Ex ante heuristic measures of schedule reliability

Measures of reliability and punctuality of scheduled public transport services are important in planning, management, operating and marketing of these services. Various methods can be used to measure reliability. Analytic methods are usually practical for only very simple structured systems. Simulation methods are very time consuming and require data which may not be available. As a result, the most widely used measures are ad hoc or heuristic. However, the assumptions and properties of these measures, and the relationships between them, are seldom discussed, hence we discuss them here. We consider existing measures, extensions of these, and new measures. For specificity, we use the example of train arrivals and departures at a train station: stations with several hundred trains per day and multiple platforms are common in many countries, for example throughout Europe. Some measures of reliability are based on the observed delays, hence can be used only after the event. However, we here focus on measures which can be used in advance, for example for estimating the reliability of proposed schedules or changes in schedules at the design stage. In this we distinguish between measures which require some information about probabilities of delay and those which do not. We also distinguish between exogenous delays, which are beyond the influence of the scheduler (delays due to problems in engineering or operations), and knock-on delays which are affected by schedule design: both types are of interest for schedule reliability, but the latter are of more interest for measuring schedule robustness.