Description of the method Dynamic Potential

An important basis for the dynamic potential is the method in which pedestrians generally find their next destination area in a simulation. This is achieved because the driving force of the social force model points towards the next destination as long as the pedestrian does not walk in this direction:

Where:

: pedestrians current velocity

: desired speed of the pedestrian based on the user-defined distribution

: Direction of the desired speed (unit vector): from which the multiplication of the desired walking speed results in the current desired walking speed. is obtained from the Static Potential or Dynamic Potential or a linear combination of both values.

Using the Static Potential in Vissim always points in the direction of the path with the shortest distance.

Using the Dynamic Potential points in the direction of the path with shortest time according to the current estimation. This may not be the absolutely right direction of the path with the shortest time in terms of analytics. Due to the fact that in reality pedestrians are often confused regarding which direction at the current time can lead them to their destination the quickest, it is not a big problem that the actual direction of the quickest path cannot be precisely calculated. Therefore, the hypothetical assumption that the direction of the path with the shortest time is known in the simulation and hence the behavior of each pedestrian is optimal, is probably not realistic.

Impact parameter (Defining the Dynamic Potential for a static pedestrian route), (Dynamic potential attributes): The value ^s for the direction of the path with the shortest distance and the value ^q for the direction of the path with the shortest time. The value is derived therefrom. ^s and ^q are included in accordance with the value of the impact parameter as a weighting.

Tip: You will find further information in the document  Quickest Paths in Simulations of Pedestrians, Kretz T., Große A. u.a., Karlsruhe, 2011

Regardless of whether points in the direction of the path with the shortest distance (Static Potential is used, the Dynamic Potential is not used) or in the direction of the path with the shortest time (the Dynamic Potential is used at 100 %), when calculating the first step is to determine the values for the points of the grid which indicate either the distance or the estimated remaining travel time from the respective point to the relevant distance area. The grid is consistent with the potential. Since the distance from a grid point to the destination does not change during the simulation run, the potential that provides the distance values, referred to as static potential, acts as a "Look-up" table. In contrast, with the consideration of all pedestrians in the network at the same time, the estimated remaining travel time to the destination changes continuously for each grid point. Thus this potential is referred to as dynamic potential. If you imagine the values of this potential as rising or increasing values, points in the direction of the descent, which mathematically represents the (negative) gradient.

As soon as has been calculated based on the static or dynamic potential, the value is applied in the driving force term. The total of the driving force and the social forces is included for acceleration of the pedestrian in the respective time step.