In the realm of Mobility-on-Demand (MoD) systems, the forecasting of rider demand is a cornerstone for operational decision-making and system optimization. Traditional forecasting methodologies primarily yield point estimates, thereby neglecting the inherent uncertainty within demand projections. Moreover, MoD demand levels are profoundly influenced by both endogenous and exogenous factors, leading to high and dynamic volatility. This volatility significantly undermines the efficacy of conventional time series forecasting methods. In response, we propose an Extended Recurrent Mixture Density Network (XRMDN), a novel deep learning framework engineered to address these challenges. XRMDN leverages a sophisticated architecture to process demand residuals and variance through correlated modules, allowing for the flexible incorporation of endogenous and exogenous data. This architecture, featuring recurrent connections within the weight, mean, and variance neural networks, adeptly captures demand trends, thus significantly enhancing forecasting precision, particularly in high-volatility scenarios. Our comprehensive experimental analysis, utilizing real-world MoD datasets, demonstrates that XRMDN surpasses the existing benchmark models across various metrics, notably excelling in high-demand volatility contexts. This advancement in probabilistic demand forecasting marks a significant contribution to the field, offering a robust tool for enhancing operational efficiency and customer satisfaction in MoD systems.

翻译：在移动出行服务（Mobility-on-Demand, MoD）系统中，乘客需求预测是运营决策与系统优化的基石。传统预测方法主要提供点估计，忽视了需求预测中固有的不确定性。此外，MoD需求水平同时受内生因素与外生因素的深刻影响，呈现出高动态波动性。这种波动性显著削弱了传统时间序列预测方法的有效性。为此，我们提出一种新型深度学习框架——扩展循环混合密度网络（Extended Recurrent Mixture Density Network, XRMDN），专门用于应对上述挑战。XRMDN利用精巧的架构，通过关联模块处理需求残差与方差，灵活融合内生与外生数据。该架构在权重网络、均值网络与方差网络中引入循环连接，能够精准捕捉需求趋势，从而显著提升预测精度，尤其在强波动场景下表现突出。基于真实MoD数据集的全面实验分析表明，XRMDN在多项指标上超越现有基准模型，在需求高波动情境中尤为卓越。这一概率需求预测领域的进展为该领域作出重要贡献，为MoD系统提升运营效率与用户满意度提供了有力工具。