Dengfeng Sun

Multicommodity Eulerian-Lagrangian Large-Capacity Cell Transmission Model for En Route Traffic

A new paradigm for building an Eulerian-Lagrangian cell transmission model for air traffic flow is developed. It is based on an aggregation of track data and is applied to the full National Airspace System in the United States. The Eulerian-Lagrangian model is based on a multicommodity network flow model constructed from historical air traffic data. The flow model is reduced to a linear time invariant dynamical system, in which the state is a vector of aggregate aircraft counts. This model is called a large-capacity cell transmission model in reference to the cell transmission model in highway traffic, which inspired this work. The predictive capabilities of the model are successfully validated against recorded air traffic data by showing an accurate match between predicted sector counts (based on filed flight plans) and measured sector counts. The problem of controlling the sector aircraft count is posed as an integer program in which the dynamical system appears in the constraints. To improve the computational time for solving the problem, the integer program is relaxed to a linear program. The computational results show that a high portion of solutions of the linear program are integers, making this method appropriate for high-level traffic flow management.

A Weighted-Graph Approach for Dynamic Airspace Configuration

A method for partitioning airspace into smaller regions based on a peak traffic-counts metric is described. The three setup steps consist of 1) creating a network flow graph, 2) creating an occupancy grid composed of grid cells of specified size for discretizing the airspace and 3) assigning the grid cells to the nodes of the network flow graph. Both the occupancy grid and the grid cell assignment to nodes are computationally realized using matrices. During the run phase of the method, the network flow graph is partitioned into its two sub-graphs and these two sub-graphs and then partitioned into their two sub-graphs, and so on till a termination criterion is met. Weights of the sub-graphs are computed by summing the number of aircraft in each grid cell associated with the nodes of the sub-graphs at each time instant. This process is accomplished by using the occupancy and assignment matrices created during the setup step. The final weight is obtained as the maximum count over a time period. Spectral bisection is then used to split the sub-graph with the maximum weight into its two sub-graphs. Recursive application of the spectral bisection method and weight computation results in the final set of sub-graphs. The grid cells associated with each sub-graph then represent the geometry of the associated sector. Results of sectorization of the airspace over the continental United States are provided to demonstrate the merits and the limitations of the method. The weighted-graph technique created larger sectors in regions of light-traffic and smaller sectors in regions of heavy-traffic. Peak traffic-counts in the sectors were found to be within the range of the Monitor Alert Parameters specified in the Enhanced Traffic Management System.

A Hierarchical Flight Planning Framework for Air Traffic Management

The continuous growth of air traffic demand, skyrocketing fuel price, and increasing concerns on safety and environmental impact of air transportation necessitate the modernization of the air traffic management (ATM) system in the United States. The design of such a large-scale networked system that involves complex interactions among automation and human operators poses new challenges for many engineering fields. This paper investigates several important facets of the future ATM system from a systems-level point of view. In particular, we develop a hierarchical decentralized decision architecture that can design 4-D (space +time) path plans for a large number of flights while satisfying weather and capacity constraints of the overall system. The proposed planning framework respects preferences of individual flights and encourages information sharing among different decision makers in the system, and thus has a great potential to reduce traffic delays and weather risks while maintaining safety standards. The framework is validated through a large-scale simulation based on real traffic data over the entire airspace of the contiguous United States. We envision that the hierarchical decentralization approach developed in this paper would also provide useful insights into the design of decision and information hierarchies for other large-scale infrastructure systems.

Roadmap Based Pursuit-Evasion and Collision Avoidance

We study pursuit-evasion games for mobile robots and their applications to collision avoidance. In the first part of the paper, under the assumption that the pursuer and the evader (possibly subject to physical constraints) share the same roadmap to plan their strategies, we present sound and complete strategies for three different games. In the second part, we utilize the pursuit-evasion results to post-process the workspace and/or configuration space and obtain a collision probability map of the environment. Next, we present a probabilistic method to utilize this map and plan trajectories which minimize the collision probability for independent robots.

Investigation of Potential Fuel Savings Due to Continuous-Descent Approach

The continuous-descent approach is among the key concepts of the Next Generation Air Transportation System. Although a considerable number of researchers have been devoted to the estimation of potential fuel savings of the continuous-descent approach, few have attempted to explain the fuel savings observed in field tests from an analytical point of view. This paper focuses on the evaluation of the continuous-descent approach as a fuel-reduction procedure. This research gives insights into the reasons why the continuous-descent approach saves fuel, and design guidelines for the continuous-descent-approach procedures are derived. The analytical relationship between speed, altitude, and fuel burn is derived based on the base of aircraft data total-energy model. A theoretical analysis implies that speed profile has an impact as substantial as, if not more than, vertical profile on the fuel consumption in the terminal area. In addition, the continuous-descent approach is not intrinsically a fuel-saving procedu...

