Simulating dynamics of adaptive exit-choice changing in crowd evacuations: Model implementation and behavioural interpretations

Transportation Research Part C 103 (2019) 56–82

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Transportation Research Part C journal homepage: www.elsevier.com/locate/trc

Simulating dynamics of adaptive exit-choice changing in crowd evacuations: Model implementation and behavioural interpretations

T

Milad Haghania, , Majid Sarvib ⁎

a b

Institute of Transport and Logistics Studies, The University of Sydney Business School, Australia Department of Infrastructure Engineering, The University of Melbourne, Australia

ARTICLE INFO

ABSTRACT

Keywords: Pedestrian crowd evacuation Decision adaptation Revising decisions Adaptive dynamic decision-making Direction choice Decision updating

A crucial aspect of simulating crowds’ evacuation processes is that humans can dynamically revisit and change their decisions. While a relatively great deal of attention has been paid by recent studies to modelling directional decision making, the ‘exit decision changing (or decision adaptation)’ phenomenon has been largely overlooked. Here, we quantitatively investigate (I) how important is to include a decision changing module in evacuation simulation models, and (II) whether decision changing is beneficial to evacuation processes. We propose and implement a parsimonious discrete-choice model of decision changing. The model embodies the most influential factors that make an evacuee revise and adapt their choice of exit. This includes the effects of ‘relative queue-size imbalance at exits’, ‘visibility of exits’, ‘social influence’ and ‘inertia (for maintaining initial decisions)’. Results showed that, the inclusion of the decision changing module made a very substantial difference in enhancing the accuracy of the simulation outputs. Simulating exit choices as one-off decisions strictly limited the degree of match that could be achieved between the simulated and experimental outputs (in terms of replicating the observed exit shares and evacuation times) (question I). Further analyses also revealed that an intermediate degree of decision changing is a strategy that most benefits the system. By contrast, the extreme decision-changing strategies (i.e. “no change” and “too many changes”) were found to be suboptimal. Also, while we have observed, in our other studies, that imitative (or the so-called herd-type) behaviour in ‘exit choices’ is invariably detrimental to evacuation systems, here, we observed that when it comes to ‘adapting exit choices’, a moderate degree of imitation (or followthe-peer) tendency makes the system more efficient (question II).

1. Introduction The fact that decision-making behaviour of humans in emergency escape or evacuation scenarios in crowded places is dynamic is well known. However, the characteristics of this dynamic mechanism is not quite well understood in detail. When evacuations happen in crowded spaces, pedestrians make various types of decisions to escape in shortest possible time (Gwynne et al., 2017). A multi-dimensional process of decision-making is a shared characteristic between evacuations of indoor spaces and those of regional and urban areas as highlighted by researchers in both domains (Kobes et al., 2010b; Mesa-Arango et al., 2012; Murray-Tuite and Wolshon, 2013; Pel et al., 2011, 2012). Evacuees in confined crowded spaces often have the possibility to dynamically revisit and ⁎

Corresponding author. E-mail address: [email protected] (M. Haghani).

https://doi.org/10.1016/j.trc.2019.04.009 Received 10 June 2018; Received in revised form 5 April 2019; Accepted 8 April 2019 0968-090X/ © 2019 Elsevier Ltd. All rights reserved.

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update their decisions in response to the changes in their surroundings to ensure that they take the “best” possible strategy given the information available to them. The dynamics of the environment (e.g. the formation and propagation of the congestion) change over time during emergency evacuations and humans do have the ability and motivation to adjust their initial choices in response to those changes in order to improve their strategies. Strategy adaptation can be observed in relation to various aspects of evacuees’ behaviour including local navigation (Antonini et al., 2006a; Heliövaara et al., 2012a), global pathfinding (Kneidl et al., 2013), reaction decisions (Bode and Codling, 2018; Galea et al., 2017), exit direction choices (Bode and Codling, 2013; Duives and Mahmassani, 2012; Ehtamo et al., 2010; Fridolf et al., 2013; Haghani et al., 2015; Kinateder et al., 2018) or choice of speed (Fridolf et al., 2013). As mentioned above, the existence of this dynamism in evacuation decision-making in complex environments is intuitively acknowledged, but for modelling purposes, it is crucial for the detailed characteristics of this behaviour to be represented in models. Particular questions that need to be taken into consideration to model this phenomenon could be as follows. What are the circumstances that may make an evacuee more likely to revise their initial decisions? What types of decisions are more likely to be updated and what are the factors driving those changes for each level of decision making (i.e. for directional exit choices, or local pathfinding choices, or global pathfinding choices). And most importantly, how can these factors be represented reasonably in numerical simulation models of evacuation (while maintaining the stability of the numerical simulation process that can potentially be affected by making decisions dynamic)? In this work, we are particularly interested in understanding and quantifying how crucial it is to include an exit choice changing (or exit choice adaptation) feature in simulation models of pedestrian evacuations. We have observed in our past experiments that people do change their directional exit decisions. However, given that inclusion of this modelling layer will impose additional computational load and calibration complexities, we would like to quantify how important it is to model this phenomenon in the first place. Is it not good enough to approximate decisions of simulated evacuees’ as one-off decisions and generate a fixed decision for each simulated agent? What would be the impact of such modelling practice in quantitative terms? The second central question of this study concerns the topic of behavioural optimisation. One of the end aims of modelling evacuation behaviour is to gain knowledge that can be utilised to facilitate or ‘optimise’ evacuation strategies (Kneidl et al., 2013). While broadly addressed in the context of urban network evacuations (Huibregtse et al., 2011; Murray-Tuite et al., 2012), this topic, behavioural strategy optimisation, constitutes an aspect of research in crowd dynamics that has been overlooked to great degrees (Berseth et al., 2015; Ding et al., 2017; Kou et al., 2013; Lin et al., 2008; Luh et al., 2012; Noh et al., 2016). As the main attention is currently being paid to developing descriptive models (Duives et al., 2013; Ronchi et al., 2014a) behavioural optimisation is not receiving the attention that it requires. Among the body of studies that have looked at the optimisation of evacuation processes, the majority have investigated the problem from an architectural optimisation (Luh et al., 2012; Zhao et al., 2017) or path-planning optimisation perspective (Lin et al., 2008; Noh et al., 2016; Pursals and Garzón, 2009; Vermuyten et al., 2016). In contrast, little attention has been paid to identifying optimal evacuation strategies at the level of individuals which is a major necessity for developing efficient evacuation training and guidelines (Lu et al., 2014). The question of decision changing has practical implications from the behaviour optimisation and evacuation management perspectives. In specific terms, we would like to quantitatively examine how various degrees and kinds of decision adaptation strategy influences evacuation efficiency. The question concerns whether evacuees can benefit from a dynamic decision-making strategy or is it better for them to adhere to their initial choices rather than continuously exploring and considering all available options. And if there is a benefit in choosing a dynamic strategy, how much adaptation would be optimum. In this work, we specifically focus on adaptive decision-making in exit choices. We propose a relatively parsimonious discretechoice model of decision changing that embodies the primary factors that influence occupants’ tendency to revise their initial exit decisions. Through full parametrisation, this model is flexibly capable of representing various forms and degrees of decision changing tendency. It also has the capacity to eliminate decision changing or activate it to extreme degrees through proper parameter specification. By implementing this model, we quantify the extent to which the inclusion of this modelling layer can improve prediction accuracy. Using this model, we also generate behavioural findings based on numerical sensitivity analyses on the parameters of this model. Utilising the fact that each model parameter carries tangible behavioural interpretations and reflects certain kind and degree of adaptation tendency, we perform extensive numerical tests to identify the types of decision-changing strategy that can benefit evacuation processes. 2. State of the practice 2.1. Experimental practices In an earlier survey of the literature (Haghani and Sarvi, 2018a), we identified a substantial imbalance in the existing studies of evacuation modelling in regard to the amount of attention paid to various aspects of the evacuation decision-making behaviour. This concerns both data collection attempts as well as the development of computational methodologies for various levels of decision making. We showed that studies related to evacuees’ exit choice (i.e. tactical levels of decision making) have been noticeably on the rise (Andrée et al., 2016; Duives and Mahmassani, 2012; Fu et al., 2014; Guo Ren-Yong, 2010; Haghani and Sarvi, 2016a,c, 2017d; Heliövaara et al., 2012b; Kinateder et al., 2018; Kobes et al., 2010a; Lo et al., 2006; Wagoum et al., 2017; Xu et al., 2012; Zarita and Lim Eng, 2012) and are catching up with the great wealth of models and data available for walking behaviour (i.e. operational level) (Antonini et al., 2006b; Moussaïd et al., 2011; Seitz et al., 2016). However, the phenomenon of decision-changing has been addressed by no more than a few empirical studies and remains a major knowledge gap. An aspect that the existing studies on exit decision making have by-and-large agreed upon is that exit choice behaviour is best represented by multi-attribute trade-offs between physical 57

