Simulation investigation on crowd evacuation strategies for helping vulnerable pedestrians at different

In emergencies


Introduction
Pedestrians are faced with the risk of natural, man-made and hybrid disasters.In these emergencies, evacuation is one of the essential ways to handle these situations by moving pedestrians to safe places [1].However, inappropriate pedestrian management and evacuation strategies may have adverse consequences.For example, It is reported that on average each year more than 2000 people lost their lives in large crowd disasters [2].Therefore, the development of appropriate and efficient evacuation strategies is crucial for disaster responses and crowd safety.
Extensive research has been conducted to develop evacuation strategies through modelling and experiments.Instead of seeking to develop models that can reproduce pedestrian behaviours in the real world, simulation research on evacuation strategies usually employs well-established pedestrian dynamic models.Agent-based models and network models are typical pedestrian dynamic models.Agent-based models (e.g., social force models [3]) assume each agent moves and interacts with others based on a set of rules, making them flexible to investigate the effects of different strategies and intervention measures on individual and crowd dynamics induced from induvial interactions.Previous studies have established how evacuation efficiency can be improved by optimal exit layouts [4], use of horizontal and vertical pedestrian facilities [5,6], and route choice strategies such as least distance path choice and least travel time path choice [7,8].In contrast, network models describe the environment as a network where each node represents an intersection point, and each edge, that links nodes, represents the space pedestrians walk through.By doing so, the optimisation of evacuation strategy can be formulated as a network design problem and researchers develop optimal evacuation strategies by minimising or maximising an objective function (e.g., the total evacuation time or to maximise the number of evacuees reaching safety within a given time frame) under a set of constraints [9].Many strategies that can improve the efficiency of the evacuation process have been identified in evacuations with mixed transportation modes such as reversing lanes in the direction of evacuation [10], staging the evacuation process [11], optimally controlling traffic [12], and providing route guidance to the evacuees [13].Moreover, many evacuation systems that can dynamically develop evacuation plans have been established to guide pedestrian evacuation in various disaster scenarios including building fires [14], hurricanes [15] and floods [16].
Compared to simulation studies, while most experiments on pedestrian evacuation do not directly test the effectiveness of evacuation strategies, it is still possible to gain insights into the measures that can be taken to improve evacuation efficiency, such as appropriate route properties [17], use of wayfinding signs [18], optimal emergency sign design [19], and the use of leaders guiding pedestrian movements [20].Due to the difficulty in conducting experiments with human participants, these experiments usually involve small-scale scenarios such as evacuations in buildings [17,20] and tunnels [18].
However, previous research has suggested that the effectiveness of evacuation strategies in improving crowd evacuation is highly context dependent.For example, some studies suggest that placing an obstacle in front of exits can improve pedestrian flow in evacuations [21,22], but experimental results indicate it can only work effectively in high-density scenarios [23].Simulations on network models also reveal that no one evacuation strategy can be considered the optimal one across different network structures and the strategy performance depends on network properties and population density [24].
In terms of crowd populations, previous studies usually consider pedestrians as individuals with identical characteristics.However, in reality, pedestrians have many different physical and psychological conditions that potentially lead to different individual abilities and thus vulnerabilities for some individuals in crowd evacuation [25].For example, consider people with impaired mobility.According to the World report on disability 2011 by the world health organization, there are 75 million people who need a wheelchair on a daily basis, representing 1% of the world's population [26].It has been shown that the presence of a wheelchair user may slow the rate of descent of the evacuees on stairs, even though there is enough physical space for others overtaking [27].Some studies investigate evacuation strategies for vulnerable pedestrians such as people with disabilities and found that evacuation strategies can help evacuation such as phased evacuation strategy [28] and the separate evacuation path for vulnerable pedestrians [29,30].However, these studies mainly focus on the response stage of evacuations and do not consider how other factors affect the strategy's effectiveness.In addition, there are many other kinds of vulnerability of pedestrians that need to be considered when developing strategies for pedestrian evacuation.
The discussion above highlights the importance of research on the effectiveness of evacuation strategies in various contexts, especially when pedestrians with different vulnerabilities are involved.In this work, we distinguish two types of vulnerable pedestrians: velocity-based vulnerable pedestrians who have lower speeds and distance-based vulnerable pedestrians who are further away from exits, compared to other pedestrians.We investigate pedestrian evacuation strategies for vulnerable pedestrians using three examples, each representing an evacuation stage.In the first example, we focus on the pre-evacuation stage where pedestrians have not begun to evacuate and test the strategy of allowing vulnerable pedestrians to respond quicker than others to incidents.In the second example, we investigate the response stage where pedestrians decide which route to take and develop the strategy of giving vulnerable pedestrians priority for exit assignment in the case of limited exit resources.In the third example, we study the evacuation phase where pedestrians are evacuating and analyse the strategy of placing an obstacle in front of exits.We simulate pedestrian dynamics based on the social force model [3].We do not wish to suggest this model is superior to others.It was chosen because it has been extensively used in pedestrian dynamic research [31] and is thus a useful reference model, and it also offers properties that make it especially useful for investigating the implications of different strategies, such as allowing to estimate physical forces acting on individuals under different strategies.
Our work is not intended as research into the mechanism behind pedestrian behaviour under different evacuation strategies but serves to demonstrate how we can develop strategies to help pedestrians with different types of vulnerabilities and how the strategy effectiveness varies with contexts by giving examples in three evacuation stages.The output of this work is thus not an optimal strategy that can help vulnerable pedestrians most.In addition, we also investigate methods that could be used for strategy selection at the start of evacuations.
The remainder of this contribution is structured as follows.First, we present the method we used for this work.Second, we illustrate three examples of evacuation strategies for vulnerable pedestrians, each separately starting with a summary of a literature review on the relevant topic, followed by scenario descriptions, and ending with simulation results.Then, we summarise our findings, before concluding our work.

