This paper considers Stochastic Shortest Path (SSP) problems in probabilistic networks. A variety of approaches have already been proposed in the literature. However, unlike in the deterministic case, they are related to distinct models, interpretations and applications. W e have chosen to look at the case where detours from the original path must be taken whenever the "first-choice" arc fails. The main results obtained include the proof of some counterintuitive facts (e.g., the SSP may contain a cycle), the proof of the validity of applying stochastic programming to this problem and the proof that the computational complexity of a particular SSP problem is polynomial.
Airport congestion is one of the main causes of costly aircraft delays. Sometimes costs may be reduced by imposing on some aircraft a delay at take off time in order to later avoid a more expensive airborne delay. The objective of the Flow Management Problem (F.M.P.) is to find an optimal delay strategy so that the total expected delay cost is minimized. In this paper an idealized and greatly simplified version of F.M.P. is investigated. In particular the airways network considered is star-shaped and congestion is allowed only in the central (arrival) airport. For this particular version a model is presented and a polynomial solution algorithm is derived. Landing priorities among aircraft can also influence the total expected delay cost: the optimal priority rule for our version of the F.M.P. is derived. Another algorithm is presented for the case where the number of aircraft not to be delayed on the ground is given a priori. Possible extensions of the proposed model to more realistic situations are mentioned
Congestion in the air traffic network is becoming an increasingly serious problem that causes inconvenience to passengers, losses to airlines and, last but not least, threats to airspace safety. One way of reducing the amount of congestion is to use Ground Holding policies, i.e., to impose on selected aircraft a ground holding prior to their departure so that congestion during peak periods of time may be smoothed away. In this paper we restrict our attention to the Multiairport Ground Holding problem, where congestion may arise only at the airports due to limited arrival capacity. There are a few algorithms that, under suitable hypotheses, find an “optimal” policy for the Multiairport Ground Holding problem. In this paper we evaluate and compare computationally three of them, namely, the one recently proposed by Vranas, Bertsimas and Odoni, the one suggested by Andreatta and Tidona and that due to Bertsimas and Stock. The computational evaluation is based on two sets of test problems. The first set consists of seven problems taken from the literature. The second set consists of 32 “realistic” test problems. The results indicate the superiority of the Bertsimas and Stock approach among the three models considered.
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