Another dimension of delay propagation is the temporal transmission of delays over the course of a day at a single airport or at connected airports. When large delays are incurred in the morning, it becomes more likely that delays will take place later in the day. This phenomenon may be observed at both an airport level and a national level, with the severity of the propagation potentially related to the imbalance between demand and capacity. This is an illustration of a more general phenomenon in the study of queues: for oversaturated systems, the marginal price of a unit of delay earlier is much higher than it would be if that same delay were to occur later. This is easily illustrated in deterministic systems, but is also generally true for (more realistic) stochastic systems.A common approach for postoperational analysis of delay propagation is to apply a microscopic analytic model and then to aggregate the results. One of the original works in this area was conducted by airline personnel who used proprietary data to trace flights through their operations (1). Lovell et al. (2) and Churchill et al. (3) detailed a methodology that builds on the work of Beatty et al. (1) for differentiating flight data to separate propagated and queuing effects. Specifically, Lovell et al. (2) suggested subtracting upstream delays from empirical data records and translating downstream arrival schedules accordingly, and Churchill et al.(3) added to this idea the notion of accounting for delays as they occur rather than lumping them at the flight arrival time. Several other researchers have included similar label-conserving analytic models for tracking delays through a network (4-7 ). A non-label-conserving microscopic model was proposed by Mukherjee and Hansen (7), and it was shown to produce comparable results with less onerous data requirements.An alternative to the analytic models that still employs microscopic flight tracking is the use of simulation. Other researchers examined the effects of flight delay propagation through airline networks with simulation techniques to vary the conditions and to observe the results of various new and propagated delays (8).Several researchers have taken a more aggregate approach to tracking flight delay propagation. An aggregate statistical model for estimating temporal delay propagation trends at individual airports was proposed by Churchill et al. (9). That model is extended in this paper. Other research examined delay propagation through a network of several airports by using a Bayesian network approach to separate delay into components (10-12). A related statistical model was presented by Xu et al. to identify the quantity of delays that are generated or absorbed by each airport (13). In that research, two statistical models were presented to ferret out the so-called downstream ripple effect-one based on an autoregressive model and one on varying coefficient linear regression. In most of these models, the phenomenon under study is the same as that in the current paper.The aim of several ...

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At many congested airports, access rights are governed by a system of slot controls. A slot conveys to its owner the right to schedule an operation (flight arrival or departure). In this paper, stochastic optimization models are developed to determine the numbers of slots to make available over the course of a day, controlling for the long-term uncertainty induced in arrival or departure capacities because of weather conditions. Three related integer programming formulations for this problem are presented, which vary both in their computational properties and the economic trade-offs modeled. The models are compared both analytically and computationally. Experiments using data from New York's LaGaurdia Airport are reported to demonstrate the impact of these models on optimizing slot profiles while considering long-term capacity uncertainty and several policy objectives.

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