Potential field cellular automata model for overcrowded pedestrian flow

Abstract

A cellular automata model for overcrowded pedestrian flow is proposed by dividing a normal cell into nine small cells, among which the compressibility is such that one pedestrian referred by a central cell can share a side or corner cell with at most one or three other pedestrians. The compressibility between a pedestrian and a wall is half as much as that between pedestrians. Hence the model allows a density exceeding $10\mathrm{p}\mathrm{e}\mathrm{d}/{\mathrm{m}}^2$. The direction of motion minimizes the deviation from the negative gradient of cost potential, and the probability of movement decreases with the deviation and travel cost. The simulated fundamental diagram and evacuation process generally agree with field studies in the literature. The increased cost helps reproduce the formation of lanes in counter-flow; however, the degree depends on the amplitude of increase and the density, which is measured by the probability of gridlock and order parameter through simulation.

Keywords:

• Cost distribution
• refined cells
• evacuation
• counter-flow
• lane formation

Disclosure statement

No potential conflict of interest was reported by the author(s).

ORCID

Zhi-Yang Lin http://orcid.org/0000-0001-5370-5184

Xiao-Ning Zhang http://orcid.org/0000-0002-1644-5050

Additional information

Funding

This study was jointly supported by grants from the National Natural Science Foundation of China [grant numbers 11672348, 71531011, 11972121], the Research Grants Council of the Hong Kong Special Administrative Region, China [grant number 17201318], the National Key R&D Program of China [grant number 2018YFB1600900], the China Postdoctoral Science Foundation [grant number 2019M661362], the Science and Technology Innovation Program of the Department of Transportation, Yunnan Province, China [grant number 2019303], the Opening Research Fund of National Engineering Laboratory for Surface Transportation Weather Impacts Prevention [grant number NEL-2019-03], and the National Basic Research Program of China [grant number 2012CB725404].