Bus Headways Analysis for Anomaly Detection

The evolution of headways (time intervals between consecutive vehicles) is an important performance indicator of public transportation systems. In this paper, we develop a data processing system that processes the expected arrival time data provided by the corresponding APIs of Madrid and London bus public transport systems with the aim of modeling and supervising their evolution along the time to detect their operational anomalies. By employing only estimates of the time headways between buses, we construct joint statistical modeling along the time of these headways within a stochastic process framework. Then, this model is employed to design a deviation detection procedure that provides a simple and adjustable anomaly detection scheme, as well as a complementary index for assessing the overall Quality of Service (QoS) provided by the operator. The proposed adjustable system can be easily tuned by managers or operators for online anomaly detection, which is an important asset to increase the efficiency of bus transportation services.