An Incremental Probabilistic Model to Predict Bus Bunching in Real-Time

In this paper, we presented a probabilistic framework to predict Bus Bunching (BB) occurrences in real-time. It uses both historical and real-time data to approximate the headway distributions on the further stops of a given route by employing both offline and online supervised learning techniques. Such approximations are incrementally calculated by reusing the latest prediction residuals to update the further ones. These update rules extend the Perceptron's delta rule by assuming an adaptive beta value based on the current context. These distributions are then used to compute the likelihood of forming a bus platoon on a further stop - which may trigger an threshold-based BB alarm. This framework was evaluated using real-world data about the trips of 3 bus lines throughout an year running on the city of Porto, Portugal. The results are promising.