Social force model
We use social force models to simulate pedestrian dynamics in the room [3], which are implemented in MATLAB (Version R2022a).In the social force model, each person i of mass m i moves under the constraints of an attractive force and two repulsive forces.The attractive force indicates his/her desired speed v 0 i in a certain desired direction e 0 i (which is a unit vector) towards a particular exit based on her/his exit choice strategy.The repulsive forces are from other pedestrians f ij and obstacles f iW summed over all other pedestrians and all obstacles in the environment, respectively.Simultaneously, the person adjusts their current velocity v i (t) within a certain relaxation time τ i based on Newton's Second Law of Motion.Therefore, the movement of the person is given by Eq. 1: All pedestrians are represented by a circle of a given radius in a 2D environment and the repulsive interaction between two pedestrians, i and j, is described by: where d ij is the distance between the centres of i and j, and r ij donates the sum of their radii.A i and B i are parameters of the strength and range of the repulsive interaction force between pedestrians.k, and κ are coefficients determining the strength of body force and sliding friction force between pedestrians, respectively.g(x) is x if the two pedestrians touch each other and 0 otherwise.kg(r ij − d ij ) denotes the body force to counteract body compression, and n ij is the normalised vector between person i to j. Sliding friction Δv t ij t ij impedes relative tangential motion if the two pedestrians are in contact with each other otherwise, it is zero.t ij represents the tangential direction (perpendicular to n ij ) and Δv t ij is the difference in tangential speed between person i and j.The interaction of person i with the wall W is treated analogously and is described by: where r i is the radius of i, d iW is the distance between the centre of i to the closest point of the boundary of an obstacle, n iW is the normalised vector acting perpendicularly to d iW , and t iW is the vector acting tangentially to d iW (perpendicular to n iW ).

Implementation of vulnerability
Vulnerable pedestrians are people who need special care, support and protection such as children, older pedestrians and people with disabilities [32], due to their characteristics.However, in long-distance hurricane evacuations, people who cannot drive or who do not have access to a vehicle are identified as vulnerable pedestrians because their conditions are at a disadvantage compared to others in the process of evacuation [33].In this work, we investigate velocity-based vulnerable pedestrians, because of their characteristics, and distance-based vulnerable pedestrians, determined by their evacuation conditions.
As discussed in the introduction, distance-based vulnerable pedestrians are people who are further away from the exit than the average distance of the whole crowd, the number of which depends on the initial position of pedestrians (see Fig. 1a for an example).Velocity-based vulnerable pedestrians are people who have a lower movement speed.We randomly assign a certain proportion of the crowd to be vulnerable people (see Fig. 1b).The movements of pedestrians are simulated using the social force model as described above.In social force models, the desired velocity indicates the speed pedestrians try to achieve as soon as possible and it does not mean the pedestrians with the same desired speed will have the same actual speed.In our simulations, the speed of each pedestrian varies with time and conditions, but different desired velocities can ensure normal pedestrians and velocity-based pedestrians have different maximum velocities and thus velocity distribution over time, to represent their movement characteristics.In our simulations, the speed of velocity-based vulnerable pedestrians is 0.75 m/s (half of the normal speed).

