Accurately modeling human mobility is critical for urban planning, epidemiology, and traffic management. In this work, we introduce Markovian Reeb Graphs, a novel framework that transforms Reeb graphs from a descriptive analysis tool into a generative model for spatiotemporal trajectories. Our approach captures individual and population-level Patterns of Life (PoLs) and generates realistic trajectories that preserve baseline behaviors while incorporating stochastic variability by embedding probabilistic transitions within the Reeb graph structure. We present two variants: Sequential Reeb Graphs (SRGs) for individual agents and Hybrid Reeb Graphs (HRGs) that combine individual with population PoLs, evaluated on the Urban Anomalies and Geolife datasets using five mobility statistics. Results demonstrate that HRGs achieve strong fidelity across metrics while requiring modest trajectory datasets without specialized side information. This work establishes Markovian Reeb Graphs as a promising framework for trajectory simulation with broad applicability across urban environments.

翻译：准确建模人类移动性对于城市规划、流行病学和交通管理至关重要。本研究提出马尔可夫Reeb图（Markovian Reeb Graphs），这是一个将Reeb图从描述性分析工具转化为时空轨迹生成模型的新框架。该方法通过将概率转移嵌入Reeb图结构，捕捉个体与群体层面的生命模式（Patterns of Life, PoLs），在保留基线行为的同时融入随机变异性，从而生成逼真轨迹。我们提出两种变体：用于个体智能体的序列Reeb图（Sequential Reeb Graphs, SRGs）和结合个体与群体PoLs的混合Reeb图（Hybrid Reeb Graphs, HRGs），并在Urban Anomalies和Geolife数据集上使用五种移动性统计指标进行评估。结果表明，HRGs在各项指标上均表现出高保真度，且仅需中等规模的轨迹数据集，无需专用辅助信息。本研究确立马尔可夫Reeb图为城市环境中具有广泛适用性的轨迹模拟框架。