Quickest Paths in Simulations of Pedestrians

This contribution proposes a method to make agents in a microscopic simulation of pedestrian traffic walk approximately along a path of estimated minimal remaining travel time to their destination. Usually models of pedestrian dynamics are (implicitly) built on the assumption that pedestrians walk along the shortest path. Model elements formulated to make pedestrians locally avoid collisions and intrusion into personal space do not produce motion on quickest paths. Therefore a special model element is needed, if one wants to model and simulate pedestrians for whom travel time matters most (e.g. travelers in a station hall who are late for a train). Here such a model element is proposed, discussed and used within the Social Force Model.Comment: revised version submitte

Pedestrian Traffic: on the Quickest Path

When a large group of pedestrians moves around a corner, most pedestrians do not follow the shortest path, which is to stay as close as possible to the inner wall, but try to minimize the travel time. For this they accept to move on a longer path with some distance to the corner, to avoid large densities and by this succeed in maintaining a comparatively high speed. In many models of pedestrian dynamics the basic rule of motion is often either "move as far as possible toward the destination" or - reformulated - "of all coordinates accessible in this time step move to the one with the smallest distance to the destination". Atop of this rule modifications are placed to make the motion more realistic. These modifications usually focus on local behavior and neglect long-ranged effects. Compared to real pedestrians this leads to agents in a simulation valuing the shortest path a lot better than the quickest. So, in a situation as the movement of a large crowd around a corner, one needs an additional element in a model of pedestrian dynamics that makes the agents deviate from the rule of the shortest path. In this work it is shown, how this can be achieved by using a flood fill dynamic potential field method, where during the filling process the value of a field cell is not increased by 1, but by a larger value, if it is occupied by an agent. This idea may be an obvious one, however, the tricky part - and therefore in a strict sense the contribution of this work - is a) to minimize unrealistic artifacts, as naive flood fill metrics deviate considerably from the Euclidean metric and in this respect yield large errors, b) do this with limited computational effort, and c) keep agents' movement at very low densities unaltered