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.

翻译：准确的当前态势时空信息对于现代路由算法等智慧城市应用至关重要。此类信息通常描述静态资源的状态，例如停车位、充电站的可用性，或某地点附近等待接载的乘客数量。为充分利用这类信息，通常需要预测被监测资源的未来状态，因为资源可能在需求到达前改变状态。训练精准预测模型时，往往无法获取资源状态的连续时间序列——例如，信息可能来自以不规则频率访问资源的移动代理。因此，必须开发适用于稀疏观测数据的训练与预测方法。本文提出非齐时离散马尔可夫模型，即使在观测频率极低的情况下也能实现精确预测。该新模型能够融合近期观测数据与历史记录，并提供未来状态的有效概率估计。考虑到城市资源可用性通常具有时间依赖性，本模型在预定义时间区间内呈现非齐时循环特性。为训练该模型，我们提出改进的鲍姆-韦尔奇算法。基于真实停车场可用性数据集的评估表明，与基于完整数据训练的模型及非循环变体相比，新方法确实取得了良好效果。