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factors and social-interaction factors (as opposed to being modelled as a single-attribute form of decision making) (Bode et al., 2014; Haghani and Sarvi, 2017c; Kinateder et al., 2018). The exit choice changing behaviour has been experimentally investigated by very few studies (Bode et al., 2014, 2015; Bode and Codling, 2013; Liao et al., 2017), a sign that the phenomenon has been being largely overlooked. It has been possibly thought of as a feature whose exclusion from modelling might not be highly consequential. In the first study that attempted this topic, Bode and Codling (2013) found out that depending on the type of their treatment in computer-based virtual-reality experiments of simulated evacuations, between 7% to slightly above 15% of subjects changed their initial exit decisions. The finding suggested that participants mostly tended to stick to their initial decisions and that this tendency was not moderated by their age or gender. They also suggested based on their empirical observations that “when people felt competitive or under pressure, they were less likely to change their mind and therefore did not adapt as frequently to a developing situation (the simulated evacuation)” (p. 352). In a subsequent study, Liao et al. (2017) also observed, based on laboratory experiments with actual human crowds, that a small portion of pedestrians adjusted their route choice. They also proposed a “perception-based mechanism for human route choice that takes both time-independent and time-dependent information into account” (p. 2). They also observed that “pedestrians tended to change their mind on which exit to use roughly halfway through the time they spent inside the experiment” (p. 5). 2.2. Modelling practices The review of studies in the previous subsection summarised the experimental efforts that provided some behavioural insight about the exit choice adaptation mechanism. The aim of this stream of studies is to enable and inform evacuation models to reasonably simulate the decision changing mechanism. Yet, very few studies have been reported operational models that allow dynamic decision making. To the best of our knowledge, with few exceptions, the vast majority of prediction models reported in the field of evacuation modelling lack an explicit modelling module for decision adaptation (Duives et al., 2013; Kouskoulis and Antoniou, 2017; Santos and Aguirre, 2004). An exception in this area is the exit selection method reported is the study of Ehtamo et al. (2010) that represents the exit choice process in the form of a game between N agents (players) who each reacts optimally to other players’ strategies. A process that is described by a pure strategy Nash Equilibrium. Their method relaxes the assumption that “agents only calculate the equilibrium at a particular instant, i.e. the initial situation” (p. 124) and considers the possibility of change in the equilibrium condition as the agents move. Therefore, one can say that a decision-adaptation mechanism is implicitly included in their game-theoretic approach. This method has been integrated with the FDS + Evac model of fire evacuation (Hostikka et al., 2007; Korhonen and Heliövaara, 2011; Korhonen and Hostikka, 2009; Korhonen et al., 2010). BuildingEXODUS is another commercial software of evacuation simulation that allows dynamic adaptive exit decision making. The development of this behavioural feature in this software has been documented in the study of Gwynne et al. (1999). In this method “the occupant taking decisions based on their previous experiences with the enclosure and the information available to them” (p. 1041). The method considers occupants “prior knowledge of enclosure” and “line of sight information about queues at neighbouring exits”. 2.3. The case of this study The proposition of the decision adaptation feature in this work is in line with the premise stated by Gwynne et al. (1999) that “occupants are not oblivious to their surroundings and take a more pro-active role in their decision-making activities” (p. 1042). The current study is the latest among the very few modelling contributions that attempted to simulate the dynamic nature of decisionmaking process during evacuations. It is the first to use an econometric and fully parametric modelling approach to represent the decision adaptation. The authors note that the two primary questions driving this work have also been mentioned in the discussions provided by Gwynne et al. (1999). In their discussions, the authors have characterised the effect of implementing a decision adaptation feature “arguable” in terms of representing a more realistic behaviour by acknowledging that “more data is required concerning the decision-making process” (p. 1052). In the absence of solid evidence that demonstrate the significance of implementing a decision-change modelling layer, such argument would be legitimate especially given the fact that previous empirical work has shown only a small portion of evacuees changes their exit decisions and that the majority do not do so (Bode and Codling, 2013; Liao et al., 2017). From that point of view, it would be a legitimate and relevant question to ask whether it would be sufficient to approximate the evacuation processes by simulating a single exit decision for each simulated agent. This aspect constitutes the first question of this study. Using an extensive set of experimental data and a large number of experimental scenarios and through replicating those scenarios in a simulation setting, we ‘quantify’ the effect of adding a decision-changing module. We investigate whether this effect is substantial or trivial. Introducing this layer furthers the computational load of the modelling, and if one can establish that the modelling effect of decision adaptation is trivial, then the modeller may choose to approximate decisions as one-off instances in favour of reducing the computational burden. However, if the opposite proves to be true and the effect on simulation accuracy is substantial, then the additional computational load and calibration burden that this modelling layer requires should be acceptable and warranted. The second question that drives this study is how decision-adaptation behaviour impacts the evacuation efficiency. Gwynne et al. (1999) stated in their discussions that “the capability of the occupant to switch between available exits does not guarantee the reduction of individual and total evacuation times” (p. 1051). This is an indication that the effect has not been clear and that numerical analysis on this question is warranted in order to establish the effect of dynamic adaptive decision making on evacuation 58

