UMD Theses and Dissertations
Permanent URI for this collectionhttp://hdl.handle.net/1903/3
New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a given thesis/dissertation in DRUM.
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Item Coordinated and robust aviation network resource allocation(2010) Churchill, Andrew Michael; Lovell, David J; Civil Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)In the United States, flight operators may schedule flights to most airports at whatever time best achieves their objectives. However, during some time periods, both at airports and in the airspace, these freely-developed schedules may become infeasible because weather or other factors reduce capacity. A plan must then be implemented to mitigate this congestion safely, efficiently, and equitably. Current planning processes treat each congested resource independently, applying various rules to increase interoperation times sufficiently to match the reduced capacity. However, several resources are occasionally congested simultaneously, and ignoring possible dependencies may yield infeasible allocations for flights using multiple resources. In this dissertation, this problem of developing coordinated flight-slot allocations for multiple congested resources is considered from several perspectives. First, a linear optimization model is developed. It is demonstrated that optimally minimizing flight arrival delays induces an increasing bias against flights using multiple resources. However, the resulting allocations reduce overall arrival delay, as compared to the infeasible independent allocations, and to current operational practice. The analytic properties of the model are used to develop a rule-based heuristic for allocating capacity that achieves comparable aggregate results. Alternatively, minimizing delay assigned at all resources is considered, and this objective is shown to mimic the flights' original schedule order. Recognizing that minimizing arrival delays is attractive because of its tangible impact on system performance, variations to the original optimization model are proposed that constrain the worst-case performance of any individual user. Several different constraints and cost-based approaches are considered, all of which are successful to varying degrees in limiting inequities. Finally, the model is reformulated to consider uncertainty in capacity. This adds considerable complexity to the formulation, and introduces practical difficulties in identifying joint probability distributions for the capacity outcomes at each resource. However, this new model is successful in developing more robust flight-slot allocations that enable quick responses to capacity variations. Each of the optimization models and heuristics presented here are tested on a realistic case study. The problem studied and the approaches employed represent an important middle ground in air traffic flow management research between single resource models and comprehensive ones.Item COMPUTATIONALLY TRACTABLE STOCHASTIC INTEGER PROGRAMMING MODELS FOR AIR TRAFFIC FLOW MANAGEMENT(2010) Glover, Charles N.; Ball, Michael O; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)A primary objective of Air Traffic Flow Management (ATFM) is to ensure the orderly flow of aircraft through airspace, while minimizing the impact of delays and congestion on airspace users. A fundamental challenge of ATFM is the vulnerability of the airspace to changes in weather, which can lower the capacities of different regions of airspace. Considering this uncertainty along with the size of the airspace system, we arrive at a very complex problem. The development of efficient algorithms to solve ATFM problems is an important and active area of research. Responding to predictions of bad weather requires the solution of resource allocation problems that assign a combination of ground delay and route adjustments to many flights. Since there is much uncertainty associated with weather predictions, stochastic models are necessary. We address some of these problems using integer programming (IP). In general, IP models can be difficult to solve. However, if "strong" IP formulations can be found, then problems can be solved quickly by state of the art IP solvers. We start by describing a multi-period stochastic integer program for the single airport stochastic dynamic ground holding problem. We then show that the linear programming relaxation yields integer optimal solutions. This is a fairly unusual property for IP formulations that can significantly reduce the complexity of the corresponding problems. The proof is achieved by defining a new class of matrices with the Monge property and showing that the formulation presented belongs to this class. To further improve computation times, we develop alternative compact formulations. These formulations are extended to show that they can also be used to model different concepts of equity and fairness as well as efficiency. We explore simple rationing methods and other heuristics for these problems both to provide fast solution times, but also because these methods can embody inherent notions of fairness. The initial models address problems that seek to restrict flow into a single airport. These are extended to problems where stochastic weather affects en route traffic. Strong formulations and efficient solutions are obtained for these problems as well.