Scenario settings
We simulate pedestrian dynamics under different strategies in a room with a layout that will be separately illustrated below.Pedestrians are initially uniformly randomly distributed in the room, ensuring they do not overlap at the start of simulations.To ac- count for effects of this initial positioning, we investigate pedestrian dynamics in 1000 scenarios with different randomly generated initial population distributions.
Table 1 shows all scenarios for each example in our simulations.For each scenario, there is only a certain proportion of vulnerable pedestrians with one vulnerability type ('D' for distance-based vulnerability and 'V' for velocity-based vulnerability).Except for vulnerable pedestrians, there are many other factors that may influence pedestrian dynamics and thus we have a different focus in each examplewe investigate the influence of crowd size in example 1 and investigate vulnerability proportion in examples 2 and 3.The proportion of distance-based vulnerable pedestrians depends on the initial positions of pedestrians, as pedestrians far away from the average distance are treated as vulnerable pedestrians.Therefore, we use the mean and standard deviation to represent the proportion of distance-based vulnerable pedestrians in our simulations.Furthermore, we report the average simulation results of 1000 scenarios with different randomly generated initial population distributions.

Example 1: enhanced pedestrian response during pre-evacuation
The total evacuation of each pedestrian consists of pre-evacuation time (or reaction time and response time), indicating the time it takes this pedestrian to start to move, and travel time indicating the interval needed to reach a safe place [34].Understanding the factors affecting pre-evacuation can be helpful for model users and safety engineers [35].
Previous work has established that the pre-evacuation time of pedestrians is influenced by environmental factors, such as crowd communication systems, and individual characteristics [34].Clear emergency cues lead evacuees to respond quickly and thus shorten their pre-evacuation time [36].In contrast, ambiguous cues increase delays in pedestrians' reaction time because pedestrians tend to take time to search for information [37,38].Some studies suggest that people are more likely to respond quickly to emergencies [39,40] when the severity of the disaster is great [41] or people are close to the disaster zone [42].Moreover, social influence can also affect pedestrians' reaction time.[43] found individuals in social groups take longer to show a movement response at the start of evacuations.
Quantifying the pre-evacuation time is an essential topic in pedestrian dynamics and evacuation management.Different methods have been developed to estimate pre-evacuation time.In some models, each agent will be pre-assigning a period of delay before starting to evacuate.This delay represents their pre-evacuation time and can be deterministic depending on the conditions faced by pedestrians and their capacity to respond [44] or probabilistic obtained from a specific distribution [45].In contrast, other models first assign specific activities to certain periods and then the pre-evacuation time of each person can be calculated by his/her assigned activities sequences before evacuation [46].In addition, some data-driven methods have been employed to investigate the characteristics of pedestrian pre-evacuation time based on datasets [35,47].
In this example, we simulate pedestrian dynamics in a room with a single exit, as shown in Fig. 2, and investigate a strategy we refer to as 'quick-response strategy' in scenarios with different crowd sizes.Under this strategy, vulnerable pedestrians can respond quicker than others and thus have a shorter pre-evacuation time, which is achieved by delaying other pedestrians in our simulations.In this example, we assume that it is possible to somehow stagger the way in which individuals are alerted to an emergency in a targeted way.Technically, this is possible with modern personalised communication devices.To test the effectiveness of this strategy,  we implement a baseline strategy where we randomly assign the same number of pedestrians who have a shorter pre-evacuation time under the quick-response strategy, making the influence of the two strategies on pedestrian evacuation comparable.We first investigate which strategy is better overall in terms of evacuation efficiency by comparing the proportion of scenarios where the quick-response strategy leads to a shorter evacuation time than the normal strategy in all scenarios.As shown in Fig. 3, we found that this proportion is around 50% when considering velocity-based vulnerable pedestrians, indicating that allowing pedestrians with impaired mobility to evacuate earlier has little impact on the crowd evacuation efficiency.In contrast, if distance-based vulnerable pedestrians have a smaller pre-evacuation time, the crowd evacuation efficiency increases significantly, especially when the number of pedestrians is 10.However, the advantages of this strategy decrease as the crowd size grows and finally reaches a balance when the number of pedestrians is 50, after which the strategy becomes detrimental to the pedestrian flow, suggesting the usefulness of the quick-response strategy for distance-based vulnerable pedestrians is highly influenced by the crowd size.
We then present more details to investigate why the benefits of the quick-response strategy for distance-based vulnerable pedestrians decrease as the crowd size increases.Fig. 4 illustrates pedestrian dynamics under two different strategies when the crowd size is 10 and 80.We found that in small crowd size scenarios, allowing pedestrians far away from exits to evacuate earlier can reduce the average evacuation time because the total crowd evacuation is determined by the time when the last pedestrian reaches the safe destination.The total evacuation time certainly decreases if pedestrians who have a longer evacuation time can move earlier.However, it will not increase evacuation efficiency when the crowd size is large, because distance-based vulnerable pedestrians still need to wait anyway due to congestion.In contrast, under the normal strategy, pedestrians near the exit are more likely to evacuate earlier, which can relieve the congestion to some extent, leading to a shorter evacuation time.
In summary, we found that allowing velocity-based vulnerable pedestrians to evacuate early will not be beneficial for crowd evacuation.However, the quick-response strategy can improve evacuation efficiency when distance-based vulnerable pedestrians are involved, and its effectiveness depends significantly on the crowd size.

