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# Microscopic Models

In the present project two microscopic models are developed. The first one is a grid-based approach rooted in cellular automata (CA) models. The second one is a combination of a force based and graph based approach.

The first model is developed at the institute of mathematics and will be outlined below, the second one is developed at the institute of "Verkehrssystemplanung und Verkehrstelematik", take a look at www.vsp.tu-berlin.de/projects/laufende_projekte/simulation_of_multi_destination_pedestrian_crowds/ [1] .

In the traditional cellular automata (CA) model and its various extensions, the state change of the cell (i.e. position) is applied to describe the system dynamics of the simulation. Due to this conceptual limit, to our knowledge, the simulation participants (i.e. pedestrians) are all associated with a fixed spacial size, defined by the size of the grid cell in the CA model. Consequently the pedestrians in the simulation have a fixed exclusive personal space which differs from empirical observations. In our model this exclusive personal space is given additional attention. The effect of a modifiable exclusive personal space is achieved by defining the inaccessibility of the surrounding cell position of an arbitrary pedestrian. By this means it is possible to describe simple group behaviors, i.e. pedestrians which belong to the same group may require a smaller exclusive personal space, while toward other pedestrians in the simulation environment, the nearby cell positions are declared as inaccessible and thus keep the latter at a relatively larger distance as what we would imagine in real-world situations.

Our model also presents an advanced local step calculation to enable the so-called multi-cell-step, i.e. the transition from a start position to a destination with a distance larger than one grid cell. In the step calculation the execution sequence of the simulation participants is affected, in addition to the participant's own characteristics, by the actual system dynamics as well. This enables a substantial reduction of the "deadlock'' phenomenon. This model is applied with some simple configurations with which the pedestrians are given pre-defined start positions and destinations. With the notion of the modifiable personal space, the simulation with advanced step calculation can be realized in combination with pedestrian density control, if necessary.

kte/simulation_of_multi_destination_pedestrian_crowds/