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efficiency. This constitutes the second question of this study. Using the fully-parametric model proposed in this work and based on an extensive amount of numerical analyses, we quantitatively investigate how various kinds and degrees of decision-adaptation strategy can influence the efficiency of the system. We include both total and individual evacuation times in our numerical analyses as primary measures of evacuation efficiency. The explicit modelling module dedicated to the decision adaptation mechanism in our numerical simulation tool is a multiattribute model. It considers the joint influence of multiple factors that drive adaptation behaviour and it quantifies the choicemakers’ trade-off between them. These factors include the existence (and magnitude of) queue-size imbalance at exits, the line of sight, the social (or peer) influence and the inertia factor. The model is probabilistic and allows for sub-optimal noisy behaviour. The model is fully parametric and flexibly allows the modeller to represent and control various degrees of adaptiveness in decision making through variation in the parameter values. This particular feature enables us to investigate the effectiveness of various type and degrees of decision adaptation strategies in terms of their impact on the system performance. The model parameters are also directly calibratable through empirical observations. Through an extensive amount of experimental data, for the first time, we systematically quantify the significance of including such modelling layer in an evacuation simulation in terms of the accuracy of predictions. 3. Simulation method 3.1. Model conceptualisation for exit-choice changing The existing research on exit choice behaviour has identified a broad range of influential factors that explain such decisions including the size of queue at exits, distance to exits (Haghani and Sarvi, 2016b; Lovreglio et al., 2014), angular displacement (Duives and Mahmassani, 2012), social (or peer behaviour) influence (Haghani and Sarvi, 2017b; Kinateder et al., 2018; Kinateder et al., 2014b), exit visibility and general visibility (Cirillo and Muntean, 2013; Fridolf et al., 2013; Guo et al., 2012; Haghani and Sarvi, 2017a; Isobe et al., 2004; Jeon et al., 2011), exit width (Liao et al., 2017), exit familiarity (Kinateder et al., 2018; O'Neill, 1992), and exit signage (Zhang et al., 2017) as well as individual characteristics (Duives and Mahmassani, 2012; Lovreglio et al., 2014). Some of these factors are time-dependant and change dynamically during an evacuation process and some are fixed elements of the environment. It stands to reason to assume that the factors that determine the initial choice of exit may also play a role in motivating an evacuee to revise and adapt that choice. This appears to be particularly relevant to the factors that evolve over time (i.e. the time-dependant factors). In choosing the variables of the exit adaption model in this work, a number of criteria were considered. The first criterion, as mentioned earlier, was the relevance of the variable to the exit-choice behaviour which is informed by the literature on this topic. Also, priority was given to the factors that dynamically change over time as opposed to time-independent factors. The second main criterion was modelling parsimony and calibration considerations. Tempting as it was to include a long list of variables in a decision adaptation model, considerations had to be given to the problem of model calibration. As will be elaborated in the discussion section, direct calibration of an exit-choice-changing model poses significant challenges compared to an exit choice model. This criterion places a limit on the number of variables that the model can reasonably include. The third consideration was that we gave priority to the generic variables that do not depend on the characteristics of individual decision maker or additional exogenous information like the population composition etc. After these considerations, it was assumed that the choice of adapting an initial exit choice is mainly motivated by the imbalance between queue size at different exits (as a highly time-dependant variable that directly influences individuals’ evacuation times), as well as whether this imbalance is visually perceivable to the choice maker. Furthermore, the neighbour (or peer) behaviour was assumed to be a major factor that influences exit choice behaviour (as suggested by the majority of previous studies). And finally, the current literature informs us that the exit choice changing is in fact a relatively infrequent occurrence (compared to the proportion of occupants that do not change their decisions). And this indicates that individuals have a tendency to maintain their initial choice as much as possible (Bode and Codling, 2013; Liao et al., 2017). This tendency was reflected in the model through an inertia parameter. The underlying assumption is that the choice of changing initial decision is determined via a probabilistic trade-off over the four factors explained above. 3.2. Exit-choice changing module The model for exit-choice changing is a binary discrete-choice model based on four parameters (for three variables and one alternative-specific constant). The two alternatives that we consider for each simulated agent are ‘change’ and ‘not change’ (of the exit choice) and that constitutes the agents’ choice set. The variables are all choice-situation-specific and do not vary between the two alternatives. The utility of the ‘change’ alternative, Uchange , for a pedestrian that has already chosen exit n is formulated as Eq. (1). In this formulation, Vchange and change are respectively the systematic and error components of the utility for the ‘change’ alternative. The systematic component consists of three variables and an alternative-specific constant. The first variable is referred to in our work as ‘Congestion Ratio’ (CongRatio) variable which measures the congestion level (i.e. the size of the queue) at the chosen exit, CONGn , relative to the congestion level at the least congested exit in that room, CONGmin . This combined variable reflects the arithmetic difference between the queue size at the current (i.e. chosen) exit and that of the least crowded exit in the room. In order to convert it to a unitless variable and also to confine its range of variation to a fixed interval, we normalise this difference by dividing it by the congestion (or queue) size at the current (i.e. chosen) exit. The variable is a reflection of how poorly the initially-chosen exit is 59

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Fig. 1. Examples of observations from a past experiment in 2015 that shows how a case of decision change often triggers a herd (or cluster or burst) of subsequent decision changes. In each image, we have highlighted a herd of decision change observed in the footage of the experiment. One individual makes a decision change and a number of others abandon their initially chosen exit and follow that change almost immediately.

performing at the moment of the decision change relative to the emptiest exit in that room. The variable changes in the range of 0–1. A congestion ratio value of 0 would indicate that the initially-chosen exit is currently the ‘best’ exit in terms of the queue size. As the imbalance between the congestion level at the chosen exit and the emptiest exit becomes larger, the value of the Congestion Ratio variable tends toward 1, meaning that the initially-chosen exit is performing increasingly poorly compared to the least crowded exit in that room. Therefore, the coefficient for this variable, 1, is reasonably expected to be positive meaning that as Congestion Ratio increases, the congestion imbalance increases and thus, the utility and the probability of change increases. The second variable in the utility of the ‘change’ alternative is ‘Visibility’ (VIS) which we treat as a binary categorical 0–1 variable that equals 1 if a less congested exit in the room is visible from the position of the choice maker, and is 0 otherwise. By this definition, other alternative exits might be available to the simulated choice maker, but if none of them is less congested, the VIS for the decision change of that individual will be 0 in our model specification. Similarly, there may be less crowded exits in that room, but if they are all invisible to the choice maker (e.g. due to the presence of barricades or walls) a value of 0 will again be assigned to the VIS for the decision change of that individual. Intuitively, the decision maker is more likely to change his/her decision when the possible imbalance between the congestion at the chosen exit and those of remaining alternative exits is known to them through visual perception. Therefore, the coefficient for this variable is intuitively expected to be positive. The third variable accommodates the potential role of ‘Social Influence’ (SocInf) or ‘peer behaviour influence’ in changing decisions. We have observed in our previous experiments that the social influence is a major trigger for pedestrian evacuees to change their decisions. Often, when a person abandons the crowding jam behind an exit (chosen initially) to join the queue at another exit, a herd (or cluster or burst) of other evacuees follow that person and change their initial decisions shortly after. See Figs. 1 and 2 for examples of these cases taken from the footage of our past experiment sets. We reflect this effect in the exit-choice-changing model through a binary 0–1 variable labelled SocInf. For a simulated agent who has chosen exit n initially and is now given the chance to change decision, the variable SocInf takes the value of 1 if another simulated evacuee has changed its exit decision from exit n to another exit within the last t seconds (where t is an implicit exogenous input parameter whose value has to be specified by the modeller). If, within the last t seconds, no simulated agent has changed its decision from the current exit, then the value of SocInf for 60

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Fig. 2. Examples of observations from a past experiment in 2017 illustrating a decision changing case. Still image (1) shows a subject and his/her full movement trajectory at an instance of decision change. Still image (2) illustrates another subject that made a decision change following the decision change by the previous subject.

the subject at hand will be 0. We assigned a positive value for the coefficient of this variable, 3, to reflect the effect that makes evacuees more likely to change decisions after observing others making a similar decision change. Our experimental experiences, as well as the limited existing knowledge published by former studies on this topic, have confirmed that the decision change is not a very frequent occurrence during evacuations. The majority of evacuees do not change their exit decisions which indicates a tendency to maintain initial exit choices. Therefore, for any simulation model to produce reasonable patterns of escape behaviour, it is important to keep the likelihood of decision change at a reasonably low value. This would also prevent simulated agents from ‘flip-flopping’ between the exits too frequently and hence, producing unrealistic patterns that are not displayed in the real world by humans. We incorporate this effect into the constant for the utility of change which here we refer to as ‘Inertia’. By assigning a negative value to the constant of the utility of the ‘change’ alternative, we control the likelihood of change at desired levels. Here, we use the term Inertia for this constant with a slight compromise in meaning. The use of this word would have been more accurate should we had used it in relation with the ‘not change’ alternative (with a positive value). However, since we normalised all coefficients for the ‘not change’ alternative to zero and tend to work with only one utility (i.e. the ‘change’ utility), we accommodated this constant equivalently with a negative value in the utility of the ‘change’ alternative.

Uchange = Vchange +

change

= Inertia +

1

CONGn CONGmin + CONGn = CongRatio

2 (VIS )

+

3 (SocInf )

+

change

(1)

Since the variables of the model described above are all choice-situation-dependant and do not vary between the two alternatives, the corresponding coefficients for the utility of the ‘not change’ alternative had to be all set to zero to meet the model identification requirements. Therefore, the probability of the ‘change’ can be calculated using the simple binary logit formula in Eq. (2). 61

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Fig. 3. Visual illustration of the variables of the decision-change model. A simulated subject for which we assume a decision change has been generated is singled out (circled in red) in this image. It is assumed that the subject has changed its initial decision, Exit 1, in favour of Exit 3, a less crowded exit. The congestion ratio variable is computed using the queue sizes at Exits 1 (as the initially chosen exit) and Exit 3 (as the lest congested exit). The VIS variable is zero in this case. We assume that the two subjects singled out by the blue circle had made a change from Exit 1 moments before (within the past t = 2 s). Therefore, the SocInf value is 1 in this instance. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Pchange =

1 1+e

(2)

