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In real Mobility-on-Demand (MoD) systems, demand is subject to high anddynamic volatility, which is difficult to predict by conventional time-seriesforecasting approaches. Most existing forecasting approaches yield the pointvalue as the prediction result, which ignores the uncertainty that exists inthe forecasting result. This will lead to the forecasting result severelydeviating from the true demand value due to the high volatility existing indemand. To fill the gap, we propose an extended recurrent mixture densitynetwork (XRMDN), which extends the weight and mean neural networks to recurrentneural networks. The recurrent neurons for mean and variance can capture thetrend of the historical data-series data, which enables a better forecastingresult in dynamic and high volatility. We conduct comprehensive experiments onone taxi trip record and one bike-sharing real MoD data set to validate theperformance of XRMDN. Specifically, we compare our model to three types ofbenchmark models, including statistical, machine learning, and deep learningmodels on three evaluation metrics. The validation results show that XRMDNoutperforms the three groups of benchmark models in terms of the evaluationmetrics. Most importantly, XRMDN substantially improves the forecastingaccuracy with the demands in strong volatility. Last but not least, thisprobabilistic demand forecasting model contributes not only to the demandprediction in MoD systems but also to other optimization application problems,especially optimization under uncertainty, in MoD applications.

XRMDN: A Recurrent Mixture Density Networks-based Architecture for  Short-Term Probabilistic Demand Forecasting in Mobility-on-Demand Systems  with High Volatility