Evacuation modelling
Introduction
PiXIE is being used to study the dynamics of human crowds at a microscopic level, that is by representing a crowd as a collection of individuals, each with unique characteristics, that can interact with their neighbours and their environment. Several approaches are possible to describe the specifics of these interactions. The current model implemented in PiXIE is a modified version of the so-called Social Force Model (SFM) which enables us to easily add new behavioural variants to the model (cognitive abilities, relationship between individuals, social and psychological aspects, etc.) as additional physical forces acting on a simulated agent.
The SFM is then coupled with a navigation mesh algorithm that allows agents to navigate through a potentially complex environment. Details of the implementation is available in the report by Andrés-Thió (2019). The pathfinding algorithm has also been extended to enable agents to navigate three-dimensional structures such as multi-story buildings. The examples below show some models that have been built using the PiXIE implementation of the SFM.
Simulation of evacuation drills
These simulations aimed at reproducing evacuation drills to better understand the conditions under which the so-called Faster-is-Slower (FIS) effect (Parisi et al., 2007; Sticco, 2017) was expected to occur.
The experimental setups (Shahhoseini et al., 2018), along with snapshots of the corresponding PiXIE simulations (Andrés-Thió et al., 2021) are shown in Fig. 1.
Figure 1. The five experimental setups presented by Shahhoseini et al. (2018) (top) and their corresponding PiXIE simulations (Andrés-Thió et al., 2021) (bottom). From left to right, the scenarios are: Symmetric 90, Symmetric 180, Symmetric 270, Asymmetric 45 and Asymmetric 90.
As it turns out, the level of competitiveness of the evacuees plays a key role in the overall efficiency of the evacuation. Indeed our simulations showed that the FIS was only observed in simulations where participants pushed each other thus resulting in a slowdown of the evacuation. These results suggest that perhaps FIS should stand for “Forceful is Slower” rather than “Faster is Slower”!
Details of the study are available in our paper: Andrés-Thió et al., 2021.
Studying the spread of anxious behaviour during an evacuation
In these simulations the SFM was extended to include a model of anxiety (or “panic”) spread (see Andrés-Thió (2019)).
The floor plan is shown in Fig. 2; the sizes of the rooms go from 4m x 4m (far right) to 17m x 17m (top). In particular, the red room has size 15m x 15m. In the scenario, agents are told to evacuate the building when a loud noise is heard in the red room. Agents in the light blue rooms proceed to evacuate in an orderly manner, whereas agents in the red room get scared by the noise and start to panic as they evacuate. To provide an example of how such a model could be used to improve building design, simulations are run with the same floor plan using corridor widths of 2 meters and 1.2 meters.
Figure 2. Floor plan of the evacuation scenario. The yellow rectangles represent the exits of the building, the white areas are corridors, and the light blue/red areas are rooms of the building.
An animation of a simulated evacuation in a building with wide corridors is shown in Fig. 3.
Figure 3. Evacuation of a building with wide corridors (click on the image to run the animation).
In this situation the calm agents and the ones under panic barely interact as the ones under panic evacuate quite quickly. Furthermore, since there is ample room within which to move, the agents do not panic from waiting and pushing, although the panic level does rise. Due to this, the overall panic during the evacuation stays relatively low.
Figure 4. Evacuation of a building with narrow corridors (click on the image to run the animation).
On the other hand, when the same evacuation is simulated with narrow corridors (Fig. 4), one can see panic readily arises in the crowd due to two factors. The first is the spread from the agents with an already high level of panic; since they take longer to evacuate, calm agents are exposed to panicking agents over a longer period of time and so start to panic themselves. Furthermore, since there isn’t much room to move due to the narrow corridors, agents experience higher pressures and longer waiting times, leading to an increase in panic. This is particularly true for the largest room in the simulation (top) where the presence of many agents leads to a spontaneous appearance of panic. What follows is the emergence of the faster-is-slower effect, leading to a much longer evacuation time. In this case, in order to design a safer building one might consider wider corridors as well as multiple exits for rooms used by large amounts of people.
Multi-storey building evacuation model
One of the possible applications of PiXIE is the evacuation of large-scale venues such as multi-storey buildings, shopping malls, stadiums, etc. As an illustrative example we built a model of a three-floor building being evacuated under different scenarios to show how the model can be utilized to assist with evacuation planning.
The building consists of three floors with offices and each floor can be evacuated through two exits located on each side of the building, Fig. 5a. Moreover, the west and east exit doors lead to straight and spiral staircases, respectively (Fig. 5b,c).