Example 2: priority strategy at the response stage
In evacuations, pedestrian dynamics can be distinguished into three levels: strategic-level which is concerned with how pedestrians select destinations, tactical-level which deals with how pedestrians make route choices, and operational level which describes how pedestrians avoid collisions with others and obstacles [48].Pedestrian route choice under the tactical level is particularly important in evacuations, especially when the evacuation resources (e.g., exit capacity) are limited, because unreasonable exit choices may lead to blockages and slow down the whole pedestrian flow.
Previous research has investigated pedestrian route choice behaviour using experiments and modelling.Empirical findings reveal pedestrian social-demographic factors, built environment factors and trip characteristics are key factors affecting how pedestrians choose their routes [49] and the decision-making mechanism of pedestrians during this process has also been investigated [50].How-  ever, conducting experiments is usually expensive, time-consuming and limited to specific scenarios, with additional examinations required to extend to general scenarios [51].In contrast, modelling can be a possible solution and a large number of models have been developed that can reproduce realistic pedestrian dynamics [52].Researchers have developed many route choice strategies to improve evacuation efficiency in emergencies through modelling such as the shortest exit strategy that will assign each pedestrian to the respective spatial nearest exit [53] and the least travel time exit strategy where pedestrians tend to choose the quickest exit [54].
The majority of previous evacuation strategies are associated with minimum total evacuation time or maximising the number of evacuees to achieve optimisation of evacuation efficiency [55,56].However, these objectives are achieved by sacrificing population outliers, possibly leading to unfair allocations of evacuation resources for pedestrians who should enjoy priority.Imagine that in a smoky room with multiple exits, vulnerable people, such as people with impaired mobility or near the disaster zone, are far away from the nearest exit than others.They can avoid the disaster and escape to safe places if they use the nearest exit and other heads for the further exit, even though this may reduce the overall efficiency.Suppose the principle of efficiency optimisation is followed.In that case, evacuees are likely to compete at the nearest exit, possibly causing congestion and injury, although the overall time becomes shorter.
In this example, we propose a priority exit choice strategy that aims at helping vulnerable pedestrians by giving them exit choice priority.We assume that evacuation resources are limited and thus each exit will be pre-allocated with a certain quota.All pedestrians will be ranked according to their level of vulnerability, the more vulnerable they are, the more priority they have.If the quota of their preferred exit has been completely used, the subsequent pedestrians will have to take the suboptimal exit.Here we assume again that individuals can be communicated with directly and at individual level.As in the last example, we investigate distance-based vulnerable pedestrians who are far from exits and velocity-based pedestrians who have limited mobility.We simulate pedestrian dynamics in the room with two symmetric exits (see Fig. 5a).As shown in Table 1, for this example we implement four scenarios to investigate the impact of crowd size, vulnerability type and proportion on pedestrian dynamics.In each scenario, we compare pedestrian dynamics under the nearest exit choice strategy (Fig. 5b) and the priority exit choice strategy (Fig. 5c).More details about the implementation of the strategy can be found in Appendix A.
