Dynamic user-optimal assignment in continuous time and space

To support planning, design, and management of pedestrian infrastructure, dynamic assignment models are useful tools. However, current models are network-based and presume that travelers can choose between a finite number of discrete route alternatives. For walking facilities, where pedestrians can choose their paths freely in two-dimensional space, applicability of these traditional network models is limited. This article puts forward an approach for user-optimal dynamic assignment in continuous time and space. Contrary to network-based approaches, the theory allows the traffic units to choose from an infinite non-countable set of paths through the considered space. The approach consists of three interrelated steps, that is: determining the continuous paths using a path choice model, assigning the origin-destination flows, and calculating the resulting traffic conditions. The approach to determine a user-optimal assignment is heuristic and consists of a sequence of all-or-nothing assignments in continuous time-space. The article presents the mathematical problem formulation, solution approaches, and application examples.