Vchange

A visual representation of the variables included in the decision-changing model has been provided in Fig. 3 that is basically a still image from the process of the simulation. This is a case of simulation in a room with three alternative exits. The simulated agents shown in the red colour represent the ones that have had at least one decision change. We have singled out one of these simulated subjects and have visualised the relevant aspects (variables) of the environment to its decision change. We assume that the image is taken at the exact moment when the subject was given a chance to revisit and possibly change its initial decision, and we also assume that the change was successful (i.e. that the subject chose to change its initial decision). We also assume that the initial choice of the subject was Exit 1 in this image and that the revised decision was to go to Exit 3. Exit 1 is not the least congested exit in that room at the moment that has been captured by the snapshot. Exit 1 is relatively more congested than Exit 3 (which is the emptiest exit at that moment). The CongRatio is simply calculated by measuring and comparing the crowding level at these two exits. To calculate the VIS, assuming that Exit 2 is not less congested than Exit 1, the only less congested exit would be Exit 3 which is not located in the line of sight of the subject due to the presence of the barricade in the room. Therefore, the VIS takes the value of 0 for this simulated subject. We assume that the two other subjects circled by dashed blue lines had made a decision change from Exit 1 moments before the snapshot was taken. In this case, a value of 1 is assigned to the SocInf variable for our subject of interest. It is important for us to emphasise that the list of the variables influencing the decision change is not claimed to be comprehensive nor is the model specification using these variables claimed to be necessarily the fittest form. The model was kept parsimonious for 62

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various reasons. Firstly, to keep the computational burden of this modelling layer to an acceptable level, given that such models are often required to simulate large crowds where computational efficiency could become a problem. Secondly, to make potential calibrations possible. Having included too many variables in the model, one would have needed a massive amount of data to calibrate the parameters, a dataset that might not be practically collectable. Or alternatively, if one desires to specify the coefficient values with no reference to empirical data and based on try and error; it would be important not to face too many degrees of freedom, otherwise the search for a reasonable set of values might never end. Even given the same set of variables used in our model, alternative model specifications could potentially be proposed. For example, we treat SocInf as a binary variable, whereas it could alternatively be treated as a non-binary integer variable that counts the number of agents that have made decision changes moments before. We, however, recommend the use of unit-less variables (like categorical variables, or unitless ratios such as Congestion Ratio) that would help maintain the maximum level of generalisability in the model parameter values. This feature makes it more likely for a set of parameters chosen or estimated for one physical setting to perform reasonably well in other physical setting that differ from that of the original setting. As another aspect of the model specification, the variable VIS could have been implemented in interaction with CongRatio as opposed to being used directly as an independent variable in the model. In the absence of empirical data, it would be hard to answer which specification is a better fit to the real behaviour. However, the specification presented in Eq. (1) was favoured in this case mainly because of the subsequent behavioural sensitivity analysis we performed in this work. In order for the outcomes of such analysis to be readily interpretable from a behavioural perspective, it is important for the variables to have clear-cut and straightforward definitions. With that consideration in mind, mixed interacted variables would make subsequent interpretations less straightforward and that is the primary reason these variables were avoided in analyses of this work. Another aspect that has an impact on the performance of the decision-change model once employed for simulation is the frequency at which the agents are given a chance to revise and change their decisions. It is not a plausible feature to let agents revise decisions too often, but in order for changes to occur when they are likely to occur in real-world scenarios, it is important that the agents get the chance to revise their initial choice frequently enough. In the simulation setting used in this work, at each time step, one agent gets the chance to update. The simulation is performed at a time resolution of 0.004 s. We use an update cycle of 100 which means at every 100 cycles all ‘eligible’ agents in the scene are given a chance to revise their decisions. We keep this frequency of giving decision change opportunity to agents constant and control the frequency of the changes at desirable levels using the more explicit coefficient of Inertia in the model. Another crucial aspect of modelling the decision changes is to avoid giving this opportunity to agents for whom a change is not physically feasible. This particularly includes the agents that are “trapped” inside a crowd jam around an exit (i.e. confined by the surrounding crowd jam) and thus, are not physically able to change decisions. This condition was extremely difficult to be fully guaranteed in the model, but measures were taken to embody the decision-change feasibility (or eligibility) in the simulation model. Our aim was to give change opportunity only to ‘eligible’ agents, those that are at the ‘edge’ of the crowd and thus have the option to change their decision if they desire to do so. On the other hand, we want to give this opportunity to agents that are experiencing a delay, because it is not very likely for an agent that is progressing well towards its initially-chosen exit to make any change of decision. Therefore, we used the following set of criteria to determine whether or not an agent is eligible. We measure a pseudodensity factor for each agent as a measure of the local crowd density experienced by that agent. The number of agents located in a R = 2 m distance from the agent is counted, and the number is divided by the area of this circle to produce a local density for that subject. In order for the subject to be eligible, the following two conditions have to be met (simultaneously) for the local density and velocity of that agent. The simultaneous imposition of a minimum on the density as well as a maximum on the velocity of the subject makes sure that the subject is experiencing a delay. Whereases, the imposition of an upper bound on the density is to make sure that the subject is not trapped inside a crowd and thus can feasibly revise its initial decision.

Densitymin < Local Density < Densitymax (I ) AND Velocity < Velocitymax

(II)

It is also important to note that the model is probabilistic, and even when an agent is given the chance to revisit the initial decision, this does not guarantee that the agent will choose to change. The probability of change is calculated based on which the choice to keep or change the initial decision is simulated probabilistically. If the outcome is to change the initial decision, then the initially-chosen exit is excluded from the choice set when the agent makes the new exit choice. The input values of the model were chosen here arbitrarily based on an extensive try-and-error search process and by observing the pattern of behaviour (while visualising the changes) under various physical and congestion settings. We used the following values as the ‘base values’ for our analysis and the values that we believed would produce reasonable patterns of decision changing: t (time horizon for SocInf measurement) = 2 s, Inertia = −7.5, CongRatio coefficient = 3.5, VIS coefficient = 0.8, SocInf coefficient = 0.8, Densitymin = 1 ped/m2, Densitymax = 3 ped/m2, Velocitymax = 1 m/s. The set of reasonable parameter values is not necessarily unique, and by fine-tuning different parameters in different directions, one could produce similar reasonable patterns using different sets of parameter values. 3.3. Exit choice module The choice of exit for each simulated agent is determined by a multinomial logit model that we formulated and calibrated based on a previous experiment and reported in a previous study (Haghani et al., 2016). A choice of exit between all available exits in the room is simulated for each agent at the moment that the agent enters a room. The choice is made based on a trade-off between the size of congestion at each exit (CONG), the size of flow moving to each exit (FLOW), the visibility of each exit (VIS) and the spatial 63

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Fig. 4. Visual illustration of the exit choice model. It is assumed that the singled-out subject (by the blue circle) is at the point of exit choice making. We measure the size of congestion (CONG) at each alternative exit as well as the size of the flow (FLOW) to each alternative exit. We also measure the distance to each exit (DIST) and the visibility status (VIS) of each exit. A utility-based trade-off between these attributes determines the choice of exit simulated for each agent. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

distance of the agent to each exit (DIST). These factors are included in the utility of each exit with the note that the FLOW enters the utility in interaction with the VIS. Thus, the model accommodates separate coefficients for the flow sizes moving to visible exits than that of the flows moving to invisible exits. The simulated agent may, later on in the simulation process, be given the possibility to change this decision, and if the choice is to change the initial decision, a new choice of exit is simulated using the same modelling rule while excluding the previously chosen exit (i.e. the current exit) from the choice set. We have visually illustrated in Fig. 4 the variables of the exit-choice model on a still image of the simulation visualisation. We assume that the subject singled out and circled in blue is approximately at the point of the exit decision making. At such moment in the (simulated) time, we measure the exit attributes (DIST, CONG, FLOW and VIS) and whereby the utility of each exit and their associated choice probabilities. The simulated agents shown in Fig. 4 with a black arrow have already chosen Exit 1, and those with a red arrow have chosen Exit 2. By counting the number of the subjects moving to or jamming at each exit, we determine the CONG and FLOW attributes for each exit. The attributes DIST and VIS are physical attributes and are determined by connecting the position of the subject to the centre point of each exit, measuring the distance and determining whether or not the line is intersected with barricades or walls. 3.4. Local pathfinding module Once the choice of exit is simulated for each agent, the agent is moved towards the chosen exit. This process is performed using two integrated additional layers of modelling. This integrated layer combines an A*-pathfinding algorithm (Cui and Shi, 2011) with a 64

