Langrangian Delay Predictive Model for Sector-Based Air Traffic Flow

Bayen, Alexandre M.; Grieder, P.; Meyer, George E.; Tomlin, Claire J.

doi:10.2514/1.15242

Cited by 62 publications

(35 citation statements)

References 15 publications

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“…Given the monitoring accuracy in the current system, it has been shown previously that kinematic equations are sufficiently predictive of high altitude traffic (see [48] and the references therein), which makes (7) an accurate enough model of the relative motion of two aircraft. The main task of Air Traffic Controllers is to prevent losses of separation: To keep the aircraft separated by more than five nautical miles.…”

Section: B the Collision Avoidance Differential Gamementioning

confidence: 98%

A time-dependent Hamilton-Jacobi formulation of reachable sets for continuous dynamic games

Mitchell

Bayen

Tomlin

2005

IEEE Trans. Automat. Contr.

983

779

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Abstract-We describe and implement an algorithm for computing the set of reachable states of a continuous dynamic game. The algorithm is based on a proof that the reachable set is the zero sublevel set of the viscosity solution of a particular time-dependent Hamilton-Jacobi-Isaacs partial differential equation. While alternative techniques for computing the reachable set have been proposed, the differential game formulation allows treatment of nonlinear systems with inputs and uncertain parameters. Because the time-dependent equation's solution is continuous and defined throughout the state space, methods from the level set literature can be used to generate more accurate approximations than are possible for formulations with potentially discontinuous solutions. A numerical implementation of our formulation is described and has been released on the web. Its correctness is verified through a two vehicle, three dimensional collision avoidance example for which an analytic solution is available.

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Section: B the Collision Avoidance Differential Gamementioning

confidence: 98%

A time-dependent Hamilton-Jacobi formulation of reachable sets for continuous dynamic games

Mitchell

Bayen

Tomlin

2005

IEEE Trans. Automat. Contr.

983

779

View full text Add to dashboard Cite

show abstract

“…In addition Lagrangian models have been used to predict sector capacities allowing them to be put into the framework of Eulerian models. Key progress in this area has been in improved differential models of air traffic flow, improved hybrid state estimation and the creation of application specific polynomial time algorithms that can be used in lieu of integer programming [6,22,36,45]. Instead of predicting the path of individual aircraft, Eulerian and aggregate flow models predict flow patterns in the airspace [7,13,32].…”

Section: Traditional Air Traffic Management Approachesmentioning

confidence: 99%

“…Lagrangian models for air traffic flow management involve computing the trajectories of individual aircraft [6,28]. These models can be used for a range of problems, from collision avoidance to congestion reduction.…”

Section: Traditional Air Traffic Management Approachesmentioning

confidence: 99%

A multiagent approach to managing air traffic flow

Agogino

Tumer

2010

Auton Agent Multi-Agent Syst

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Abstract. Intelligent air traffic flow management is one of the fundamental challenges facing the Federal Aviation Administration (FAA) today. FAA estimates put weather, routing decisions and airport condition induced delays at 1,682,700 hours in 2007 [18], resulting in a staggering economic loss of over $41 Billion [42]. New solutions to the flow management are needed to accommodate the threefold increase in air traffic anticipated over the next two decades. Indeed, this is a complex problem where the interactions of changing conditions (e.g., weather), conflicting priorities (e.g., different airlines), limited resources (e.g., air traffic controllers) and heavy volume (e.g., over 40,000 flights over the US airspace) demand an adaptive and robust solution.In this paper we explore a multiagent algorithm where agents use reinforcement learning to reduce congestion through local actions. Each agent is associated with a fix (a specific location in 2D space) and has one of three actions: setting separation between airplanes, ordering ground delays or performing reroutes. We simulate air traffic using FACET which is an air traffic flow simulator developed at NASA and used extensively by the FAA and industry. Our FACET simulations on both artificial and real historical data from the Chicago and New York airspaces show that agents receiving personalized rewards reduce congestion by up to 80% over agents receiving a global reward and by up to 90% over a current industry approach (Monte Carlo estimation).

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“…There are several examples of such aircraft-by-aircraft level models for the TFM problem (TFMP) and related problems. 1,2 Other models attempt to capture the dynamics of the system through aggregation of flights. 3,4 The main reason for aggregating flights into flows is to make the problem computationally tractable.…”

Section: Introductionmentioning

confidence: 99%

Parallelization of the Traffic Flow Management Problem

Rios

Ross

2008

AIAA Guidance, Navigation and Control Conference and Exhibit

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This paper describes a parallel approach to solving the national air traffic flow management problem. High fidelity, aircraft-level approaches to this problem can determine which flights should be held on the ground or in an enroute sector. The major drawback to such aircraft-by-aircraft approaches lies in the large amount of data and resulting massive problem instances to be solved for nationwide or long planning horizon scenarios. The presented approach solves twenty individual problems, one for each Air Route Traffic Control Center in the continental United States. Individual client processes coordinate with a central server to solve their respective problems over multiple iterations. Experiments are performed using recent, historic data within a nominal scenario and a weather scenario. These experiments demonstrate the potential for solving this problem using parallel approaches in greatly reduced time. The initial results show solutions that would have taken over 24 hours to obtain optimally in a monolithic system were shown obtainable to within 3% optimality in less than one hour using the parallel architecture. In addition to the runtime and delay cost analysis, delay results from successfully running a high-fidelity, nationwide traffic flow scenario are also detailed.

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Langrangian Delay Predictive Model for Sector-Based Air Traffic Flow

Cited by 62 publications

References 15 publications

A time-dependent Hamilton-Jacobi formulation of reachable sets for continuous dynamic games

A time-dependent Hamilton-Jacobi formulation of reachable sets for continuous dynamic games

A multiagent approach to managing air traffic flow

Parallelization of the Traffic Flow Management Problem

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