Abstract

We present extensions to the Online Delay Management Problem on a Single Train Line. While a train travels along the line, it learns at each station how many of the passengers wanting to board the train have a delay of delta. If the train does not wait for them, they get delayed even more since they have to wait for the next train. Otherwise, the train waits and those passengers who were on time are delayed by delta. The problem consists in deciding when to wait in order to minimize the total delay of all passengers on the train line. We provide an improved lower bound on the competitive ratio of any deterministic online algorithm solving the problem using game tree evaluation. For the extension of the original model to two possible passenger delays delta_1 and delta_2, we present a 3-competitive deterministic online algorithm. Moreover, we study an objective function modeling the refund system of the German national railway company, which pays passengers with a delay of at least Delta a part of their ticket price back. In this setting, the aim is to maximize the profit. We show that there cannot be a deterministic competitive online algorithm for this problem and present a 2-competitive randomized algorithm.

Abstract

xtabstractPassenger railway transportation plays a crucial role in the mobility in Europe. Since the privatization of the railway sector in the 90s, passenger satisfaction has become an important performance indicator in this sector. A key aspect for passengers is the reliability of transfers between trains. When a train arrives at the station with a delay, passengers might miss their connection if the next train departs on time. These passengers then prefer the connecting train to wait, but this introduces delays for many other passengers. Delay Management is a field in railway operations that deals with this situation. It determines whether a connecting train should wait for the passengers that arrive with a delayed train or should depart on time. In this thesis, we apply techniques from Operations Research to develop models and solution approaches for Delay Management. The objective in our models is the minimization of passenger delay. First, we extend the classical delay management model with passenger rerouting. This allows us to compute the exact delays for passengers. We develop an exact algorithm and several heuristics to solve this extension. Then, we incorporate the limited capacity of the stations in our models. Stations are the bottlenecks of the railway infrastructure, where delays of one train can easily propagate to other trains. When optimizing the wait-depart decisions, these secondary delays should be considered. We therefore develop an integrated model that includes headway constraints for trains on the same track in the station and an iterative approach that evaluates the timetable microscopically.