We first investigate which strategy can lead to a higher evacuation efficiency.As shown in Fig. 6, the distribution of the difference in total evacuation time in D1 and D2 is significantly skewed left (skewnesses are −0.96 and −0.62, respectively) but the skewness decreases in V1 and V2 (skewnesses are −0.52 and 0.48, respectively), suggesting that the shortest exit choice strategy tends to be more beneficial for distance-based vulnerable pedestrians.As shown in Fig. 6b, the proportion of scenarios where priority strategy leads to a shorter evacuation time confirms our findings.In most cases pedestrians need more time to evacuate when a priority strategy is present (all proportions are below 0.5).There is only a small proportion of scenarios (below 0.1) where the priority strategy is better than the nearest exit strategy in terms of evacuation time when the crowd size is 10, but this proportion increases when the crowd size grows to 50 (D2, V1 and V2).This suggests that the increased crowd size and presence of vulnerable pedestrians somewhat enhance the advantages of the priority strategy.
We then investigate how priority strategy affects pedestrian dynamics in different scenarios.We distinguish all scenarios into two groups where the nearest exit strategy is better/worse than the priority strategy in terms of evacuation time.We compare the following parameters: accumulated force per person, average velocity, and walking distance.Accumulated force reflects the average force acting on each pedestrian during the evacuation, calculated by the magnitude of the sum of the corresponding vectors.Average velocity is the average speed of each pedestrian and walking distance is the total average walking distance of each person.As shown in Figure C1, we found that when the number of people is small there is no significant difference in the pedestrian accumulation force between the two strategies, but when the crowd size increases to 50, the accumulation force of the group where the priority strategy leads to a shorter evacuation time becomes larger than the other group, indicating that in high-density evacuation scenarios higher evacuation efficiency might be at the expense of more pedestrian collisions.In all scenarios, the two strategies maintain relatively consistent effects on the average velocity and walking distance of pedestrians.Specifically, when the priority strategy is introduced, pedestrians tend to travel longer distances, but at the same time have larger average speeds.
The above findings suggest that which strategy is better depends on the context and initial conditions.If we can make such a prediction before simulations, based only on the pedestrian initial distribution, this would present a useful tool for strategy selection at the start of evacuations.Therefore, we test whether machine learning methods can be used for strategy performance prediction.We extract the data generated from the simulations as the input data.The predictor variables are the x and y coordinates of all pedestrians, their speed, and their distance to the exit.The response variable is a Boolean indicating whether the priority strategy leads to a shorter evacuation time than the nearest exit choice strategy.We employ a variety of methods to perform supervised machine learning, as shown in Table 2, and implement 5-fold cross-validation for testing: the dataset would be split into 5 groups and the model would be trained and tested 5 separate times so each group is used as the test set once.More details can be found in Appendix B. Results show that machine learning methods including logistic regression, kernel naïve Bayes and Linear SVM can predict well which strategy performs better in terms of evacuation time with a maximum accuracy of 87.3%.However, the highest accuracy decreases to 65.5% when the crowd size increases from 10 to 50, and even drops to around 50% if vulnerable pedestrians are involved.This suggests that machine learning methods do not have a high performance in predicting strategy performance in complex scenarios.
In summary, our simulation results indicate that compared to the nearest exit strategy, giving vulnerable pedestrians priority for exit assignment in the case of limited exit resources can relieve crowd congestion to a certain extent but lead to a higher average ve- locity and longer walking distance.However, which strategy increases evacuation efficiency significantly depends on the initial distribution of pedestrians.We found machine learning methods including kernel naïve Bayes and Linear SVM can predict well which strategy is better based on the initial distribution of pedestrian positions in low-density scenarios, but the accuracy decreases in more complex scenarios.In addition, the increased crowd size and proportion of vulnerable pedestrians somewhat enhance the advantages of the priority strategy.

