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：精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。本文提出马尔可夫里布图这一创新框架，将里布图从描述性分析工具转化为时空轨迹的生成模型。该方法能够捕捉个体与群体层面的生命模式，并通过在里布图结构中嵌入概率转移机制，生成既保持基准行为特征又包含随机变异性的真实轨迹。我们提出两种变体：针对个体代理的序列里布图，以及融合个体与群体生命模式的混合里布图。基于Urban Anomalies和Geolife数据集，采用五项移动性统计指标进行评估。结果表明，混合里布图在所有指标上均表现出优异的保真度，且仅需适规模的轨迹数据集而无需特定辅助信息。本研究确立了马尔可夫里布图作为轨迹模拟的潜力框架，在城市环境中具有广泛适用性。