Models of maximum flows in airspace sectors in the presence of multiple constraints

Recently, the ATM community has made important progress in collaborative trajectory management through the introduction of a new FAA traffic management initiative called a Collaborative Trajectory Options Program (CTOP). FAA can use CTOPs to manage air traffic under multiple constraints (manifested as flow constrained areas or FCAs) in the system, and it allows flight operators to indicate their preferences for routing and delay options. CTOPs also permit better management of the overall trajectory of flights by considering both routing and departure delay options simultaneously. However, adoption of CTOPs in airspace has been hampered by many factors that include challenges in how to identify constrained areas and how to set rates for the FCAs. Decision support tools (DST) providing assistance would be particularly helpful in effective use of CTOPs. Such tools would need models of demand and capacity in the presence of multiple constraints. This study examines different approaches to using historical data to create and validate models of aircraft counts in sectors and other airspace regions in the presence of multiple constraints. A challenge in creating an empirical model of aircraft counts under multiple constraints is a lack of sufficient historical data that captures diverse situations involving combinations of multiple constraints especially those with severe weather. The approach taken here to deal with this is two-fold. First, we create a generalized sector model encompassing multiple sectors rather than individual sectors in order to increase the amount of data used for creating the model by an order of magnitude. Secondly, we decompose the problem so that the amount of data needed is reduced. This involves creating a baseline demand model plus a separate weather constrained sector count reduction model and then composing these into a single integrated model. A nominal demand model is a sector aircraft count model (gdem) in the presence of clear local weather. This defines the flow as a function of weather constraints in neighboring regions, airport constraints and weather in locations that can cause re-routes to a location of interest. A weather constrained flow reduction model (fwx-red) is a model of reduction in baseline counts as a function of local weather. Because the number of independent variables associated with each of the two decomposed models is smaller than that with a single model, need for amount of data is reduced. Finally, a composite model that combines these two can be represented as fwx-red (gdem(e), l) where e represents non-local constraints and l represents local weather. The approaches studied to developing these models are divided into three categories: (1) Point estimation models (2) Empirical models (3) Theoretical models. Errors in predictions of these different types of models have been estimated. In situations when there is abundant data, point estimation models tend to be very accurate. Also, empirical models do better than theoretical models when there is sufficient data available. The biggest benefit of theoretical models is their general applicability in wider range situations once the degree of accuracy of these has been established. Quantile regression methods are used to create models of different quantiles of aircraft counts as well as probability distribution functions. Such models can be used in CTOP DSTs in providing assistance with recommendations about CTOP parameters and in supporting what-if reasoning about consequences of potential decisions.