Effects of Environment Knowledge in Evacuation Scenarios Involving Fire and Smoke: A Multiscale Modelling and Simulation Approach

Fire safety of buildings has always been an important aspect of societal research. An important development in recent years is the shift from prescriptive building codes to performance-based building [1], meaning that instead of requiring aspects of buildings to satisfy certain regulations, new building structures increasingly have to be able to attain certain goals, without exactly specifying how these can be accomplished. This increases the need of understanding the different aspects of fire emergencies. Models and simulations of fire spread and evacuation scenarios play an important role in this trend, since they are able to complement experimental research. This paper aims to contributes in models of the latter category: how and under what circumstances occupants evacuate from a building.

Building evacuations are too complex to be investigated exhaustively in short time. Differences in psychological state, rational, panicked or altruistic behaviour have significant impact on the progress of the evacuation. Moreover, not all occupants share the same degree of familiarity with the building they are in, which greatly affects their behaviour. In this paper, we focus on the interaction between two groups of occupants; one group is very familiar with the building and its layout and one group misses this familiarity and must thus rely on the former group for evacuating safely. One example of its relevance is described in [2]—an investigation of an evacuation from an office building, where, in hindsight, evacuees where asked about their knowledge of the building and their actions regarding the evacuation. Among the conclusions drawn was that there were significant behavioural differences between habitual occupants and one-time guests. Not including this feature in crowd simulations can, in some cases, lead to large deviations from realistic evacuation behaviour. This is precisely the place where we contribute.

We concern ourselves with a scenario resembling the one described in [2]: occupants with different levels of knowledge evacuate from a large indoor building. By placing the occupants in a simulation-based framework including complex geometries, we computationally explore the effects the environment knowledge has on the evacuation speed and pedestrian flow congestion. We stress the importance of knowledge by modifying the evacuation conditions to include fire and smoke production, limiting agents visual perception and freedom of movement.

This paper is the start of a larger initiative designed to develop interactive simulations as a decision support tool for crowd management, in which interactive evacuations can be steered and optimized based on real-time feedback. For this reason, any simulations proposed should be executable fast in different configurations and complex domains. To achieve this goal, we design a multiscale model that is averaged and fast on a macroscale as well as accurate and slow on a microscale, but, for large crowds, it performs much faster than the usual agent-based models and is significantly more accurate than the purely macroscopic transport models. By screening the crowd both in agent-based representation and continuum representation, we avoid costly agent-to-agent based interactions by deferring the counting of interactions to a macro (observable) scale.

In line with Pinter-Wollman et al. [3], we show in this paper that knowledge of the building layout drastically affects the collective behaviors of occupants walking through smoke towards the exits. Several other related contributions exist. For instance, [4] reports on the effect of smoke using a social force model à la Helbing. Cirillo and Muntean [5] look into the effects of limited visibility on the group dynamics during an evacuation from a (dark) room without obstacles. Their work has been expanded in [6] to the investigation of the effects of communication efficiency and exit capacity on fundamental diagrams for pedestrian moving through an obscure tunnel. Lovreglio et al. [7] focus on measuring the toxicity due to the smoke inhaled by the occupants. Using a lattice model, [8] looks into the effect of using leader-agents in improving evacuations. When locomotion is biased by a reduced visibility, behavioral rules dominate the choices in the pedestrian flow velocity, see e.g. [9] for a social force model based on behavioral rules. Further relevant literature can be found in [10‐13] and references cited therein.

Despite the obvious influence of distance and vision on social interactions, constraints imposed by the built environment are significant especially when one wants to forecast specific types of collective behaviors of humans during an evacuation in the presence of an unexpected fire (e.g. group formation or boundary-following lanes). Understanding the collective behavior of humans in built environments will certainly lead to a better foundation of environmental psychology as well as to an improved efficiency of way-signaling of route choices, setting the stage for an intelligent crowd management system; see [14] for a list of challenges that environmental psychology currently encounters and [15] about shortcomings in existing crowd management policies.