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Fig. 5. Visual illustration of the simulation process and the pathfinding module. Still image (1) shows the process of evacuation in progress, image (2) illustrates the concept of penalty weights for the shortest path finding. Image (4) visualises the shortest and truncated shortest paths. Image (3) illustrates the actual trajectories.

social-force model (Helbing et al., 2000). The A*-pathfinding algorithm requires discretisation of the movement space. This layer acts as an intermediate layer between the exit choice and the social force model. A system of discrete spatial mesh is overlaid on the movement space (see Fig. 5). Once the choice of exit simulated for an agent, this information is given as input to the pathfinding module. The A* pathfinding algorithm returns the shortest weighted path between each agent’s location and the position of the chosen exit (dictated by the exit choice module) and is updated at a certain frequency. If the choice of exit changes as a result of interaction between the exit-choice and exit-choice-adaption modules, then this information is updated for the pathfinding algorithm too. The algorithm penalises the links based on the presence of agents and obstacles. The calculated path is then truncated (smoothed) to generate a more realistic pattern of movement with lesser spatial fluctuations. See Fig. 5 for the visualisation of the penalty weights as well as the path-generation process. Also, see the online supplementary videos for a dynamic visualisation of this process while calculations are in progress. Once the path is generated, the subsequent target point of the agent on the mesh system is determined. This information is fed to a social-force model of pedestrians to calculate the desired direction and whereby the desired force of the pedestrian. The vector that connects the current position of the agent to the next target point on the mesh system (informed by the pathfinding algorithm) is given as the desired direction input to a social-force model (Haghani and Sarvi, 2019c). The net outcome of the social force, wall force, and desired force are calculated to determine the actual next step (next position) of the pedestrian at the next time step. 4. Numerical simulation test setups 4.1. Comparisons with empirical observations In order to quantify the magnitude of the effect of including a decision-change module in the simulation tool on the accuracy of the simulated modelling outputs, we resorted to two sets of experimental observations. While these experimental scenarios have been performed originally for individual-level analyses of exit choice (a type of analyses that is beyond the scope of this work), we merely used them for their macro-level (or aggregate) outputs in this work. We do not report on the analysis of the choice data extracted from these scenarios as they are about exit choice and thus, irrelevant to the main topic of this work. We simply use them for the measurement of the Total Evacuation Time and Exit Shares (or Exit Utilisations, that is to say, the number/percentage of evacuees exited through each gate). These experiments of evacuations have been conducted in 2015 and 2017 in three general geometries. Figs. 6–8 show the blueprint of these physical setups. Each scenario is a unique combination of certain control factors, including the size of the crowd, the number of available alternative exits, the widths of exits and the spatial distribution of available exits. We 65

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Fig. 6. Experimental geometry type 1.

use a total of 37 scenarios of this kind from our previously collected experimental datasets. These scenarios are consistent and comparable in terms of their context in that they all simulate escape from imminent dangers or in other words; they simulate rapid evacuations. We do not use the experimental scenarios that have been treated as orderly evacuations or treated as cases of nonimminent danger (or low level of urgency). Table 1 summarises the details of all these experimental scenarios, and Figs. A1–A3 in the Appendix provide a snapshot from each of these 37 scenarios. We replicated each of these experimental scenarios using the simulation method described earlier. Figs. A4–A6 in the Appendix show still images from the simulation process associated with each experimental scenario. Simulated subjects are generated in the yellow rectangular auxiliary rooms at a rate of 10 pedestrians per second while maintaining the total number of simulated pedestrians equal to that of the corresponding experimental scenario. The desired velocity is kept at 3 m/s which was the most frequent maximum velocity value observed in our experiments. Each scenario is simulated for two cycles of 100 runs. Our preliminary analyses indicated that for a number of nearly 30 repetitions, the average of evacuation times and exit shares converged to a satisfactory stable quantity. However, in order to be on the safe side and mitigate the effect of the behavioural uncertainty (Ronchi et al., 2014b) from the analysis, we chose a very conservative value of 100 repetitions for each scenario. The first cycle of 100 runs is performed while the decision update feature is disabled; and the second cycle of 100 runs is performed whilst this feature is enabled. For each cycle of 100 runs, we measured the average of the total (simulated) evacuation times (in seconds) and the average of the exit shares (in percentage) as well as the standard deviations of these measurements. In total, 7400 simulation runs were performed for this analysis. 4.2. Comparisons across various behavioural tendencies The second aspect of our analyses focused on the impacts of decision-changing behaviour on the evacuation efficiency through analysing the sensitivity of the simulated outputs to the values of the decision-changing parameters. We performed these analyses by gradually changing the value of each parameter at small step sizes (to ensure continuity of the response variable) while measuring the evacuation outcomes and keeping the values of every other parameter constant. For each given set of parameter values, and for each given simulation setup, we repeated the process of simulation 50 times and recorded four measurements at each run. The measurements included the total evacuation time, the mean of individual evacuation times, the number of decision-change attempts; and the number of (successful) decision changes. We averaged these measurements over each cycle of 50 simulation runs. To make sure that the outcomes of this analysis are not artefacts of a specific physical setup of the simulation, we performed and repeated these tests on three different physical setups. These setups have been presented in Fig. 9. Red agents in these images are the ones that have had a decision change since the moment they stepped into the room. Each setup includes three 100 cm-wide exits and 66

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Fig. 7. Experimental geometry type 2.

Fig. 8. Experimental geometry type 3. 67

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Table 1 Details of the experimental scenarios. Scenario No.

Experiment year

Geometry type

Crowd size

Available exits

Exit widths (w)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37

2015 2015 2015 2015 2015 2015 2015 2015 2015 2015 2015 2015 2015 2015 2015 2015 2015 2015 2015 2017 2017 2017 2017 2017 2017 2017 2017 2017 2017 2017 2017 2017 2017 2017 2017 2017 2017

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3 2 2 2 3 3 3

75 75 75 75 75 75 142 142 142 142 142 142 142 152 142 142 142 142 142 61 53 61 53 61 53 61 53 61 53 61 53 114 114 114 114 114 114

1,2,3,4 1,2,3,4 1,3,4 1,3,4 1,2,4 1,2,4 1,2,3,4 1,2,3,4 1,3,4 1,2,3 2,3 1,4 2,5 2,5 2,5 2,5 2,3,5 2,3,5 2,3,5 1,2,4 2,3,5 1,2,3,4,5 1,3,4,5 1,3,4,5 1,2,3,4,5 1,2,4 2,3,5 1,2,3,4,5 1,3,4,5 1,3,4,5 1,2,3,4,5 1,2,4 1,3,4,5 1,2,3,4,5 1,2,4 1,3,4,5 1,2,3,4,5

w1 = w2 = w3 = w4 = 100 cm w1 = w2 = w3 = w4 = 100 cm w1 = w3 = w4 = 100 cm w1 = w3 = w4 = 100 cm w1 = w2 = w4 = 100 cm w1 = w2 = w4 = 100 cm w1 = w2 = w3 = w4 = 100 cm w1 = w2 = w3 = w4 = 50 cm w1 = w3 = w4 = 50 cm w1 = w2 = w3 = 50 cm w2 = w3 = 50 cm w1 = w4 = 50 cm w2 = w5 = 50 cm w2 = w5 = 50 cm w2 = 50 cm, w5 = 100 cm w2 = 100 cm, w5 = 50 cm w2 = w3 = w5 = 50 cm w2 = w5 = 50 cm, w3 = 100 cm w2 = w3 = 50 cm, w5 = 100 cm w1 = w2 = w4 = 50 cm w2 = w3 = w5 = 50 cm w1 = w2 = w3 = w4 = w5 = 50 cm w1 = w3 = w4 = w5 = 50 cm w1 = w3 = w4 = w5 = 50 cm w1 = w2 = w3 = w4 = w5 = 50 cm w1 = w2 = w4 = 50 cm w2 = w3 = w5 = 50 cm w1 = w2 = w3 = w4 = w5 = 50 cm w1 = w3 = w4 = w5 = 50 cm w1 = w3 = w4 = w5 = 50 cm w1 = w2 = w3 = w4 = w5 = 50 cm w1 = w2 = w4 = 50 cm w1 = w3 = w4 = w5 = 50 cm w1 = w2 = w3 = w4 = w5 = 50 cm w1 = w2 = w4 = 50 cm w1 = w3 = w4 = w5 = 50 cm w1 = w2 = w3 = w4 = w5 = 50 cm

