A universal model for mobility and migration patterns (1111.0586v2)

Abstract: Introduced in its contemporary form by George Kingsley Zipf in 1946, but with roots that go back to the work of Gaspard Monge in the 18th century, the gravity law is the prevailing framework to predict population movement, cargo shipping volume, inter-city phone calls, as well as bilateral trade flows between nations. Despite its widespread use, it relies on adjustable parameters that vary from region to region and suffers from known analytic inconsistencies. Here we introduce a stochastic process capturing local mobility decisions that helps us analytically derive commuting and mobility fluxes that require as input only information on the population distribution. The resulting radiation model predicts mobility patterns in good agreement with mobility and transport patterns observed in a wide range of phenomena, from long-term migration patterns to communication volume between different regions. Given its parameter-free nature, the model can be applied in areas where we lack previous mobility measurements, significantly improving the predictive accuracy of most of phenomena affected by mobility and transport processes.

• The paper introduces a radiation model that replaces parameterized gravity laws with a parameter-free framework to predict mobility and migration patterns.
• It employs a two-step job selection process using local population data to forecast commuter flows accurately without needing prior traffic data.
• Validation with real-world data from regions like New York and Utah demonstrates its superior predictive accuracy and analytical consistency.

Analytical Framework for Predicting Mobility and Migration Patterns

This paper presents a comprehensive model termed the "radiation model" to predict human mobility and migration patterns, addressing notable limitations of the conventional gravity law in this domain. Traditionally, the gravity model, drawing inspiration from Newton’s gravitational principles, has functioned as the primary framework to forecast population movement across various contexts. Despite its ubiquity, the gravity model is hindered by several conceptual inconsistencies, tuning parameters that vary across geographical regions, and systematic predictive inaccuracies. The proposed radiation model aims to provide a parameter-free, analytically robust alternative that attains superior predictive accuracy without requiring prior traffic data.

Limitations of the Gravity Model

The gravity model dictates that the flow of individuals, $T_{ij}$, is proportional to the populations of the origin ($m$) and destination ($n$) and inversely related to the distance ($r_{ij}$) between them. Key limitations include:

• The absence of a theoretical derivation for the deterrence function, which inadequately fits empirical data across different scenarios.
• Necessitation of multiple adjustable parameters prone to inaccuracy without prior traffic data, rendering the model ineffectual in new regions.
• The assumption of consistency in commuter flow with scaling populations, which is analytically inconsistent.
• An inability to account for stochastic fluctuations between locations.

The paper highlights these flaws and contrasts them with the intervention of alternative models like intervening opportunity and random utility models, which, despite relying on basic principles, also suffer from adjustable parameter requirements that curtail their predictive power.

The Radiation Model

Introduced as an advancement over the gravity law, the radiation model leverages stochastic processes based on local mobility decisions and is devoid of adjustable parameters. The model assumes that individuals follow a two-step job selection process, considering job opportunities proportional to resident populations and selecting the nearest superior offer beyond their home county. This process yields the mobility fluxes independent of benefit distributions, offering a rigorous foundational derivation through radiation and absorption analogies.

The model’s principal equation is:

$$T_{ij} = \frac{m_i n_j}{(m_i + s_{ij})(m_i + n_j + s_{ij})}$$

This equation integrates the population of origin, destination, and intermediate populations $s_{ij}$ within the commutation fluxes and addresses six previously identified weaknesses of the gravity law. Notably, it resolves analytical inconsistencies, caters to unmeasured regions, and reflects real-world commuter data more accurately.

Comparative Analysis and Implications

In comparison with the gravity law, the radiation model achieves consistent agreement with observed patterns across multiple domains, including hourly travel, migration, communication, and commodity flows. Specifically, examples from New York County demonstrated the gravity model's tendency to underestimate high fluxes, while the radiation model adhered more closely to empirical commuting data, capturing variances in flux magnitude across different regions like Utah and Alabama.

Furthermore, the radiation model discerns an inherent self-similarity in human mobility, revealing a probabilistic pattern invariant under certain population scaling transformations. The findings suggest fundamental decision mechanisms underpinning broader transport and mobility-driven processes beyond mere local commuting.

Future Directions

The paper identifies potential refinements to the radiation model, such as incorporating home-field advantages in job selection processes and accounting for subjective variations in effective commuting distances. These enhancements could yield further insight and precision, supporting urban planning, epidemiological modeling, and transportation logistics.

Ultimately, the radiation model affords a robust framework applicable across varying environments without pre-existing data, offering a promising foundation for continued exploration and refinement of human mobility patterns in complex systems.