A time-inhomogeneous Markov model for resource availability under sparse observations

Accurate spatio-temporal information 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. Predicting future states of the monitored resources is often mandatory because a resource might change its state within the time until it is needed. It is often not possible to obtain complete history of a resource's state. 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 resource availability in a city is typically time-dependent, our Markov model is time-inhomogeneous and cyclic within a predefined time interval. We propose a modified Baum-Welch algorithm capable of training our model with sparse data. Evaluations on real-world datasets of parking bay availability show that our new method indeed yields good results compared to methods designed for training on complete data and non-cyclic variants.