Evaluation Method of Robustness for Train Schedules

Although trains are operated according to predefined schedules, unexpected incidents sometimes occur and trains inevitably experience delays. An example of such a delay is when dwell time increases due to an object caught between the doors; this leads to a build-up of passengers on the platform, who then rush onto the train when the doors are reopened to release the object. Train delays may also occur due to various meteorological conditions such as rain, snow or fog, and can eventually affect other trains. This paper looks at the development of a robust train schedule under which stable transportation services can be provided regardless of unexpected incidents. In order to consider a robust train schedule, we need to define a measure of robustness. Generally, train delays lead to a reduced level of transportation service, and References 1)3) have suggested robustness indices based on train delays. Such a concept, however, does not apply from the viewpoint of passengers, as individual train delays do not reflect the reduced level of transportation service that each one suffers. As an example, it is more important for passengers who transfer trains several times to be able to make their connections as planned. We have therefore proposed a new concept in Reference 4) involving a robustness index based on passenger convenience. We calculate the specific robustness index for train schedules using the level of passenger disutility derived from the traveling time, congestion rates, the number of transfer lines and the waiting time. Any attempt to calculate robustness indices deterministically is inappropriate, since it is impossible to know the frequency, location, timing and length of delays in advance. It is possible, though, to anticipate such data probabilistically based on measurement surveys. In light of this, we introduce a method to define robustness indices probabilistically. Specifically, we determine that the robustness index should be calculated using a value that represents the expected increase in passenger disutility when delays occur. We calculated the robustness index by applying a Monte Carlo simulation method iteratively to estimate train operation from passenger behavior. In Section 2, we explain passenger disutility and define the robustness index, and Section 3 illustrates the calculation method for the robustness index using the simulator developed and Monte Carlo simulation. In Section 4, we calculate robustness indices for an actual train schedule and a modified one, and give a comparison of the results. Section 5 outlines the conclusions reached.