Example 3: obstacle effect at the evacuation phrase
Previous work has investigated interventions to improve pedestrian dynamic evacuation and found the obstacle effect that indicates placing obstacles in front of exits can improve evacuation outflows [3].While the obstacle effect has been investigated through modelling and experiments, there is no consensus on how and to what extent the obstacle effect can enhance pedestrian flow in evacuation.
Most simulation studies indicate the benefits of obstacles if they are appropriately placed.However, the improvement of this measure depends on various factors including obstacle arrangement [57], shape [58,59], position [22] and size [60], door width [61], crowd density [23] and evacuation strategy [21].In terms of the mechanism behind the obstacle effect, different explanations are given.One explanation is the obstacle can avoid the "faster is slower" effect and help to prevent the build-up of fatal pressures [3].[23] explain using the concept of "waiting room", the small area near the exit that can adjust pedestrian flow based on the crowdedness.Another explanation is the enhancement in pedestrian flow comes from a significant reduction of the high-density region by effective separation in space caused by placed obstacles [21].However, empirical data from experiments with human participants produced diverse results.Some studies reveal that the obstacle effect can improve pedestrian outflows [57,62,63].In contrast, other studies found placing an obstacle around the exit may increase [64,65] or have no effect [66] on evacuation time.Therefore, previous research has established the effectiveness of placing obstacles in front of exits in improving evacuation efficiency.However, there is a lack of investigation on its improvements in evacuation efficiency when vulnerable pedestrians are involved.
In this example, we investigate the performance of the obstacle effect in helping vulnerable pedestrians through modelling.As in the previous examples, we investigate two types of vulnerable pedestrians in scenarios with different crowd sizes and proportions of vulnerable people, as shown in Table 1.In each scenario, we compare pedestrian dynamics in the presence and absence of the obstacle in front of the exit.Furthermore, we study the influence of the obstacle position on the performance of the obstacle effect by comparing pedestrian dynamics when the obstacle is in different locations (see Fig. 7).
We first investigate the effects of the crowd size and vulnerability type on pedestrian dynamics.As shown in Fig. 8a, the distribution of the difference in total evacuation time in D1 is significantly skewed right indicating that putting an obstacle is likely detrimental to evacuation efficiency.However, when we increase the crowd size from 10 to 50 or introduce the distance-based or velocitybased vulnerable pedestrians, the skewness decreases (from 0.26 to 0.06, 0.03 and −0.05) and the peak drops significantly (from 0.29 to 0.11, 0.12 and 0.13), suggesting that the obstacle can be more beneficial in these scenarios.We found that when the crowd size is low (D1), the presence of the obstacle is more likely to decrease the evacuation efficiency, leading to a longer evacuation time-only about 25% of all scenarios are beneficial from it (see D1 in Fig. 8a and b).However, the proportion significantly increases to about 50% when the number of pedestrians is 50 (see D2, V1, V2 in Fig. 8a and b) and is slightly influenced by the vulnerable pedestrian type, suggesting the crowd size is essential for the performance of the obstacle effect in these cases.Figure C3 in the appendix confirms the impact of crowd size on the obstacle effect.As the crowd size increases, placing an obstacle in front of the exit is more likely to reduce the crowd evacuation time.
We then investigate the influence of obstacle position on the effectiveness of the obstacle effect.As shown in Fig. 8c, we found that if the obstacle is close to the exit (less than 1.75 m), it will reduce the evacuation flow.If the obstacle is too far from the exit (more than 3.75 m), it has little effect on the evacuation flow.Only if the obstacle is placed in a specific region the evacuation efficiency can  be improved.Fig. 8d shows the average evacuation time with standard deviation as the x coordinate of the obstacle changes.We found that when the obstacle is present, the average evacuation time first decreases then increase and thus there is an optimal point where the obstacle effect functions best.However, the error bar of this point is very high, suggesting that the initial distribution also affects the performance of the obstacle effect.
Finally, we investigate how the presence of the obstacle affects pedestrian dynamics in different scenarios.We distinguish all scenarios into two groups by whether the obstacle presence can/cannot improve evacuation efficiency.As shown in Figure C2, we found on average the existence of the obstacle in front of the exit leads pedestrians to have a bigger accumulated force, which increases significantly when the crowd size grows.In low-density scenarios, placing an obstacle does not have a consistent effect on pedestrian average velocity and walking distance but it does in high-density scenarios-increasing the average velocity and total walking distance of pedestrians.
In summary, we found placing an obstacle near an exit can be beneficial for evacuation efficiency in high-density scenarios.It increases pedestrian velocity in high-density scenarios but leads pedestrians to have a higher accumulated force and a longer walking distance.The position of the obstacle significantly affects how well it can improve evacuation efficiency and an optimal position exists.However, it has a small effect on vulnerable pedestrian evacuations.

