Modeling Spatial-Temporal Patterns of Bus Delays at and between Stops Using AVL and APC Data and Semi-Markov Techniques

Most transit operators produce automatic vehicle location (AVL) and automatic passenger counter (APC) data to assess and improve transit performance. Conventional analyses usually extract data at stops, and, therefore, underutilize vehicle location data collected between stops. This paper develops a model to study bus stopping patterns using AVL and APC data collected at and between stops. The model contains three major steps: (1) linear-referencing AVL and APC data along transit routes, (2) visually exploring the spatio-temporal patterns of delays, and (3) modeling vehicle movements as continuous-time semi-Markov processes and calibrating them using the revealed patterns. The model can be used to identify locations and times that are more likely to get congested and lead to delays and provide more accurate arrival times to transit users. To demonstrate the model, the paper uses AVL and APC data collected along A-Line rapid route within an eight-day period in Minneapolis, Minnesota.