Fig. 9. Still images from the simulation process and the three physical setups used as the bases for the sensitivity analyses while the decision change module is active. The agents turned red illustrate the ones that have made more than one exit decision (i.e. had a decision change). Images (1), (2) and (3) represent physical setups 1, 2 and 3, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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Fig. 10. contrasting the (dis)similarity between the simulated and observed exit shares (first row) as well as the simulated and observed evacuation times (second row). The plots on the left are associated with the simulations without the decision-change feature (i.e. while decision-change is deactivated). The plots on the right are associated with the simulations while the decision-change module was active. The error bars show the standard deviations of the simulated measures averaged over the cycles of 100 repetitions. The correlation (Corr) and the average (of absolute) difference (Avg diff) between the simulated and observed quantities are reported on each plot.

one barricade. Setups 1 and 2 are asymmetric, and setup 3 is symmetric. For each simulated setup, 400 evacuees are generated in the yellow rectangular auxiliary rooms that are connected to the main room through a wide gate. The agents are generated at the rate of 15 pedestrians per second. In total, more than 35,000 simulation runs were performed for this analysis. 5. Simulation outcomes 5.1. How important is an exit-choice-changing module? The outcomes of the comparison between the simulated and observed measurements have been summarised in scatterplots in Fig. 10. We contrast the observed exit shares with the simulated exit shares under the condition where the decision-change module was and was not active (plots 1 and 2, respectively). We also contrast the observed total evacuation times with the simulated total evacuation times while the decision-change module was active and while this feature was disabled (plots 3 and 4, respectively). In each scatterplot, each point corresponds to a particular experimental scenario (and its equivalent simulated scenario). The xcoordinate of each point is the observed measurement for that scenario in the experimental setting, and the y-coordinate is the corresponding average of the simulated measurement. The error bar shows the standard deviation of the simulated measurement. The bisector line y = x is superimposed on the plot to facilitate the comparison. The scatter of the points around the bisector line is a measure of the dissimilarity between the observed and the simulated outputs. In an ideal case, all points would line up on the bisector line (for an imaginary ideal model that perfectly replicates all macro-level observations). The dissimilarity between the simulated and observed measurements have also been aggregated and quantified based on two quantities. These include the correlation (Corr) between the simulated and the observed measurements as well as the average of (the

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Fig. 11. The sensitivity of the simulation measures to the values of the Inertia factor in the decision-change module. The plots on the first, second and third rows are associated respectively with physical setups 1, 2 and 3. The plots on the left show the sensitivity of the average total evacuation time (left vertical axes, continuous black curves) and average individual evacuation times (right vertical axes, dashed red curves) to the Inertia value. The plots on the left show the sensitivity of the number of decision change attempts (left vertical axes, continuous orange curves) and the number of decision changes (right vertical axes, dashed blue curves) to the Inertia value (averaged over the simulation repetitions under each parameter value). Error bands represent the standard deviations of the measurements. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

absolute value of) the relative differences (Avg diff) between the observed and the simulated measurements. These quantities have also been reported on their corresponding plots in Fig. 10. According to these results, it is very clear that the inclusion of the decision-change module made a very substantial difference in terms of the accuracy of the predictions. Without this feature, we had a large amount of overestimation and underestimation of the exit shares while also having a systematic pattern of overestimating the total evacuation times. The inclusion of the decision-change module alleviated both problems to great degrees. It appears that without an option for simulated agents to adapt their exit choices, the simulation model would grossly underestimate the intelligence of the humans’ decision-making as well as the optimality of their behaviour; and thus, incurs a substantial amount of prediction error and systematic bias. Based on the exit-share measurements, the addition of the decision-change modelling layer doubled the correlation between the observed and the simulated shares (from 0.4 to 0.8). It also reduced the average relative differences between the simulation and observations from about 35% to nearly 20%. Based on the total evacuation time measurements, the correlation between the observed and simulated outputs increased from 0.9 to 0.95 as a result of enabling the decision-change option while the average differences between the simulated and observed evacuatrion times decreased from about 70% to nearly 30% (more than a 100% relative improvement in the prediction accuracy). 5.2. How changing exit choices influences evacuation efficiency The outcomes of the sensitivity analyses have been summarised in Figs. 11–14. In each of these figure sets, the first, second and third rows are related to the measurements obtained from setups 1, 2 and 3 respectively (as detailed in Fig. 9). The left-side line charts in each of these figure sets report on the measurements of the average total evacuation times (left vertical axis, continuous black curves) and the average of (average) individual evacuation times (right vertical axis, red dashed curves) for each parameter value. The right-side line charts report on the measurements of the number of change attempts (left vertical axis, continuous orange curves) and the total number of (successful) decision changes (right vertical axis, blue dashed curves) for each value of the parameters, averaged over the cycle of 50 simulation runs for each parameter value. The vertical dashed line superimposed on each of these charts

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Fig. 12. The sensitivity of the simulation measures to the values of the Congestion Ratio factor in the decision-change module. The plots on the first, second and third rows are associated respectively with physical setups 1, 2 and 3. The plots on the left show the sensitivity of the average total evacuation time (left vertical axes, continuous black curves) and average individual evacuation times (right vertical axes, dashed red curves) to the Congestion Ratio. The plots on the left show the sensitivity of the number of decision change attempts (left vertical axes, continuous orange curves) and the number of decision changes (right vertical axes, dashed blue curves) to the Congestion Ratio value (averaged over the simulation repetitions under each parameter value). Error bands represent the standard deviations of the measurements. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

show the base value of the decision-change model parameter represented by the horizontal axis, as specified and detailed in the previous sections. In all these charts, the error bands represent the standard deviation of the measurements. According to these figures, the number of decision changes as well as the aggregate outputs of the simulation are both sensitive to all decision-change parameters (to varying degrees). The decrease in the magnitude of Inertia parameter, or the increase in the magnitude of the CongRatio or VIS or SocInf all resulted in greater numbers of decision changes and made the change a more likely occurrence. The graphs, in comparison with one another, show that the likelihood of change is least sensitive to the value of the physical parameter of the model, that is, VIS. The likelihood of change is, by comparison, more heavily dependent on the attributes of the model that are related to interaction between people (i.e. CongRatio and SocInf). In terms of the impact on the aggregate prediction outcomes (i.e. the evacuation time measures), the least degree of sensitivity was observed in relation to the VIS factor. There was only a small degree of case sensitivity (i.e. the dependency of the outcomes on the type of the physical setup) for almost all our measurements in these analyses. This gives us the suggestion that the outcomes are by-and-large generic regardless of the simulated physical setup. In relation to the two measurements of the evacuation times, total and individual evacuation times, results suggested that the patterns of change for both quantities are mostly analogous and consistent with one another. This suggests that either one of these two measures (i.e. total evacuation time or mean of individual evacuation times) could be used almost interchangeably in our analysis, or even in other applications like evacuation optimisation programs. According to the evacuation time sensitivity analyses in Fig. 11, it is the intermediate amounts of Inertia (the tendency to keep the initial decisions) that is optimum for the system (i.e. corresponds to the minimum evacuation time) while all other factors are kept constant. The value of Inertia = 0 is indicative of a situation in which evacuees do not have any particular tendency or preference for sticking to their initial decisions. According to our analyses outputted in Fig. 11, this tendency is not optimum from a system perspective. Similarly, a large negative value of Inertia is indicative of a situation where evacuees are not willing at all to change their initial decisions under any circumstances (i.e. a one-off decision-making strategy). According to our analyses outputs, this behavioural conduct is not optimum either. A certain intermediate amount of Inertia would be most beneficial to the system of evacuees, and too much or too little of it both make evacuation processes less efficient.

