Modeling the movement of customers in retail space under conditions of social distancing

DOI: 10.31673/2412-4338.2021.028082

Abstract

The paper considers the problem of modeling the movement of customers in retail space under conditions of social distancing, which is caused by the requirements to prevent infection and further spread of the coronavirus infection COVID-19. A discrete model of a retail space, a model of a customer, a model of customers' movement according to the principles of functioning of a two-dimensional cellular automaton without memory have been developed. The retail space model allows to take into account the key objects of a retail space such as a supermarket/hypermarket: racks, cash desks, entrance, exit from the premises. In contrast to the classical models of representing a person using cellular automata, the customers' model ensures that social distance is taken into account by expanding the Moore neighborhood to about 2. In this case, the Moore neighborhood of order 1 is used to directly move the cell of the automaton representing the customer, and the cells of the neighborhood of order 2 are used to determining compliance with social distancing restrictions. The model of the customer behavior takes into account real-life situations: just like people, the cells of an automaton can “violate” the rules of social distancing. The set of rules for the customer's model is based on the general strategy of bypassing the retail space and contains additional restrictions regarding conflict situations for violating social distance, as well as a description of behavior in normal traffic and movement in the event of extreme situations. These models are implemented in software, which allows to control the settings of the simulation parameters. Heatmaps are used to visually represent the simulation results, showing the zones of pollution and zones of violation of social distance. The simulation results show that even with a slight increase in the probability of customers violating social distance, the number of distance violation cases grows exponentially.

Keywords: human movement model, discrete model of retail space, customer, cellular automaton, social distance.

References
1. Employer's Guide to Workplace Management during COVID-19. URL: https://www.ilo.org/wcmsp5/groups/public/---ed_dialogue/---lab_admin/documents/publication/wcms_745603.pdf
2. About carrying out public discussion of some requirements to anti-epidemic measures at weakening of quarantine. Order of the Ministry of Health of Ukraine № 32 from 18.05.2020. URL: https://zakon.rada.gov.ua/rada/show/v0032488-20#Text
3. Helbing, Dirk, and Peter Molnar. "Social force model for pedestrian dynamics." Physical review E 51.5 (1995): 4282.
4. Apel, Marko. "Simulation of pedestrian flows based on the social force model using the verlet link cell algorithm." Poznan University of Technology 79 (2004).
5. Helbing, Dirk, et al. "Simulation of pedestrian crowds in normal and evacuation situations." Pedestrian and evacuation dynamics 21.2 (2002): 21-58
6. Zheng, Linjiang, et al. "Simulation of pedestrian evacuation considering emergency spread and pedestrian panic." Physica A: Statistical Mechanics and its Applications 522 (2019): 167-181.
7. Blue, Victor J., and Jeffrey L. Adler. "Cellular automata microsimulation of bidirectional pedestrian flows." Transportation Research Record 1678.1 (1999): 135-141.