2025/11/04 by Shah, Syed Haseeb
Engineering · Medicine · Social Sciences · #Applications (stat.AP) #Evacuation and Crowd Dynamics #Evolutionary Game Theory and Cooperation #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Physical sciences #Mathematical and Theoretical Epidemiology and Ecology Models #Physics and Society (physics.soc-ph) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · doi:10.48550/arxiv.2511.02648
openalex publication_date 2025/11/04 · openalex created_date 2025/11/06 · openalex updated_date 2026/07/28
This paper presents a discrete-event stochastic model for the redistribution of indistinguishable personal items, exemplified by socks, among multiple cohabitants sharing a communal laundry system. Drawing on concepts from ecological population dynamics, diffusion processes, and stochastic exchange theory, the model captures the probabilistic mechanisms underlying item mixing, recovery, and loss. Each cohabitant is represented as an autonomous agent whose belongings interact through iterative cycles of collective washing, sorting, and partial correction. The system's evolution is characterized by random mixing events, selective recollection, and attrition over time. Implemented using the SimPy discrete-event simulation framework, the model demonstrates that even minimal exchange probabilities can generate emergent asymmetries, quasi-equilibrium distributions, and long-term disorder. The findings illustrate how stochastic processes inherent to shared domestic systems can produce persistent imbalances, offering a quantitative perspective on an everyday social phenomenon.