Who: Nicky Cordua Mattson (CP3-Origins)
When: Friday, January 2, 2015
Some of the precautions we encounter in our everyday life are results of the officials trying to control how crowds of people move and behave, and by that try to prevent panic induced casualties. For instance, one might consider the queuing system at Theme parks: If the officials did not guide the crowd and control the queue, everyone would try to come first. Another characteristic, which describes the difficulty of simulating pedestrian behaviour, that is there is typically nothing to guide the pedestrians. If we consider cars and roads, then we have signs and lines on the road to tell people where to drive. This is not the case with pedestrians there is nothing to tell them, where and how they should move, we try using fences, however whenever panic starts, it often breaks down those fences.
To this end, the research has been two fold as you are interested in two basic properties of the model: efficiency and precision. This has made the research go in two directions: A microscopic direction, where each pedestrian is simulated how to move, and a macroscopic, where densities of people are of interest and not the placement of a single pedestrian. The problem is, however, that the microscopic models are in most cases the most precise models, but you have to calculate the force on every pedestrian, making it ineffective.
The macroscopic model, which is resulting in a partial differential equation (PDE) model is efficient as the time complexity solving the PDE, with V mesh points, to an acceptable tolerance is about O(V) by using the method of generalised minimal residual, but all this is at the expense of precision. Another aspect is that macroscopic methods only consider this problem on large scales – typically the interesting length scale is the size of the pedestrians. Using microscopic models we can consider what happens at doors and other bottlenecks which is at the same length scale as the pedestrians, which is of significantly more interest, than how pedestrians can flee without serious constraints.
In this project I will focus on the microscopic approach and therefore extend the existing models, in an attempt to implement group behaviour. Further, instead of creating new techniques and methods for pedestrian behaviour, I would like to use already existing methods used in statistical mechanics to simulate pedestrian behaviour.
Another important aspect of this thesis is to address the problem of runtime or complexity of microscopic methods. I will therefore investigate the actual runtime of a standard problem, using different methods to solve the system of differential equations.