Adjusting bus timetables considering observed delays and passenger numbers

This paper discusses the problem of creating fast, but vulnerable versus slow but robust bus schedules. Buses are subject to delays at stops due to congestion, dwell time variations and other reasons. The problem for bus operators is hence how to create a timetable that considers these uncertainties. We utilize vehicle location data matched with timetable data to estimate delays and in addition smart card (AFC) data to understand the number of passengers affected by these delays. We firstly cluster lines according to their delay patterns in order to extract lines of most need for timetable revisions. We then develop a simple approach to modify the timetable. The main effect of the different timetable options can be illustrated graphically by showing the aforementioned trade-off as Pareto optimal front of timetable options. Utilising data from Shizuoka, Japan we illustrate this for two lines, one of which appears to be scheduled too much on the slow/robust side, whereas the other is scheduled clearly too fast and vulnerable.