XRMDN: An Extended Recurrent Mixture Density Network for Short-Term Probabilistic Rider Demand Forecasting Considering High Volatility

In the realm of Mobility-on-Demand (MoD) systems, the forecasting of rider demand is a cornerstone for operational decision-making and system optimization. Rider 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. Furthermore, traditional forecasting methodologies primarily yield point estimates, thereby neglecting the inherent uncertainty within demand projections. 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 evaluation metrics, notably excelling in high-demand volatility contexts. Most importantly, XRMDN outperforms the benchmark models up to 93.0%, 72.7%, and 31.3% in terms of the log-likelihood value, MAPE, and rejection rates compared to the benchmark models. 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.