Open Access

Patricia Ebert

• In railway traffic, delays occur every day, causing deviations from the planned timetable and potentially leading to significant delays for passengers, crew members, and trains. In such cases, the original timetable may become infeasible. Therefore, the delay management problem focuses on the construction of a disposition timetable that minimizes the inconvenience for passengers. In this context, two dispatching decisions must be made: wait–depart decisions, which determine whether trains should wait for delayed feeder trains in order to maintain passenger transfers, and precedence decisions, which define the order of trains while respecting the limited capacity of the railway network. For the extensively researched Offline Delay Management Problem (ODM), it is assumed that source delays are fully known and stable over an extended planning period. In this thesis, we relax this assumption and propose the Stochastic Delay Management Problem (DM), which handles source delays as constant within an initial control horizon and as random variables following a delay distribution thereafter. We introduce a two-stage stochastic mixed-integer linear programming formulation for the problem and prove NP-hardness for a special case. Moreover, we analyze different fixations of the wait-depart and precedence decisions. For those, we derive bounds for optimal solutions as well as for the optimal objective values, including tightness results. In practice, numerous simple dispatching rules are applied to guide decisions. To achieve comparability with DM, we integrate seven different rules for wait-depart and precedence decisions into our optimization framework. We then study the price of the rules and show that each examined rule can lead to arbitrarily poor disposition timetables compared to DM. In particular, we present an algorithm corresponding to the case where no dispatching is performed and study the price of non-dispatching. We compare the performance of DM to the performance of the Offline Delay Management Problem and the seven dispatching rules in a computational experiment for the Berlin S-Bahn with different delay scenarios. It becomes evident that taking stochastic delays into account yields on average 1.7% better disposition timetables, but at the cost of higher runtime. Additionally, the average price of non-dispatching of 2.7% indicates that dispatching is desirable, but not as much as one might expect. Three dispatching rules achieve similarly satisfactory results compared to DM. In particular, the rule that neglects all wait-depart decisions finds similarly good or slightly better disposition timetables than DM within a marginally shorter average runtime.