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Fig. 13. The sensitivity of the simulation measures to the values of the Visibility factor in the decision-change module. The plots on the first, second and third rows are associated respectively with physical setups 1, 2 and 3. The plots on the left show the sensitivity of the average total evacuation time (left vertical axes, continuous black curves) and average individual evacuation times (right vertical axes, dashed red curves) to the Visibility value. The plots on the left show the sensitivity of the number of decision change attempts (left vertical axes, continuous orange curves) and the number of decision changes (right vertical axes, dashed blue curves) to the Visibility value (averaged over the simulation repetitions under each parameter value). Error bands represent the standard deviations of the measurements. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

According to the evacuation time sensitivity analyses presented in Fig. 12, higher sensitivity to the existing imbalance in the exit congestions is invariably non-detrimental to the system of evacuation (although its marginal benefit tends to diminish for large values of this parameter). The tendency to take exit congestion imbalance into account is reflected in the CongRatio parameter. A value of CongRatio = 0 is associated with a situation in which there is no regard of the exit congestion imbalance in the decision-changing behaviour. This tendency appears to be the worst strategy among all possible values of this parameter. As sensitivity to the congestion imbalance increases (or equivalently, as the value of CongRatio increases), the system becomes more optimum and the evacuation times drop. However, there is only certain amounts of benefit that the system can achieve through increasing the sensitivity to the congestion imbalance. As demonstrated by Fig. 12, values of the CongRatio greater than certain intermediate values do not result in further decreases in the evacuation times as the curves flatten out after some point. However, the results suggest that the system never incurs any detriment from high degrees of congestion imbalance vigilance (or sensitivity). According to the evacuation time sensitivity analyses in Fig. 13, the system’s efficiency is not much sensitive to the VIS factor in the decision-change model. However, the overall but not-so-strong message from this figure was that it is to some degrees good for evacuees to take visibility into account when changing decisions to go to another exit, but the magnitude of the effect on the system efficiency is not substantial. One of the most interesting aspects of this analyses was related to the effect of the SocInf in decision-change behaviour on the system efficiency. Prior to performing the simulation analyses, we were not able to intuitively predict the direction of the effect that changing the value of this parameter could cause. Increasing the value of this parameter increases the tendency to imitate peers’ change of decisions and produces a pattern of follow-the-peer behaviour in decision changing. Once the value of this parameter becomes large enough, the imitation becomes the dominant factor in decision changing and one would frequently observe large herds (or bursts or clusters) of decision changing during the simulation process. However, the question that arises is that whether that behaviour would be an efficient strategy from a system performance perspective. We have observed in our other studies that humans do avoid others when making exit choices (and display a behaviour opposite to the herding) (Haghani and Sarvi, 2017a, 2018a). Interestingly though, they tend to follow decision changes of others and show herding tendencies when it comes to revising and changing decisions. Also, we have observed based on our other analyses that herding in exit choices is almost invariably detrimental

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Fig. 14. The sensitivity of the simulation measures to the values of the Social Influence factor in the decision-change module. The plots on the first, second and third rows are associated respectively with physical setups 1, 2 and 3. The plots on the left show the sensitivity of the average total evacuation time (left vertical axes, continuous black curves) and average individual evacuation times (right vertical axes, dashed red curves) to the Social Influence value. The plots on the left show the sensitivity of the number of decision change attempts (left vertical axes, continuous orange curves) and the number of decision changes (right vertical axes, dashed blue curves) to the Social Influence value (averaged over the simulation repetitions under each parameter value). Error bands represent the standard deviations of the measurements. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

to the efficiency of a system of evacuees (Haghani and Sarvi, 2019b), but we had no prior reliable knowledge of this effect in relation to the decision-changing behaviour. According to the evacuation time sensitivity analyses in Fig. 14, the system can actually benefit from moderate degrees of imitative tendencies in decision changing (and maybe that is the reason humans do show such tendency when considering the problem from a survival strategy or evolutionary perspective). A value of SocInf = 0 is associated with a situation where evacuees are not affected by observing decision changes of others. And according to our analyses, this tendency is not optimal. As the herding tendency in decision changing increases from zero, the system becomes more efficient and that enables the crowd becomes to evacuate in shorter times. However, the evacuation time curves all show their minimums at certain intermediate values for this parameter beyond which the system starts to become inefficient again. In comparison, extreme degrees of follow-the-peer tendency in decision changing is more inefficient (i.e. worse to the system) than a zero tendency to follow the peer. 6. Conclusions This work followed two distinct questions in relation to the evacuation behaviour and modelling of crowds. The first question concerned how crucial it is for the evacuation simulation models to represent the dynamic adaptive nature of the evacuees’ decisionmaking. We examined this question specifically in relation to the exit-choice behaviour. The second question looked at the effect of decision-changing mechanism on the system performance in terms of the total and individual evacuation times. As opposed to the first question that mainly concerns the descriptive power and accuracy of the evacuation model (Gwynne et al., 2017), the second question relates to the problem of optimising evacuation strategies (Vermuyten et al., 2016) which has practical applications in evacuation management and training. This work was the first to quantify the significance of representing the dynamism of evacuation decision-making in simulation models in terms of their ability to produce realistic estimates. Using a multi-attribute binary discrete-choice model, we represented this aspect of the behaviour in a fully parametric modelling framework. By utilising an extensive number of experimental scenarios and replicating them in simulated setups, we observed that the inclusion of this modelling feature in the evacuation simulation makes a substantial difference in the accuracy of the simulated outputs. This finding adds further evidence about the importance of maintaining a reasonable balance across the accuracy of various levels (or layers) of evacuation simulation models (Haghani and 73

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Sarvi, 2018a) and ensuring that all major and relevant modelling layers are represented adequately in the simulation process. It highlights the necessity of adequately covering all major aspects of the behaviour (or all major levels of decision-making) relevant to the evacuation behaviour, as opposed to perfecting certain layers and omitting other layers or representing them in poor forms. The second aspect of our study was about examining how the optimality of evacuation systems could be influenced by changing evacuees’ tendency to actively revise and adapt their decisions. The main outcome of our analysis on this question was that neither the ‘too-frequent-decision-update’ strategy nor the ‘no-update-at-all’ strategy is optimum. The system of evacuation benefits most from an intermediate tendency to revise and adapt exit decisions. It was also striking to note that moderate degrees of follow-theneighbour (or the so-called, herd-type) behaviour in decision-changing can help the system and shorten evacuation times. Whereas, our findings from other studies have shown that imitation in exit decision making is never of any benefit to the system (Haghani and Sarvi, 2019a; Haghani and Sarvi, 2019b). This highlights the significance of drawing clear distinctions between the peer influence on various aspects of evacuation behaviour and studying them separately and in their own terms. Humans might show imitative tendencies in some aspects of their decisions and exhibit an opposite behaviour in other aspects of evacuation decision-making. Similarly, a follow-the-peer tendency in certain aspects of behaviour might have a completely different effect on the system than such tendency in other aspects of evacuation decision-making. These findings could have important implications for the management of evacuations and for developing simple but useful guidance as to how occupants should be advised or trained to conduct themselves in cases of emergencies in crowded spaces. 7. Discussion As will be discussed in the followings, calibration of a decision-changing model (when formulated as a choice between “change” and “not change” alternatives) is relatively challenging compared to the calibration of an exit choice counterpart model. As a result, it was crucial in this work to maintain the feature of modelling parsimony in proposing the model and to limit the number of independent variables in the model. This ensures that the model remains calibratable. However, the authors would like to emphasise that this does not equate an intentional dismissal of other potential factors that may influence the problem at hand, that is, decision adaptation. As listed in the model conceptualisation section of this article, the variables used in the model are those that were believed to be most generic in various scenarios and most common according to the previous studies (on exit choice behaviour). One may also include the possibilities that different individuals may have different tendencies for changing their decisions. Individuals are more likely to follow decision adaptation actions of those with whom they are socially affiliated as opposed to following complete strangers (Gwynne et al., 2016). The aspect of individual differences in decision changing tendencies or social affiliations were left out of the modelling framework merely since we do not have adequate descriptive knowledge on this dimension of the behaviour. As mentioned in the literature review section, experimentation on decision-changing behaviour has been very limited and while we have some knowledge about individual differences in exit choices (Haghani and Sarvi, 2016b), there has been no counterpart empirical evidence for exit-choice changing. The need for the study of individual differences on this aspect of behaviour could include simple observable factors such as gender or age or individual’s ability to walk or even the latent (unobservable) characteristics of the choice maker. When choosing to represent such individual characteristics in the model, it is important to note that apart from the problem of estimation, these factors require an extra layer of input information (e.g. the distribution of age or gender or the proportion of disabled individuals etc) in order for the model to be able to function. The problem of social affiliation was also not considered in this work and the model merely represented crowds of unaffiliated individuals. The mechanisms of decision changing by social groups may require a dedicated study and further experimentation. But the role of this factor is intuitively understandable as occupants may be more likely to follow decision adaptation behaviour of those who are socially connected to them as opposed to copying the act of complete strangers (Gwynne et al., 2016). Further to the variables mentioned above, we would like to highlight the potential role of a number of context-specific variables that could be included in models of exit-choice-changing behaviour. Such factors could include the level of urgency/stress, the level of familiarity with the environment and the general condition of visibility in the escape environment (Fridolf et al., 2013; Isobe et al., 2004; Jeon et al., 2011; Kinateder et al., 2014a; Kinateder et al., 2014b; Muir et al., 1996; Nagai et al., 2004). It is possible that the change in any of these contextual elements impact on the tendency of occupants to revise their initial decisions. For example, a question would be whether evacuees tend to change their decisions less often under higher levels of stress or urgency (as suggested by Bode and Codling, 2013). We believe that the existing knowledge on these context-specific factors are extremely limited and this calls for systematic experimentations on this topic so one can innovatively introduce the role of stress level or familiarity level to the experimentation treatment. Desirable as it is to include all such theoretically influential factors in one modelling framework, it is important to consider the complications that each bring to the modelling process. This includes further complication to the calibration process or further computational burden. Therefore, it is of great importance to prioritise such variables, identify their relative significance through experimentation and also identify the amount of difference that adding each additional variable makes in terms of improving the modelling accuracy. In some cases, the difference may be substantial and therefore the extension is warranted. And for some factors, the additional modelling complications may not be justified by an incremental modelling improvement. The case of this study looked particularly at including or excluding a modelling ‘layer’ or ‘feature’ (as opposed to looking at including additional independent variables within a model). Analysis revealed a substantial difference between simulating with and without the decision adaptation feature (while using only limited number of variables). However, whether this gain in accuracy will marginally diminish or it can continue at the same extent by adding more independent variables is a question that should be systematically investigated by further studies. Future studies could also explore different variations of the model proposed in this work (in terms of the variable definition, 74

