# Delay Management in Regional Railway Transport
## 2 Materials and Methods  
### Background: State-of-the-Art  
The authors' research in determining appropriate transfer waiting times and delays is based not only on their innovative approach, but also on previously published works on the topics of train scheduling, traffic control, dispatching, and delay management. [PERSON] [1] analyzed the dispatcher's decision-making process in a single-track railway and developed a heuristic algorithm for rescheduling trains by modifying existing meet/pass plans in conflicting situations. He determined dynamic priorities and their weights, based on them the algorithm chooses the best alternative resolution that results in less total consequential delay in the system. [PERSON] [2] developed a binary linear optimization model for discrete time rescheduling in complex central railway station areas. The approach was successfully applied to an operational day at the central railway station in Berne, Switzerland. [PERSON] [3] proposed an optimization approach based on a macroscopic delay management model that determines which transfer connections to maintain. The resulting disposition timetable was then validated microscopically in a bottleneck station within the network. [PERSON] [4] developed a multi-criteria decision support methodology for dispatchers, incorporating safety regulations and considering key performance indicators. Mixed-integer linear programming (MILP) formulations were proposed and solved via a commercial approach, wherein a well-established non-parametric benchmarking technique provided an efficient/inefficient classification of the best solutions for each instance. Computational experiments were held on a Dutch railway network with mixed traffic and multiple disturbances. [PERSON] [5] dealt with the integration of real-time traffic management and train control. He developed three innovative integrated optimization approaches to deliver a solution for train dispatching and train control, using mixed-integer nonlinear programming (MINLP) and mixed-integer linear programming (MILP). [PERSON] [6] focused on two streams of research from the perspectives of operations managers and passengers. He developed microscopic passenger-centric models and proposed several fast heuristic methods based on alternative decompositions of the model. He also proposed a tabu search scheme [7] consisting of effective rescheduling algorithms and local rerouting strategies. A fast heuristic method and a truncated branch-and-bound algorithm were combined to compute the optimal solution in small instances and a relatively accurate solution for large situations with complex disturbances in short time periods. [PERSON] [8] developed a branch-and-bound algorithm that included rules to enable faster computation. [PERSON] combined this algorithm with [PERSON]'s tabu search in the AGLIBRARY system [9]. The procedure computed a first-feasible schedule, in which each train followed its default route. Then, the procedure iteratively looked for better solutions, in terms of delay minimization, by changing the routes for some trains. The AGLIBRARY system was tested on a railway line near London, and the data computed to better solutions than those of an MILP formulation using the same computing time. [PERSON] [10] applied lean philosophy in risk management to the impact of train delays in railway passenger transport. For data assessment, she used multiple statistical tests. The research focused on highlighting the need for a systematic approach to train delays and avoiding delays via risk management. [PERSON] [11] added time margins (i.e., headway buffers and running time supplements) to the planning process for timetables. His research relocated time margins to proper positions to minimize the sum of train delays. For this task, he treated the train timetable as a directed arc graph (DAG) and proposed a heuristic technique, critical time margins allocation (CTMA), which is based on CPM. [PERSON] [12] examined the updating of railway timetables to reduce delays in cases of unexpected events.