Figure 5. Layout of the three-floor building used in the simulation. a) Floorplan ; b) west exit, straight staircase; c) east exit, spiral staircase. (Source of the CAD model: https://grabcad.com/library/office-building-14)
The following evacuation scenarios were considered:
- Agents in the simulation could only exit via the spiral staircase;
- Agents could only exit via the straight staircase;
- Agents could use either staircase but did not practice evacuation before, meaning they chose their exit randomly;
- Agents could use either staircase, but they chose to go to the closest one (training option 1);
- Agents were allocated a specific staircase based on floor level (training option 2).
Additionally, the tests were conducted under “calm” and “panic” conditions, represented as follows in the model:
- Calm condition: Agents stop if another is in front of them. They are assigned a desired speed of 2 m/s. No pushing occurs between agents;
- Panic condition: Agent do not stop for others. They move towards a high desired speed of 4 m/s. Pushing can occur at bottlenecks, as agents come closer to one another.
Finally, different occupancy densities were considered by running all scenarios with 300, 1000 and 1500 agents.
Examples of simulations for some of the scenarios considered are show in Fig. 6. As can be visually seen on this figure, the flow of evacuees for each of these scenarios varies significantly depending on the choice of exit made by each agent at the start of the simulation. This is confirmed when looking at the outcome for each evacuation, measured by the total evacuation time and summarized in Table 1.
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Figure 6. Different evacuation scenarios, for “panicking” agents (click on an image to play the corresponding animation). a) No prior training, exit randomly chosen; b) Agents exit through the west end of the building; c) Agents choose exit door based on their floor level (level 2= east exit, level 1= west exit, ground floor = closest staircase).
Table 1. Overall evacuation times for each of the scenarios considered.
Several conclusions may be drawn from these results:
- Evacuating via the spiral staircase is consistently worse than using the straight staircase, which in this particular example can be easily explained by the fact that the spiral staircase is very narrow.
- The evacuation run without prior training leads to evacuation times similar to those predicted when agents used the straight staircase only.
- The option 1 training (choosing the nearest exit) appears to be the most efficient option compared to option 2 (choice of exit based on level) and leads to an improvement in evacuation time of about 30-40% under calm conditions compared to no training, and about 15-20% under “panic conditions”.
Upon closer inspection of the flow of the evacuation it was observed that the most critical issue was the occurrence of bottlenecks at staircase landings, which led to overall delays. This explains why option 2 for training was not optimum as this option did not remove the bottlenecks, given that everyone on the same level aimed for the same staircase landing.
Finally, it may be seen that simulations under panic conditions always predict faster evacuation time compared to calm conditions. This should not be interpreted as meaning that evacuees should panic! In fact, the term ‘panic’ here is misleading and should be interpreted as rather a proxy for evacuees moving faster and in a slightly more competitive way. Whilst in the particular conditions of this test such behaviour led to more efficient evacuations overall, the model did not account for potential injuries as a result of pushing others, nor did it account for potential delays caused by individuals falling when evacuating under more aggressive conditions.
Uncertainty quantification and data assimilation in crowd modelling for evacuation
This work was carried out in collaboration with Drs. Sophie Ricci and Isabelle Mirouze from CERFACS. The objective was to improve our understanding of crowd evacuation modelling using sensitivity analysis with surrogate modelling and ensemble data assimilation to reduce the uncertainties associated with some of the interaction force parameters of the SFM. The poster below summarizes the early results obtained by coupling PiXIE with the CERFACS tools Batman-OpenTurns and SMURF.
References
Parisi, D.R. and Dorso, C.O., 2007. Why “Faster is Slower” in Evacuation Process. N. Waldau, P. Gattermann, H. Knoflacher, and M. Schreckenberg, eds. In: Pedestrian and Evacuation Dynamics 2005. Springer Berlin Heidelberg, Berlin, Heidelberg, pp. 341–346.
Sticco, I.M., Cornes, F.E., Frank, G.A. and Dorso, C.O., 2017. Beyond the faster-is-slower effect. Phys. Rev. E, 96(5), p.052303.
Shahhoseini, Z., Sarvi, M., and Saberi, M. (2018). Pedestrian crowd dynamics in merging sections: Revisiting the “faster-is-slower” phenomenon. Physica A: Statistical Mechanics and its Applications, 491:101-111.
Andrés-Thió, N., Ras, C., Bolger, M. and Lemiale, V., 2021. A study of the role of forceful behaviour in evacuations via microscopic modelling of evacuation drills. Saf. Sci., 134, p.105018. https://doi.org/10.1016/j.ssci.2020.105018.