All these modeling descriptions reflect the evacuation situation of a given length scale, either micro (at the pedestrian level) or macro (at the level of a continuum crowd), or perhaps at some intermediate mesoscopic level (compare [16], e.g.). In [17], the authors start thinking of connecting relevant microscopic and macroscopic crowd scales by looking for mathematical arguments to ensure the consistency of eventual micro-to-macro transitions between agent-based and continuum representations. On the other hand, Richardson [18] proposes detailed explanations of a micro–macro model (originally proposed to the computer vision community by Narain et al. [19]) and checks its suitability in a number of test cases (including also a music festival setup). In the framework of this paper, we develop further the micro–macro approach from [18] and expand it to allow for the presence of a fire as well as for smoke production and dissipation in two different types of confinements.

The proposed model is hybrid. This is not only because it mixes information captured at two separated space scales (micro and macro), but also because it combines continuum, discrete and stochastic elements; see Sect. 3 for a detailed presentation of the main model ingredients.

To get an intuitive level of description of the multiscale features of our model, we suggest the following Gedankenexperiment: Imagine a flow of a fluid, whose internal microstructures (particles) have their own dynamics. Depending on the time-space distribution of particles (i.e. of the approximated density) within the chosen geometry mimicking the built environment, the fluid exhibits both compressible and incompressible regions with a priori unknown locations. The model is able to automatically detect these zones, by relying on a switching on/off relation, usually referred in the literature as unilateral incompressibility constraint. Interestingly, since in our setting we do not allow for agglomerations of particles (groups) exceeding a certain threshold (a priori prescribed maximum-allowed density), a macroscopic repulsion term arises in the setting of the equations for the microscopic dynamics (cf. Sect. 6). Our simulations show pressure plots that clearly exhibit the effect the macroscopic repulsion has on the local arrangements of individual evacuees in the neighborhood of densely packed zones. We then point out the effect the environment knowledge has on our evacuation scenario, where both fire and smoke are present. While contributions exist on modelling the mixing of pedestrians with different levels of knowledge in evacuation scenarios (see e.g. [20] for environment knowledge modelling in a lattice model), to our knowledge, there exists no contribution that combines these crowd dynamics aspects with the appearance and evolution of both smoke and fire, even though several contributions have indicated its significance on human behaviour (see e.g. [2, 21])

The paper is organized as follows. Section 3 contains the presentation of our multiscale crowd model. The obtained simulation results are reported in Sect. 8. We conclude the paper with a short discussion of the main outlets as well as with a concrete to-do-list for the upcoming work. Details on the implementation of our model and related variants can be found in [22].

We propose a micro–macro pedestrian dynamics model composed of a space-continuous agent-based representation (the micro level) and a continuum compressible flow model (the macro level). Hybrid crowd models, in varying degree resembling ours, have been presented, for instance, in [23, 24].

The main ingredients of our micro–macro model are:

As case study, we consider the evacuation of a single floor in a large enclosure with interior walls and multiple exits much like a large office building or shopping mall, filled with occupants. In this enclosure a hydrocarbon pool fire is ignited. The model investigates the situation where all occupants have acknowledged the need to evacuate, although they are not necessary aware where the fire is located. While evacuating, the radiation and heat from the fire repels occupants from moving too close to the location of the fire. A particularly important aspect of our investigation is that the fire produces a dense smoke that reduces the visibility of the occupants, diminishing the locomotion speed.

The occupants belong two one of two groups: those familiar with the local geometry, and those who have to rely on visual cues and on following other people. The complexity of the geometry accentuates the relevance of the environment knowledge on the evacuation.

Our simulation takes place in a two-dimensional rectangular domain, which we refer to as \(\varOmega \). Parts of the domain are filled with rectangular obstacles; their collection is denoted by G. Multiple exits are available. At the start of the evacuation, N evacuees are positioned inside \(\varOmega \). We assume all evacuees have acknowledged the need of evacuation and are attempting to move towards the nearest exit. Figure 1 shows an example geometry. Its complex structure asserts the need of environment knowledge to find the exit in a reasonable time frame. As a specific feature of our choice of geometry, when a fire blocks one of the corridors, alternative options to the exit are available from each location.