Disaggregation Method for an Aggregate Traffic Flow Management Model

A linear time-varying aggregate traffic flowmodel can be used to develop traffic flowmanagement strategies using optimization algorithms. However, there are few methods available in the literature to translate these aggregate solutions into practical control actions involving individual aircraft. In this paper, a computationally efficient disaggregation algorithm is proposed by employing a series of linear program and mixed integer linear program methods, which converts an aggregate (flow-based) solution to a flight-specific control action. Numerical results generated by the optimization method and the disaggregation algorithm are presented and illustrated by applying them to generate traffic flow management schedules for a typical day in the U.S. National Airspace System.

MILP control of aggregate Eulerian network airspace models

A new Eulerian model of airspace is derived and applied to high altitude traffic for a full air traffic control center of the National Airspace System. The Eulerian model is reduced to a linear time invariant dynamical system, in which the state is a vector of aggregate aircraft counts. The model is validated against ASDI data and applied to the Oakland airspace. The problem of controlling sector aircraft count is posed as an integer program, in which the dynamical system appears in the constraints. To improve the computational time of calculating the solution, the integer program is relaxed to a linear program, solved for instances with more than one million variables. The computational results show that a high proportion of solutions of the LP are integers. The computational time is satisfactory for two hour traffic flow management problems

Algebraic Connectivity Maximization for Air Transportation Networks

It is necessary to design a robust air transportation network. An experiment based on the real air transportation network is performed to show that algebraic connectivity is a fair measure for network robustness under random failures. Therefor, the goal of this paper is to maximize algebraic connectivity. Some researchers solve the maximization of the algebraic connectivity by choosing the weights for the edges in the graph. Others focus on the best way to add edges in a network in order to optimize the connectivity. In this paper, the authors formulate a new air transportation network model and show that the corresponding algebraic connectivity optimization problem is interesting because the two subproblems of adding edges and choosing edge weights cannot be treated separately. The new problem is formulated and exactly solved in a small air transportation network case. The authors also propose the approximation algorithm in order to achieve better efficiency. For large networks, the semidefinite programming with cluster decomposition is first presented. Moreover, the algebraic connectivity maximization for directed networks is discussed. Simulations are performed for a small-scale case, large-scale problem, and directed network problem.

Traffic Flow Management Using Aggregate Flow Models and the Development of Disaggregation Methods

A linear time-varying aggregate traffic flow model can be used t o develop Traffic Flow Management strategies based on optimization algorithms. However, there are no methods available in the literature to translate these aggregate solutions into actions involving individual aircraft. This paper describes and implements a computationally efficient disaggregation algorithm, which converts an aggregate (flow-based) solution to a flight-specific control action. Numerical results generated by the optimization method and the disaggregation algorithm are presented and illustrated by applying them to generate TFM schedules for a typical day in the U.S. National Airspace System. The results show that the disaggregation algorithm generates control actions for individual flights while keeping the air traffic behavior very close to the optimal solution.

A Parallel Computing Framework for Large-Scale Air Traffic Flow Optimization

Optimizing nationwide air traffic flow entails computational difficulty as the traffic is generally modeled as a multicommodity network, which involves a huge number of variables. This paper presents a framework that speeds up the optimization. Nationwide air traffic is modeled using a link transmission model (LTM), to which a dual-decomposition method is applied. The large-scale problem is decomposed into a master problem and a number of independent subproblems, which are easy to solve. As a result, the execution of solving the subproblem is parallelizable. A parallel computing framework is based on multiprocessing technology. The master problem is updated on a server, and a client cluster is deployed to finish the subproblems such that the most computationally intensive part of the optimization can be executed in parallel. The server and the clients communicate via Transmission Control Protocol (TCP)/User Datagram Protocol (UDP). An adaptive job allocation method is developed to balance the workload among each client, resulting in maximized utilization of the computing resources. Experiment results show that, compared with an earlier single process solution, the proposed framework considerably increases computational efficiency. The optimization of a 2-h nationwide traffic problem involving 2326 subproblems takes 6 min using ten Dell workstations. The increased computational workload due to the increased number of subproblems can be mitigated by the extension of computer deployment.