, the less aggressive the pedestrians are under the same circumstances, the greater the probability of successfully resolving the competition between pedestrians, and the shorter the overall evacuation time) is determined to be 3 and parameter $K_s$ (the larger $K_s$ is, the more persistent the pedestrians are in reducing the static field value, which will increase the evacuation time when aggressiveness is greater and the allowed conflict coefficient is smaller, and vice versa) is determined to be 10. The pedestrian’s initial perception of the environment increases from 0 to 1 with a step size of 0.1. Each situation is repeated 100 times, and the change in evacuation time with different perceptions under different allowable conflict coefficients is shown in Figure 5.

The pedestrian’s perception of the environment is 0, which means it is completely non-aggressive. At this time, no matter what the allowed conflict coefficient is, the conflict can be successfully resolved. Therefore, under different allowed conflict coefficients, the average evacuation time of perception of 0 is the same; therefore, we did not show this in Figure 5. When the allowed conflict coefficient is very small (0.01), the average evacuation time first decreases and then increases with the increase in the pedestrian’s perception of the environment (aggression), that is, the “faster is faster” effect first, and then the “faster is slower” effect, but at a larger allowed conflict coefficient (greater than 0.2), the pedestrian evacuation time shows the “faster is faster” effect. In addition, when the allowed conflict coefficient is greater than or equal to 0.6, the average evacuation time under the same perception is very close, indicating that the conflict is well resolved, and the continued increase in the allowed conflict coefficient has a very slight impact on the evacuation time. After comparison, the permissible friction coefficient was selected as 0.2. The pedestrian walking state (speed is 1.32 in the actual experiment) corresponds to the situation where the perception is 0.2 in the model, and the average simulated evacuation time is 15.8 s (16 s in the actual experiment). The pedestrian jogging state (speed is 2.6 in the actual experiment) corresponds to the situation where the perception is 1 in the model, and the average simulated evacuation time is 12.2 s (12.5 s in the actual experiment).

After the model parameters were selected, we set obstacles of different shapes, locations, and numbers upstream of the emergency exit and repeated each condition 100 times to study the impact of obstacles on the evacuation efficiency. Due to the nature of the grid discretization in the cellular automaton model, the size of the obstacle and the distance from the emergency exit can only be an even multiple of the grid size (500 mm). Firstly, we consider the evacuation situation when the obstacle is one grid away (0.5 m) from the safety exit, and the obstacle setting is shown in Figure 6. Each situation is repeated 100 times, and the 95% confidence interval of the evacuation time is shown in Figure 7.

Regardless of whether pedestrians evacuate to the emergency exit by walking or slow running, the presence of obstacles prolongs the average evacuation time, resulting in a decrease in evacuation efficiency. The presence of obstacles has a very small impact on evacuation efficiency when pedestrians are walking but has a very large effect on jogging (evacuation efficiency is greatly reduced). In addition, when pedestrians evacuate to the emergency exit by walking, the effects of the four obstacle arrangements in Figure 6 on the average evacuation time are almost the same; however, when pedestrians evacuate to the emergency exit by slow running, the decrease in evacuation efficiency is most serious when the obstacles are arranged as shown in Figure 6c, around 24.6%.

We continue to set the obstacles to two grids away from the exit (as shown in Figure 8) and study the obstacles’ impact on the evacuation efficiency. Each situation is repeated 100 times, the 95% confidence interval of the evacuation time is shown in Figure 9.

As can be seen from the figure, for obstacle settings a and b, regardless of whether the pedestrians are walking or jogging, the appearance of obstacles does not increase the evacuation efficiency or shorten the average evacuation time, similarly to when the obstacle is set at 0.5 m from the safety exit. However, for settings c and d, obstacles have little effect on the evacuation time when walking. Among the four obstacle settings, the evacuation efficiency is relatively high under the settings of d (about 17.0% lower), the evacuation efficiency of setting a is the lowest, and the reduction in evacuation efficiency is most obvious (about 32.1 lower) when jogging. We continue to change the obstacles to both sides of the exit, as shown in Figure 10. Each situation is repeated 100 times, the 95% confidence interval of the evacuation time is shown in Figure 11.

As can be seen from Figure 11, among the four obstacle settings, setting c has the highest evacuation efficiency. When pedestrians are walking to the exit, the four ways of setting obstacles have a very slight impact on evacuation efficiency, within 1%. When pedestrians are slow-running to the exit, the evacuation efficiency will be greatly reduced regardless of the setting, ranging from 15.8% to 18.5%.

In general, when the load of the emergency exit is small (two grids for 50 people), and therefore the congestion at the exit is small, the setting of obstacles has a very small effect on the evacuation efficiency of walking but a very large impact on the evacuation efficiency of jogging. Next, we studied the effect of obstacles on the evacuation efficiency when the exit load is large (the exit occupies only one cell). We first study the situation when the obstacle is set on the opposite of the exit, as shown in Figure 12. Each working condition is repeated 100 times, and the 95% confidence interval of the evacuation time is shown in Figure 13.