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variable specification, utility specification, decision rule specification, etc.) to identify the effect of these relatively subtle variations on simulated outcomes. While we did not systematically investigate this question, our preliminary analysis before running the main numerical tests indicated that once the module is included in the model, variations within the model make relatively minor differences in the simulation outputs. Given that the general framework of modelling in this work was based on the notion of random utility maximisation, one question that may arise is that whether the model imposes an assumption of ‘perfect behaviour’. In other words, one may ask whether this approach can be reconciled with the previous statements such as “People tend to satisfice rather than optimise. People are more likely to choose an option that is perceived as ‘good enough’ rather than the best option” (Gwynne et al., 2016). The answer is that there is no contradiction between these two notions. To the contrary, the random-utility framework, as a stochastic model, does in fact allow noisy and suboptimal behaviour. It gives greater probabilities to ‘better’ options than to ‘worse’ options, but it does not rule out the possibility of suboptimal decisions (Haghani and Sarvi, 2018b). For example, one may imagine an evacuation scenario in a room with two exits where there is no line of sight between the two queues formed at the two exits (one may imagine that there is an obstacle in between). It is possible to imagine a scenario where one queue size is shorter than the other and some occupants, to their detriments, leave that smaller queue to join the other just because a number of other individuals took this action in their vicinity. The probabilistic model proposed in this work certainly allows for this action (i.e. a probabilistic trade-off between the attributes which may often result in suboptimal actions too). The simulated probability for ‘change’ in this case would of course depend on how the modeller has specified the coefficient for social influence compared to those of other factors. While the problem of model calibration was beyond the main focus of this work and besides its main purpose, we believe that some notes on the calibration of the decision-change model could be of use. The model of decision adaptation has only few parameters whose values can be specified arbitrarily and based on the reasonableness of the outcomes that they produce. This reasonableness can be judged both visually or numerically by an analyst in a tryand-error search procedure. However, direct calibration is also possible, should the appropriate data is available at sufficient quantities. For that purpose, the discrete-choice model of decision adaptation would require disaggregate observations. These observations can be obtained from experimental settings. In our earlier work, we have shown how exit-choice models can be directly calibrated using disaggregate choice observations (Haghani and Sarvi, 2017c). Although the method is theoretically extendable to the decision-changing model too, the decision-changing model calibration poses further layers of complexity. First, decision changing is not a frequent observation. When we organise an experimental scenario, only a small portion of evacuees will show decision changes (Liao et al., 2017). In that sense, in order to generate an adequate number of ‘change’ observations, a relatively large number of repetitions would be required. Moreovere, the design needs to ensure that the situation developed in the experiment would be complex enough (in terms of the crowding level, etc.) to persuade subjects to make decision changes. Another challenge would be to ensure adequate degrees of attribute variation over instances of decision change in the experiment design that is a requirement for efficiently estimating the model. However, the main challenge of preparing the data is actually the fact that if we exclusively record observations of decision change, then the resultant data would be of no modelling use. That data would suffer from an extreme degree of sampling exogeneity (or choice-based sampling) since we are only collecting observations from those who chose one particular alternative (i.e. ‘change’). This data will not contain any information about why evacuees do “not” change decisions and thus, cannot serve to estimate the model that we formulated. Therefore, it will be crucial for the analyst to take sufficient and innovative measures that compensates for this sampling exogeneity and include observations of ‘not change’ in the data alongside the observations of ‘change’. Further on the topic of calibration, it is important from the modelling perspective that calibration of a simulation model is subject to error at all layers. From this perspective, an important question that is often overlooked is how robust a model (or a particular layer of a model) is to mis-calibration (or calibration error). The answer to this question has direct implications in terms of the confidence in evacuation time estimates and other important metrics produced by such models. It determines the margin of error and the level of confidence in the predictions (or estimates). A desirable modelling feature is being robust to mis-calibration. This feature is possessed by a model when making slight alterations to the value of a single calibrated parameter does not change the results dramatically. This means that the model predicts well at a reasonable level of confidence and that the model is not critically affected by the calibration error at the level of individual parameters. We believe that the problem of dynamic adaptive decision simulation has pertinence to this issue. It is possible that part of the modelling improvements that we observed in terms of the two most common aggregate measures, exit shares and evacuation times, after introducing the decision-change module is because the module, to some extent, corrects the errors of the exit-choice module. While we are not able to disentangle these two effects based on our analyses, the outcomes still convinced us of the great significance of including this module in the simulation tool (and indirectly, of the significance of investing in its further calibration). The outcomes showed that even a decision-change module with few critical variables can substantially improve the accuracy of macro-scale simulated outputs. When exit choices are simulated as one-off decisions, the decision will be more consequential as opposed to a case where the simulated agent will have the opportunity to revise that decision later on during the simulation process. This is likely to make the exit-choice layer of the general model susceptible to mis-calibration. We believe that, in addition to improving the overall accuracy of the model, the inclusion of the decision-changing feature can potentially make the parameters of the exit-choice module more robust to mis-calibration, thereby, increasing our confidence in the predicted estimates. Acknowledgements The authors extend their sincere gratitude to the Associate Editor and three anonymous reviewers for their constructive feedback. 75

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Appendix A Figs. A1–A3 show still images from the experimental scenarios that were used for model evaluation in this work. Figs. A4–A6 provide snapshots from the process of replicating those experimental scenarios in the computer simulation setting.

Fig. A1. Still images from the video footage of the experimental scenarios 1–15. 76

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Fig. A2. Still images from the video footage of the experimental scenarios 16–30.

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Fig. A3. Still images from the video footage of the experimental scenarios 31–37.

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Fig. A4. Still images from the simulation process of the experimental scenarios 1–15.

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Fig. A5. Still images from the simulation process of the experimental scenarios 16–19.

Fig. A6. Still images from the simulation process of the experimental scenarios 20–37. 80

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Appendix B. Supplementary material Supplementary data to this article can be found online at https://doi.org/10.1016/j.trc.2019.04.009.

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