Mobility Trajectories from Network-Driven Markov Dynamics

TL;DR

This paper introduces a network-based Markov model for generating human mobility trajectories that reflect realistic spatial and temporal flow patterns without relying on individual behavioral data.

Contribution

It develops a hierarchical, time-dependent Markov model on a spatial network that reproduces structured mobility flows and identifies a unique steady-state distribution using Perron-Frobenius theory.

Findings

Trajectories match origin-destination flow structures

Discrepancies due to finite population sampling

Model preserves privacy and captures network effects

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.