As shown in Figure 13, under the walking condition, the evacuation time under the three obstacle settings is almost the same as when there is no obstacle, but under the slow running condition, the evacuation efficiency is the lowest under setting a, which reduces the evacuation efficiency by 17.4%, followed by setting c, which reduces by 3.6%, and the obstacle setting b slightly increases the evacuation efficiency, by about 4.3%. This shows that when pedestrians evacuate by walking, obstacles have almost no effect on the evacuation efficiency, but when pedestrians evacuate by jogging, obstacles that are farther or harder will reduce the evacuation efficiency, while obstacles at an appropriate distance can increase the evacuation efficiency. We continue to change the obstacles to both sides of the exit, as shown in Figure 14. Each situation is repeated 100 times, the 95% confidence interval of the evacuation time is shown in Figure 15.

Figure 15 shows that when pedestrians evacuate by walking, settings a and b slightly reduce the evacuation efficiency, while settings c and d slightly improve the evacuation efficiency. Overall, the change is very slight, within 3.4%. However, when pedestrians evacuate by slow running, obstacle settings a and b significantly reduce the evacuation efficiency, reaching a maximum of 15.5. Setting c has almost no effect on the evacuation efficiency, and setting d slightly increases the evacuation efficiency by about 4.42%.

4. Discussion and Conclusions

This paper uses a cellular automaton model that considers pedestrian aggression and friction conflicts, which is more realistic than the traditional floor field CA model and more convenient than the social force model, to study the impact of obstacles on evacuation efficiency and analyze the changes in evacuation efficiency under different settings. In addition, the width of the emergency exit is adjusted to study the impact of obstacles on evacuation efficiency under different emergency exit loads. The findings are summarized as follows:

• The upstream obstacles have a small effect on the evacuation efficiency in the low emergency level (walking), but greatly affect the evacuation efficiency in the high emergency level (slow running).
• When the exit load is low, and the “faster is faster” effect exists, the appearance of obstacles will seriously reduce the evacuation efficiency under high emergency levels, and the obstacles placed directly opposite to the emergency exit will reduce the evacuation efficiency more than those placed on both sides of the emergency exit.
• When the exit load is high, and the “faster is slower” effect exists, placing obstacles directly opposite to the exit, both close (Figure 12a) and far away (Figure 12c), will reduce the evacuation efficiency. The evacuation efficiency can be improved by placing obstacles at an appropriate distance (Figure 12b).
• When the exit load is high with a “faster is slower” effect and obstacles are set on both sides, only the obstacles set in the middle position with a longer shape (Figure 14d) can slightly improve the evacuation efficiency.

This paper studies the impact of different obstacle settings on evacuation efficiency under different emergency levels in combination with pedestrian aggressiveness. Through simulation, it is found that when the evacuation pressure of the exit is low, setting obstacles upstream of the exit cannot improve the evacuation efficiency, but when the evacuation pressure of the exit is high, setting obstacles reasonably can improve the evacuation efficiency. This is mainly because when the evacuation load is low, there will be no serious congestion near the safety exit, and the obstacles will hinder the smoothness of the evacuation. Meanwhile, when the evacuation load is high, there will be serious congestion near the safety exit, and the reasonable setting of obstacles can reduce the number of pedestrians involved in a conflict, thereby better resolving the conflict and making the evacuation smoother. Our results are consistent with previous simulation and experimental studies, that is, obstacles at the exit do not always improve evacuation efficiency but depend on their location and size [60,71], and depend on the shape of the obstacles according to our simulation. Our finding that obstacles have little effect on evacuation efficiency under low competition conditions is somewhat different from the researchers’ belief in the literatures [72,73] that obstacles (columns) can also play a beneficial role under low levels of competition (normal conditions), which requires further research.

However, the setting of obstacles is a challenge for people with limited mobility and existing building regulations, which also needs to be considered comprehensively. In addition, only a single case of low load and high load was discussed, but we believe that the form of obstacle setting that increases or decreases evacuation time has a certain universality. We believe that if the congestion at the exit is serious, it can be classified as a high load, and if the congestion at the exit is not serious, it can be classified as a low load, but this requires more research to demonstrate. Although our findings are meaningful, there are also some shortcomings. Firstly, due to the discrete rules of cellular automaton, the shape and size of obstacles are severely restricted, both of which are even multiples of the grid, and the impact of other obstacles on evacuation efficiency is not studied. Secondly, this paper does not consider the effect of obstacles on evacuation efficiency when the emergency exit is in other locations, like the edge of the side. Thirdly, we only considered pedestrians at normal speed (1 m/s) or jogging speed (2.6 m/s) and did not consider other speeds. While in real evacuations, speeds are diverse. Although there are certain limitations, our findings help to understand the impact of obstacle placement on evacuation efficiency under different situations.