Accurate spatio-temporal information about the current situation is crucial for smart city applications such as modern routing algorithms. Often, this information describes the state of stationary resources, e.g. the availability of parking bays, charging stations or the amount of people waiting for a vehicle to pick them up near a given location. To exploit this kind of information, predicting future states of the monitored resources is often mandatory because a resource might change its state within the time until it is needed. To train an accurate predictive model, it is often not possible to obtain a continuous time series on the state of the resource. For example, the information might be collected from traveling agents visiting the resource with an irregular frequency. Thus, it is necessary to develop methods which work on sparse observations for training and prediction. In this paper, we propose time-inhomogeneous discrete Markov models to allow accurate prediction even when the frequency of observation is very rare. Our new model is able to blend recent observations with historic data and also provide useful probabilistic estimates for future states. Since resources availability in a city is typically time-dependent, our Markov model is time-inhomogeneous and cyclic within a predefined time interval. To train our model, we propose a modified Baum-Welch algorithm. Evaluations on real-world datasets of parking bay availability show that our new method indeed yields good results compared to methods being trained on complete data and non-cyclic variants.

为智能城市应用功能，如现代路径算法，提供准确的时空信息是至关重要的。本文提出了一种针对稀疏观测数据的改进马尔可夫模型，能够基于历史数据和最近观测进行准确预测，并在特定时间间隔内周期性地适应城市环境的资源可用性变化。通过改进的Baum-Welch算法的评估，证明了该方法在停车位可用性的实际数据集上相较于使用完整数据和非周期变体的方法取得了良好的结果。

资源稀缺情况下的时间不均匀马尔可夫模型