A Cellular Automaton Approach for Lane Formation in Pedestrian Counterflow
The formation of lanes is a well known emergent behavior in pedestrian counterflow as well as in some other physical systems. Nevertheless, not much is known quantitatively which is related to the fact that the empirical situation is quite poor. Here we a
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Abstract The formation of lanes is a well known emergent behavior in pedestrian counterflow as well as in some other physical systems. Nevertheless, not much is known quantitatively which is related to the fact that the empirical situation is quite poor. Here we analyze lane formation in a two-dimensional cellular automaton for pedestrian dynamics. To quantify the lane structure, we make use of a laning order parameter which has been used previously to detect lanes in colloidal systems. The main purpose of our work is to determine a phase diagram in dependence on the coupling constants and the particle density. Furthermore, we compare the results of our simulation with experimental data.
1 Introduction In recent years, pedestrian dynamics has become more and more attractive for scientists from different fields. This is not very surprising because there are many applications which require a profound knowledge of crowd dynamics. It can help to make forecasts of evacuation scenarios as well as to plan the layout of buildings and venues. Furthermore, pedestrian dynamics is very interesting from a physical point of view. Human crowds are many-body systems which show many interesting collective effects like jamming at bottlenecks, density waves, flow oscillations and lane formation [1]. The latter is also known from other driven systems [2], e.g., from complex plasmas [3], molecular ions [4] and colloidal suspensions [5–7]. There are many models which are able to reproduce the collective phenomena mentioned above [8, 9], but quantitative studies are rare. Especially, lane formation in counterflow is often used as a validation to check whether a model is realistic. However, there are very few studies that go beyond the statement that lanes S. Nowak () A. Schadschneider Institut für Theoretische Physik, Universität zu Köln, 50937 Köln, Germany e-mail: [email protected]; [email protected] V.V. Kozlov et al. (eds.), Traffic and Granular Flow ’11, DOI 10.1007/978-3-642-39669-4__15, © Springer-Verlag Berlin Heidelberg 2013
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are present in the system, even though simulations of bi-directional pedestrian movement are made very often [9–24]. Comparisons with empirical data are even made less frequently. This is related to the fact that the empirical situation is not very satisfying. Even for quite simple scenarios, like the fundamental diagram in a corridor, there is no consensus [1, 25]. But the situation has been improved recently within the Hermes project [26, 27] where several large scale experiments were performed [28–31] with high accuracy [32] and automatized evaluation [33]. The goal of this article is to make quantitative statements about lane formation with help of an order parameter adopted from the analysis of colloidal suspensions [7]. The results of the simulations will also be compared with experimental data.
2 Definitions 2.1 Floor Field Cellular Automaton The Floor Field Cellular Automaton (FFCA) [14,34] is defined on a square lattice of size LW . Each cell cor
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