Summary and discussion
Our work explores the effectiveness of strategies for helping vulnerable pedestrians by giving three examples that involve different evacuation stages.One of the main conclusions of this work is that the potential of strategies to improve evacuation efficiency depends on the context.For example, the strategy of allowing vulnerable pedestrians to have exit choice priority is beneficial for the evacuation process only for particular initial spatial distributions of pedestrians.Placing an obstacle near an exit can be beneficial for evacuation efficiency in high-density scenarios and the effectiveness depends on the obstacle position.We also found that crowd characteristics can affect the success of strategies.For example, the quick-response strategy can improve evacuation efficiency for distance-based vulnerable pedestrians but does not work for velocity-based vulnerable pedestrians.While some strategies can improve pedestrian evacuation flow, they may have other, possibly undesirable, consequences.For example, placing an obstacle in front of the exit increases pedestrian velocity, but leads pedestrians to have a higher accumulated force and longer walking distance.In addition, our work demonstrates that machine learning methods including kernel naïve Bayes and Linear SVM can predict which strategy works well based on the pre-evacuation pedestrian distribution, but only in some circumstances.We only investigate the performance of machine learning for example 2, because compared to other examples, our proposal strategy in example 2 does not show a signifi-cant effect on evacuation efficiency and it might be caused by the initial pedestrian distribution.Therefore, we test whether machine learning methods can be used for strategy performance prediction based on the initial pedestrian distribution.
Our work highlights the importance of contextual factors and crowd characteristics, which have been suggested in previous work, but our work is the first systematic research that covers different evacuation stages and focuses on pedestrians with different types of vulnerability.The strategies in this work allow vulnerable pedestrians to take more advantages than others in different evacuation stages (except the evacuation phrase) but they can only work in certain scenarios for certain vulnerable pedestrians and may have negative effects on pedestrian dynamics, suggesting an evacuation strategy for vulnerable pedestrians is not only required to be personalised by context and crowd characterises but also need to consider the trade-offs between efficiency improvements and negative consequences that may result.While we investigate several factors that may affect the strategy performance through modelling, there are many other potential factors to be important for pedestrian dynamics even in simple scenarios considered here.Therefore, it is necessary to discuss applicable scenarios and possible negative effects of a developed optimal evacuation strategy.
One of the limitations of this work is that we use the social force model to simulate pedestrian dynamics in three examples.While the validity of social force models has been examined extensively in previous research, it may not reflect realistic pedestrian behaviours.For example, the lack of a self-slowing mechanism in social force models leads simulated pedestrians to continuously push over other pedestrians [67] and the lack of a collision avoidance mechanism makes pedestrian dynamics less realistic [68].It is necessary to examine our findings using more diverse models.Furthermore, the prerequisites for the strategies we develop make them difficult to put into practice.For example, implementing the priority strategy should meet the following requirements: (1) The individuals can be located and notified with 100% accuracy.(2) There should be a central system that can access data on pedestrian properties (e.g., mobility), evaluate vulnerability based on locations or properties, and direct pedestrians based on the priority strategy.(3) Pedestrians should follow the instructions.Technically, this might be approximately possible with a mobile application that can access GPS data and personalised information.
Another limitation of this work is that we only consider certain scenarios for each strategy.For example, we only compare pedestrian dynamics when the crowd size is 10 and 50 for the priority strategy, which may not represent a high-density scenario, and we only investigate the influence of crowd size and obstacle position while there are other important factors such as door width.We suggest our work is not an exhaustive investigation of how different factors can affect pedestrian behaviour but an exploration of how we can develop strategies for helping vulnerable pedestrians and whether these strategies can work across contexts.Therefore, we believe that our work can still serve as a starting point for studying the effectiveness of evacuation strategies in different scenarios.Moreover, our examples cover several strategies in different stages and demonstrate pedestrian dynamics in scenarios with simple room layouts.The simple evacuation scenarios can help eliminate the influence of other potential factors on pedestrian dynamics and thus easily compare the strategy performance in simulations.Although more complex scenarios with realistic building settings are necessary, the evidence obtained from our simulation results is sufficient to support the conclusions we draw in this work.
Our work investigates three strategies for helping vulnerable pedestrians at different stages of egress.Some of the results confirm previous findings.For example, consistent with work by [23], we found placing an obstacle in front of exits can increase evacuation efficiency in high-density scenarios.In contrast, the strategies of allowing vulnerable pedestrians to respond quickly or to be preferentially assigned to exits in the case of limited exit resources are not investigated so far and more empirical work can be done.We suggest that while our work does not exhaustively investigate how vulnerable pedestrians behave under different conditions, it still demonstrates the importance of contextual factors and crowd characteristics for the effectiveness of evacuation strategies.

