Delay management for public transport consists of deciding whether vehicles should wait for delayed transferring passengers, with the objective of minimizing the overall passenger discomfort. We model the underlying transportation network as a directed acyclic graph, where edges represent trains, and weighted paths represent passenger flows. Given initial delays of some of the passenger paths, our goal is to decide which edges wait for delayed passenger paths, such that the sum of all passenger delays is minimized. This paper classifies the computational complexity of delay management problems with respect to various structural parameters, such as the maximum number of passenger transfers, the graph topology, and the capability of edges to reduce delays. Our focus is to distinguish between polynomially solvable and NP-complete problem variants. To that end, we show that even fairly restricted versions of the delay management problem are hard to solve.
We consider delay management in railway systems. Given delayed trains, we want to find a waiting policy for the connecting trains minimizing the weighted total passenger delay. If there is a single delayed train and passengers transfer at most twice along fixed routes, or if the railway network has a tree structure, the problem can be solved by reduction to min-cut problems. For delayed passenger flows on a railway network with a path structure, the problem can be solved to optimality by dynamic programming. If passengers are allowed to adapt their route to the waiting policy, the decision problem is strongly N P-complete.
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