Over the last year, I have been working on a computer game about crowd evacuations – scenarios when many people have to leave buildings or vehicles in an emergency. This is a serious topic. People can die in evacuations. So why do I think there should be a computer game about crowd evacuations? And what does this have to do with maths?
Hopefully you agree that we should plan for emergencies and make sure buildings and vehicles are designed in such a way that it is safe for people to get out quickly. In some cases, we can test designs by getting lots of paid volunteers involved. Passenger aircraft evacuations have been investigated in this way. Some infamous experiments even use monetary incentives to simulate competitive evacuation behaviour, such as a $50 bonus to be among the first 25% to exit. This can have a strong effect on participants, who can become “…more aggressive, climbing over seats, outmanoeuvring other passengers, etc. to get out quickly.” (from Aircraft Evacuations Onto Escape Slides and Platforms I: Effects of Passenger Motivation, DOT/FAAAM-96/18). However, realistic evacuation drills are not always an option. Imagine testing every new building, including large football stadiums, in this way. That would be prohibitively expensive.
So, we need an alternative approach. Ideally, we would like to have a tool for testing building designs when all we have are the plans and a rough idea of how many people might be in the building. Mathematical or computational models provide a solution. Based on a few assumptions, they can make predictions for how pedestrian crowds might move through a planned building. Let’s look at two examples.
One approach is to describe the behaviour of individual pedestrians using mathematical equations or algorithmic rules. For instance, we could model forces acting on pedestrians (F=ma) as a combination of their desire to reach a target (Fpersonal), to not get too close to others (Fsocial) and to avoid walking into walls (Fwall; see figure below, inspired by: Helbing et al. (2000) Nature, 407: 487-490).
When we solve such equations of motion for many pedestrians numerically, we obtain crowd simulations like the one shown in this video, where a crowd leaves a room with one exit.
A different modelling approach starts with the observation that crowds can seem to ‘flow’ through pedestrian facilities like a liquid. The dynamics of fluids is a mathematically well-established field and aspects from it can be adapted to develop models for the flow or density of pedestrian crowds. The results look similar to the figure below that shows the pedestrian density for the same one-room-one-door scenario as in the video above.
Models for crowd movements are flexible and already used widely in building design and event planning. But there is a problem: the models are based on assumptions for how people behave. Really, we should check that our assumptions are appropriate. This could be done by running more experiments or evacuation drills with volunteers and comparing them to our models. In the image below you can see an experiment for the same scenario that we looked at with our models (to watch a video of the experiment, click here). Experiments are fun and often involve people wearing silly hats, so that their movements can be tracked easily. But that’s a different story.
Experiments are perhaps the best ways for testing models. However, they are expensive and we cannot test everything. Crowd evacuations are often very stressful. But if we make experiments very stressful, people might get hurt (remember the airplane story…). As an alternative, researchers have started to use virtual environments to conduct experiments and to explore in a safe and controlled way how people behave in emergencies. These experiments are in effect computer games: real people interact either with other people or with a model simulation on a computer screen or in more advanced virtual reality setups.
Over the last few years, I have run experiments like this to investigate peoples’ decision making about exit routes, whether they help others and what affects the risks they take. I have taken my virtual environment experiments …computer games… to various places, including museums and university open days, and thousands of people have taken part in my research. Running these experiments, I was struck by peoples’ curiosity and interest. And that’s how I got the idea of creating an online computer game that everyone can play to find out more about research on crowd evacuations.
At this point, I could explain in detail what our research has found and how this led to the games. But I think it’s a much better idea if you try it out yourself here.
Written by Dr. Nikolai Bode. Research funded by @AXAResearchFund
 Bode, N. W., & Codling, E. A. (2013). Human exit route choice in virtual crowd evacuations. Animal Behaviour, 86(2), 347-358.
 Bode, N. W., Miller, J., O’Gorman, R., & Codling, E. A. (2015). Increased costs reduce reciprocal helping behaviour of humans in a virtual evacuation experiment. Scientific reports, 5, 15896.
 Kinateder, M., Ronchi, E., Nilsson, D., Kobes, M., Müller, M., Pauli, P., & Mühlberger, A. (2014, September). Virtual reality for fire evacuation research. In Computer Science and Information Systems (FedCSIS), 2014 Federated Conference on (pp. 313-321). IEEE.