Residents and visitors are seen as elements from the sets \(X_A = \{a_1,\ldots ,a_{N_A}\}\) and \(X_B = \{b_1,\ldots ,b_{N_B}\}\), respectively, where \(N_A + N_B=N\). For ease of notation, we denote the complete set of evacuees with \(X:=X_A \cup X_B\). Since we want to emphasize the difference in environment knowledge between the evacuee groups, we employ different path finding algorithms for each group.

In our implementation, we discretize \(\varOmega \) in a rectangular grid fine enough to resolve the obstacles and the exit. We discretize u by averaging (5) over each grid cell so that we obtain an approximation of \(\varPhi \) by numerically solving (6) using a fast marching algorithm [40]. This preferred path minimizes the cost of moving from \({\mathbf {x}}_p\) to \({\mathbf {x}}_q\) where, if this path leads past a fire, a trade-off is made between choosing a short path and maintaining a safe distance from the fire source.

In the pre-processing phase of the simulation, two potential fields are computed, one accounting for the fire, while the other one does not. By keeping track which pedestrians are aware of the fire, the updating of knowledge can be handled in an efficient manner. Equation (10) is discretized as follows: at each time step of the simulation, in any location \({\mathbf {x}}\), if the local density of evacuees \(\rho ({\mathbf {x}})\) exceeds a threshold \(\rho _{\max }\), the UIC takes effect and, if needed, the crowd flow locally changes from a compressible to an incompressible flow regime. We can do this by making sure the macroscopic velocity field \({\mathbf {v}}\) is divergence-free in \({\mathbf {x}}\). As a result, \(\rho ({\mathbf {x}})\) cannot increase and a pressure \(p({\mathbf {x}})\) is introduced that exerts a force on the crowd proportionally to \(\nabla p({\mathbf {x}})\). This way, we are able to control the maximum density of the evacuees for any patch in the domain. The unilateral constraints ensure that no pressure-related forces are applied outside of the high-density zones.

We discretize \(\rho \) and v on the same grid as (1) and (6) as vector objects denoted by \({\varvec {\rho }}^n\) and \({\mathbf {v}}^n\), respectively. The discretized pressure \({\mathbf {p}}^n\) is the solution of the quadratic problem:

Minimize \(f({\mathbf {p}}^n)\), defined assubject to the constraintswhere we abuse the notation of \(\hbox {div}\,{\mathbf {u}}\) and \(\nabla {\mathbf {u}}\) to denote a consistent discrete approximation of continuous counterpart \(\hbox {div}\, u\) and \(\nabla u\), respectively.

Exploiting the complementary relation between \(\rho _{\max } - {\varvec {\rho }}^n\) and \({\mathbf {p}}^n\), we can convert (12) to a linear complementarity problem and solve it using the projected Gauss–Seidel algorithm on each time step without creating a bottleneck for the simulation. For more details regarding the algorithm and the implementation, we refer to [18, 19] respectively.

Because of our discretization of the UIC, the avoidance tendency is not maintained on distances smaller than the grid size. Therefore, to model size exclusion, we manually need to move evacuees apart to prevent them occupying locations too close to each other.

Each time step, we compute the propagation of the smoke according to (1), we update the sight radii and the new positions of the agents according to the model in Sect. 6. When an agent reaches the exit, his residence time is recorded and he is removed from the geometry.

The results are run in crowd simulation prototyping application Mercurial [22]. This is an open-source framework developed in Python and Fortran to simulate hybrid crowd representations as the one described in Sect. 3. It provides both agent-based- and continuum-level visualizations. Mercurial supports the design of arbitrary two-dimensional geometries, and has features for collecting and post-processing simulation results. More details on the structure and implementation of Mercurial are found in [18].

We ran the simulation 15 times in our case study containing 1000 evacuees, each time varying the ratio of visitors and residents. We started with a scenario filled with only residents. We indicate the simulation configuration by the ratio of visitors in the environment (\(\frac{N_B}{N_A+N_B}=0\)), and increased this number with 0.05 for each subsequent run. Figures 9 and 10 display two snapshots of the geometry for ratios 0.3 and 0.7, respectively.

