Modeling the scaling properties of human mobility

Modeling the scaling properties of human mobility

| Chaoming Song, Tal Koren, Pu Wang, Albert-László Barabási
This paper investigates the scaling properties of human mobility using empirical data from mobile phone traces. While the fat-tailed jump size and waiting time distributions suggest the relevance of continuous time random walk (CTRW) models, empirical results show systematic conflicts with CTRW predictions. The authors introduce two principles governing human trajectories to build a statistically self-consistent model for individual mobility. The model accounts for empirically observed scaling laws and allows analytical prediction of scaling exponents. Human mobility is characterized by three empirical observations: (A) the number of distinct locations visited follows a scaling law with an exponent smaller than that predicted by CTRW; (B) visitation frequency follows Zipf's law; and (C) the mean square displacement (MSD) grows slower than expected in CTRW models. These anomalies suggest that traditional CTRW models fail to capture the basic features of human mobility. The authors propose an individual mobility (IM) model that incorporates exploration and preferential return mechanisms. Exploration refers to the tendency to visit new locations, while preferential return refers to the tendency to return to frequently visited locations. The model predicts the observed scaling laws and allows for analytical prediction of scaling exponents. The IM model has two parameters, ρ and γ, which control the user's tendency to explore new locations versus returning to previously visited locations. The model's predictions align with empirical data, showing that the scaling exponent for the number of distinct locations is smaller than that predicted by CTRW. The model also explains the Zipf's law observed in visitation frequency and the ultra-slow growth of MSD, which is rare in diffusion and has been observed in disordered systems. The model is dynamically quenched, meaning that after exploring a new location, the user has an increasing tendency to return to it, leading to a recurrent and stable mobility pattern. The model is validated against empirical data, showing that it accurately reproduces the scaling properties of human mobility. The model's parameters are determined from empirical data, and the results show that the model's predictions are consistent with the observed scaling exponents. The model offers a conceptual framework that can be extended to improve the temporal fidelity of short-term dynamics.This paper investigates the scaling properties of human mobility using empirical data from mobile phone traces. While the fat-tailed jump size and waiting time distributions suggest the relevance of continuous time random walk (CTRW) models, empirical results show systematic conflicts with CTRW predictions. The authors introduce two principles governing human trajectories to build a statistically self-consistent model for individual mobility. The model accounts for empirically observed scaling laws and allows analytical prediction of scaling exponents. Human mobility is characterized by three empirical observations: (A) the number of distinct locations visited follows a scaling law with an exponent smaller than that predicted by CTRW; (B) visitation frequency follows Zipf's law; and (C) the mean square displacement (MSD) grows slower than expected in CTRW models. These anomalies suggest that traditional CTRW models fail to capture the basic features of human mobility. The authors propose an individual mobility (IM) model that incorporates exploration and preferential return mechanisms. Exploration refers to the tendency to visit new locations, while preferential return refers to the tendency to return to frequently visited locations. The model predicts the observed scaling laws and allows for analytical prediction of scaling exponents. The IM model has two parameters, ρ and γ, which control the user's tendency to explore new locations versus returning to previously visited locations. The model's predictions align with empirical data, showing that the scaling exponent for the number of distinct locations is smaller than that predicted by CTRW. The model also explains the Zipf's law observed in visitation frequency and the ultra-slow growth of MSD, which is rare in diffusion and has been observed in disordered systems. The model is dynamically quenched, meaning that after exploring a new location, the user has an increasing tendency to return to it, leading to a recurrent and stable mobility pattern. The model is validated against empirical data, showing that it accurately reproduces the scaling properties of human mobility. The model's parameters are determined from empirical data, and the results show that the model's predictions are consistent with the observed scaling exponents. The model offers a conceptual framework that can be extended to improve the temporal fidelity of short-term dynamics.
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[slides and audio] Modelling the scaling properties of human mobility