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Arrive in Time by Train with High Probability

Very often, a train passenger must meet a deadline at the destination, for example, to catch a plane or to arrive at an important meeting on time. Train delays and broken connections let the passenger arrive later than scheduled. Events of this kind are usually not foreseeable before the journey commences. To be on the safe side, a connection should be prebooked such that, in case the connection breaks anywhere, alternative continuations guarantee arrival prior to the deadline with acceptably high probability. For busy people, the challenge is to commence the journey as late as possible, provided the risk of failing to meet the deadline is negligible. This scenario translates into the problem to find the latest connection plus alternative continuations such that the probability of meeting the deadline is not lower than a given required probability of success (close to 100%). We present a dynamic-programming approach to this optimization problem and report on an empirical study based on comprehensive real-...