Modeling examples: Quickest or shortest path?
On YouTube, you can find a very complex animation of various scenarios for modeling pedestrian traffic (external site):
http://www.youtube.com/watch?v=8SmRBTJ-jeU.
This animation demonstrates the principle of how simulated pedestrians in Vissim are made to walk along the path of estimated least remaining travel time in due consideration of other pedestrians and obstacles. The animation demonstrates as well the effect of the Dynamic Potential method. It compares pedestrians who select the quickest path with those who choose the shortest one (beginning at 01:42).
Much like vehicle drivers, pedestrians try to minimize their travel times to the destination. This desire can in some situations superimpose over all other aspects. Moreover, the walking direction for the quickest path cannot always be determined without problems.
Details of the method were published in an article in Advances in Complex Systems (external site):
http://dx.doi.org/10.1142/S0219525911003281
Available at arXiv (external site):
http://arxiv.org/abs/1107.2004
List of scenarios in the demo video
The following list shows at what time in the video which scenario begins.
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Notes:
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About 800 passengers alight from two trains arriving simultaneously at the station at the south entrance of Berlin's congress center (ICC). To create a model of a large group of pedestrians walking realistically and efficiently around a corner, mainly the Dynamic Potential method is used. With only a small group of pedestrians the trajectories of both the quickest and the shortest path would be almost identical, because both paths would have approximately the same course. |
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Here a large group of pedestrians has to take an almost complete U-turn in the course of their path. This is more difficult and therefore the difference between the two methods (left and right) is even more distinct. |
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In this scenario two large pedestrian groups meet as opposing flows. This is a situation where the use of the dynamic potential does not necessarily produce better results. However, it provides an alternative pedestrian behavior that becomes clear after a few seconds. The behavior on the left side is more realistic if the pedestrians assume that the counterflow will persist only for a short time, for example during the green phase at the pedestrian crossing, the behavior on the right side is more realistic, if the pedestrians assume that the constellation will persist longer, for example when visiting a public event. |
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If counterflow occurs at a 90° corner, the dynamic potential (right side) is able to better reproduce the fact, that the pedestrians move more efficiently in such situations and most of them are able to resolve the situation. However, with extremely high pedestrian traffic in reality it can also come to such a jam as visualized on the left. |
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Counterflow at a 180° turn (U-turn). |
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Some passengers (red) are urgently rushing for their train, some (green) have just alighted from a train and are heading towards exit whereas some others (blue) have arrived at the station before departure and now spend their waiting time standing or strolling around. (Easily recognizable, the group is quite large and behaves strangely; thereby the effect of the method can be better demonstrated.) The red and green pedestrians in the upper left video follow the shortest path. However, they are increasingly being blocked by the numerically growing blue group. The upper right video and the two scenarios below were simulated with the quickest path but with different values for parameter h. For details of parameter h please refer to the publication linked above. Note that in the two scenarios below the red and green pedestrian groups manage respectively to establish a separate walking direction or to form lanes spontaneously, whereas they fail to do so with parameter h = 0 in the example at top right. |
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This is a theoretical model that does not even remotely occur in reality: However, it demonstrates very clearly and precisely the effect of the "quickest path" approach or alternatively of the dynamic potential. |
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So far all routing decisions were continuous. Thus, the pedestrian had always more path options to their destinations to choose from. This is the first example with discrete alternatives. The pedestrians have to choose if they want to use the left or the right corridor. The method of dynamic potential has not been developed for such situations. Other methods might be more helpful. In Vissim for example the partial routes are used. The Dynamic Potential method is however suited also in this case. |
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A grandstand: The interesting aspect of this example is that the grandstand for the pedestrians consists of a sequence of one-dimensional objects (links). Therefore the directions of the shortest and the quickest path can differ by 180 degrees. In this video it is very obvious when pedestrians prefer to take a detour to reduce the walk time. |
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