Mobility Trajectories from Network-Driven Markov Dynamics

2026-01-09

arXiv.org

AI Summary

This work addresses the challenge of generating human mobility trajectories that faithfully reproduce real-world network structures and temporal patterns without relying on assumptions about individual behavior. The authors propose a network-centric, privacy-preserving trajectory generation framework that constructs a time-varying Markovian dynamics model grounded in spatial interaction networks. The transition matrix is defined through a gravity-like distance decay function, exogenous temporal scheduling, and directional bias. Notably, the model introduces, for the first time, a periodic stationary population distribution as a non-transient reference state. By rigorously linking trajectory realizations to multi-step Markov dynamics, the method successfully reproduces structured origin–destination flows shaped by network geometry, temporal modulation, and connectivity constraints, achieving high consistency between individual-level trajectories and macroscopic dynamics, with discrepancies attributable solely to finite-population sampling effects.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Multiagent Systems: Agent-Based Simulation and Emergent Behavior
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Social Networks and Social Media: Generative AI / large language models and their impact on social systems
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

We present a generative model of human mobility in which trajectories arise as realizations of a prescribed, time-dependent Markov dynamics defined on a spatial interaction network. The model constructs a hierarchical routing structure with hubs, corridors, feeder paths, and metro links, and specifies transition matrices using gravity-type distance decay combined with externally imposed temporal schedules and directional biases. Population mass evolves as indistinguishable, memoryless movers performing a single transition per time step. When aggregated, the resulting trajectories reproduce structured origin-destination flows that reflect network geometry, temporal modulation, and connectivity constraints. By applying the Perron-Frobenius theorem to the daily evolution operator, we identify a unique periodic invariant population distribution that serves as a natural non-transient reference state. We verify consistency between trajectory-level realizations and multi-step Markov dynamics, showing that discrepancies are entirely attributable to finite-population sampling. The framework provides a network-centric, privacy-preserving approach to generating mobility trajectories and studying time-elapsed flow structure without invoking individual-level behavioral assumptions.

Problem

• human mobility
• Markov dynamics
• spatial interaction network
• origin-destination flows
• trajectory generation

Innovation

• Markov dynamics
• spatial interaction network
• gravity model
• Perron-Frobenius theorem
• privacy-preserving mobility