We have chosen this environment to resemble the interior of a large building, characterized by corridors. The environment is set up so that without knowledge of the environment, it is possible but quite difficult to find an exit, especially with high densities of smoke.

In Fig. 9, we observe a structured evacuation, with almost of the evacuees belonging to a group moving towards the exit. As one would expect, the evacuation in Fig. 10 progresses more chaotically. Most evacuees move in smaller groups, their direction largely influenced by the outline of the corridor they move in.

The larger groups typically are centered around a resident, constituting a “shepherding effect”: a leader/follower scenario where the leader is surrounded from all sides by a large group of followers. This allows a large number of evacuees to reach the exit in both scenarios, as observed in Fig. 11 which displays the evacuation times for the two cases. This shepherding effect is most strongly present in the beginning of the situation, when the smoke density is still low enough for visitors to maintain a large sight radius. In some configurations, we observed groups of visitor clusters with an \(X_A\) leader to move faster than a typical group of residents.

Notice how in both evacuations there exist a large crowded zone close to the fire location. This is due to the lack of information the residents have about the location of the fire. Attempting to take the fastest route to the exit, takes them through hordes of residents and visitors drawn towards the same location. Because of these conflicting directions, the visitors are not able to consistently follow other evacuees and the evacuation stagnates. This does not happen in the other corridors, regardless of their level of congestion.

Figure 11 depicts the evacuation process as a function of time. In the initial stage of evacuation, egress is controlled by the capacity of the corridors and exits (revealed by the near-constant slope). After that time, the bulk of evacuees has been removed from the scene and the remainder consists of evacuees with a high initial distance to the nearest exit. Note that in spite of the large difference in evacuee ratios, the evacuation times for most residents are quite similar. The observation that large agent systems can be driven with a relatively small number of ’active particles’ is consistent with observations made in other contributions on particle systems (cf. e.g. [41]). This illustrates the effect of the leader-follower dynamics. The evacuation stagnates after all residents have left, leaving only the visitors with a lack of information.

The difference in evacuees behavior is also revealed by the formation of the incompressibility zones, shown in Figs. 12 and 13.

The pressures experienced in simulations with low visitor ratios are substantially higher. This can be attributed to the persistence in direction the residents display. Whenever a corridor appears clogged, the visitors are more prone to find an alternative exit. The difference in the pressure plots indicates that the visitors are more successful in avoiding the fire and harmful smoke effects than the residents.

Finally, we look at the times on which \(90\%\) of all evacuees have left the geometry. These times are displayed for several visitor ratios in Fig. 14. We observe a positive trend of increasing evacuation time for increasing values of \(\alpha \), but it is apparent that for ratios up to 0.35 the evacuation times are comparable.

It should be pointed out that in this stage of development we do not aim to predict accurate evacuation times; the evacuation times reported here lose credibility for visitor-dominated simulations. This is mainly due to the assumption that visitors without information walk in random directions, without any aid of memory or evacuation signals usually present in buildings. Rather, these simulations try to provide insight in evacuation behaviors for different crowd compositions.

The simulations shown in Sect. 8 draw attention to three fundamental aspects:

Looking forward, it is our aim to extend the applicability of this simulation framework to cope with more realistic scenarios. Concretely, we would like to improve the smoke simulation by assuming the propagation of the smoke plume follows a coupled thermo-diffusion system interlinked with compressible Navier–Stokes equations, possibly in three dimensions. Additionally, it would be interesting to include the effect of smoke inhalation on evacuees.

By including more intelligence for visitors, we aim to obtain more realistic evacuation times. By validating these with data on evacuation experiments, we will be able formulate more quantitative conclusions

Finally, for safety reasons, complex buildings or festivals gathering large crowds are endowed with way-signaling systems showing route choices with indications telling people where to go, enhancing their knowledge of a path towards the exit. This brings in the discussion the complexity of social choices. We have already expanded our simulation framework to cope with way-signaling systems and plan to investigate in the near future their efficiency especially when handling critical pedestrian flow conditions.