Conclusion
Evacuation is an effective way for pedestrians to handle disasters and an appropriate evacuation strategy is crucial to ensuring pedestrian safety.Our work focuses for the first time on evacuation strategies in helping vulnerable pedestrians with impaired mobility or long distance from exits.We demonstrate three strategies that include allowing vulnerable pedestrians to evacuate earlier, giving vulnerable pedestrians exit choice priority and putting an obstacle in front of the exit by giving examples covering representative evacuation stages.Simulation results have shown that these evacuation strategies can only improve evacuation efficiency in certain scenarios and for a certain type of vulnerable pedestrians sometimes.These strategies may lead to negative consequences for pedestrian dynamics even though they can improve evacuation efficiency.Our work highlights the importance of contextual factors and crowd characteristics when developing evacuation strategies and the potential of machine learning methods including kernel naïve Bayes and Linear SVM in strategy performance prediction.Future work is also required to explore how to develop optimal strategies in complex scenarios with vulnerable pedestrians through experiments with human participants.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Fig. 1 .
Fig. 1.Two types of vulnerable pedestrians represented by blue circles: distance-based (a) and velocity-based vulnerable pedestrians (b).Pedestrians who are not vulnerable are represented by red circles.(For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

Fig. 3 .
Fig. 3. Effects of the crowd size on the proportion of scenarios where the quick-response strategy leads to a higher evacuation efficiency than the normal strategy.The dashed horizontal line shows 0.5 where the strategy is expected to have a neutral effect on evacuation efficiency.The error bars represent the standard deviations obtained by Bootstrapping (n = 1000 samples).

Fig. 4 .
Fig. 4. Examples for pedestrian movements when the crowd size is 10 (a and b) and 80 (c and d) under the normal strategy (a and c) and the quick-response strategy (b and d) at time steps 2 (left) and 7 (right).Blue and red circles represent distance-based vulnerable pedestrians and non-vulnerable pedestrians, respectively.(For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

Fig. 5 .Fig. 6 .
Fig. 5. Diagram of the room layout in simulations for example 2 (a), and two strategies: the nearest exit choice strategy (b) and the priority exit choice strategy (c) for velocity-based vulnerable pedestrians represented by blue circles.The arrows indicate their intended exit choice and the dotted boxes mark people who have a different exit choice when the priority strategy is present.The quota of the two exits is 5 pedestrians.(For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

Fig. 7 .
Fig. 7. Diagram of the room layout in simulations.The obstacle is a column with a radius of 0.5 m and the grey zone represents the possible location of the obstacle (1.25 m < x < 3.75 m, −1.25 m < y < 1.25 m).

Fig. 8 .
Fig. 8. Simulation results of the obstacle effect.(a) Distribution of the difference in evacuation time between scenarios with and without the obstacle.Figures here share the same share the same abscissa and ordinate.(b) The proportion of scenarios where the presence of the obstacle leads to a shorter evacuation time.The error bars represent the standard deviations obtained by Bootstrapping (n = 1000 samples).(c) Heatmap of the difference in evacuation time between scenarios with and without obstacles in D2.Red (blue) show the positions where placing an obstacle can improve (reduce) evacuation efficiency.(d) The average evacuation time with standard deviation as the x coordinate of the obstacle changes (y coordinate is 0.25 m).(For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

Table 1
Details for the scenarios in simulations.The proportion of distance-based vulnerable pedestrians depends on the pedestrian initial distribution and is thus represented by the mean and standard deviation.

Table 2
Prediction accuracy of different methods for four scenarios.The highest accuracy in each scenario is in bold.