Normative pedestrian flow behavior theory and applications

Abstract

Gaining insights into pedestrian flow operations and assessment tools for pedestrian walking speeds and comfort is important in for instance planning and geometric design of infrastructural facilities. Additionally, management of pedestrian flows requires knowledge of pedestrian flow behavior. However, compared to vehicular traffic, pedestrian flow operations are very complex. This is why vehicular flow simulation modeling approaches are generally not applicable to pedestrian flows. Motivated by the need for accurate pedestrian flow models, this report presents an integral theory and models for pedestrian activity scheduling, path determination in the twodimensional space, and walking behavior, under the assumption of utility optimization. In the theory put forward, pedestrians are assumed to make a simultaneous choice of the optimal activity pattern and path, on the one hand optimizing the utility of the activities, while on the other hand minimizing the cost of walking to reach the activity areas. In doing so, we formulate the pedestrian wayfinding problem as an optimal control problem in continuous time and space, where pedestrians aim to walk to the respective activity areas, while optimizing some trade-off between travel time, discomfort due to walking too close to obstacles and walking too quickly. At the same time, both the order in which the activities are performed (as far as their order is free), as well as whether an activity is performed at all, is optimized as well. Given that the pedestrian has determined both the optimal activity pattern as well as the optimal path, we postulate that pedestrian behavior at the operational level is also a result of a utility optimization process. At this level, pedestrians minimize the cost incurred while straying from the planned path, walking too close to other pedestrians, and cost due to large accelerations and decelerations. By applying calculus of variations, explicit mathematical relations are derived describing the acceleration, direction changing, and interaction behavior of a pedestrian. Throughout the report, the theory and models are illustrated by application examples.