A dual decomposition method for sector capacity constrained traffic flow optimization

An aggregate air traffic flow model based on a multicommodity network is used for traffic flow management in the National Airspace System. The problem of minimizing the total travel time of flights in the National Airspace System of the United States, subject to sector capacity constraints, is formulated as an Integer Program. The resulting solution achieves optimal delay control. The Integer Program implemented for the scenarios investigated has billions of variables and constraints. It is relaxed to a Linear Program for computational efficiency. A dual decomposition method is applied to solve the large scale Linear Program in a computationally tractable manner. A rounding algorithm is developed to map the Linear Program solution to a physically acceptable result, and is implemented for the entire continental United States. A 2-h traffic flow management problem is solved with the method.

[1]  Steven L. Waslander,et al.  Market-Based Air Traffic Flow Control with Competing Airlines , 2008 .

[2]  Banavar Sridhar,et al.  Sequential Traffic Flow Optimization with Tactical Flight Control Heuristics , 2008 .

[3]  M J Lighthill,et al.  On kinematic waves II. A theory of traffic flow on long crowded roads , 1955, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[4]  Parimal Kopardekar,et al.  Traffic Complexity Measurement Under Higher Levels of Automation and Higher Traffic Densities , 2008 .

[5]  Kapil Sheth,et al.  Aggregate Flow Model for Air-Traffic Management , 2004 .

[6]  Dimitris Bertsimas,et al.  The Air Traffic Flow Management Problem with Enroute Capacities , 1998, Oper. Res..

[7]  Amedeo R. Odoni,et al.  The European Air Traffic Flow Management Problem , 2007, Transp. Sci..

[8]  Daniel Pérez Palomar,et al.  Distributed Optimization of Coupled Systems With Applications to Network Utility Maximization , 2006, 2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceedings.

[9]  Ning Xu,et al.  Propagation of Delays in the National Airspace System , 2006, UAI.

[10]  George B. Dantzig,et al.  Decomposition Principle for Linear Programs , 1960 .

[11]  Banavar Sridhar,et al.  National Airspace System Delay Estimation Using Weather Weighted Traffic Counts , 2005 .

[12]  Thomas H. Cormen,et al.  Introduction to algorithms [2nd ed.] , 2001 .

[13]  Stephen P. Boyd,et al.  Distributed optimization for cooperative agents: application to formation flight , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[14]  B. Sridhar,et al.  Optimally and equitably distributing delays with the aggregate flow model , 2008, 2008 IEEE/AIAA 27th Digital Avionics Systems Conference.

[15]  Amedeo R. Odoni,et al.  The Air Traffic Flow Management Problem: An Integer Optimization Approach , 2008, IPCO.

[16]  Michael O. Ball,et al.  Slot Trading Opportunities in Collaborative Ground Delay Programs , 2006, Transp. Sci..

[17]  Alexandre M. Bayen,et al.  Comparison of the performance of four Eulerian network flow models for strategic air traffic management , 2007, Networks Heterog. Media.

[18]  Dengfeng Sun,et al.  Disaggregation Method for an Aggregate Traffic Flow Management Model , 2010 .

[19]  A. Odoni.  The Flow Management Problem in Air Traffic Control , 1987 .

[20]  Paolo Dell'Olmo,et al.  A dynamic programming approach for the airport capacity allocation problem , 2003 .

[21]  Michael O. Ball,et al.  A Comparison of Formulations for the Single-Airport Ground-Holding Problem with Banking Constraints , 2000, Oper. Res..

[22]  Andres G. Zellweger,et al.  Performance Measures for Future Architecture , 2001 .

[23]  James S. DeArmon,et al.  - 1-- Assessing NAS Performance : Normalizing for the Effects of Weather , 2001 .

[24]  S. Thomas McCormick,et al.  Integer Programming and Combinatorial Optimization , 1996, Lecture Notes in Computer Science.

[25]  Hanif D. Sherali,et al.  Nonlinear Programming - Theory and Algorithms, Third Edition , 2005 .

[26]  Banavar Sridhar,et al.  Some Properties of the Aggregate Flow Model of Air Traffic , 2005 .

[27]  Frank Kelly,et al.  Rate control for communication networks: shadow prices, proportional fairness and stability , 1998, J. Oper. Res. Soc..

[28]  David K. Smith.  Network Flows: Theory, Algorithms, and Applications , 1994 .

[29]  Katta G. Murty,et al.  Nonlinear Programming Theory and Algorithms , 2007, Technometrics.

[30]  David J. Lovell,et al.  Flight Delay Propagation Impact on Strategic Air Traffic Flow Management , 2010 .

[31]  Robert A. Vivona,et al.  Field Observations of Interactions Between Traffic Flow Management and Airline Operations , 2006 .

[32]  Kapil Sheth,et al.  FACET: Future ATM Concepts Evaluation Tool , 2001 .

[33]  K. Schittkowski,et al.  NONLINEAR PROGRAMMING , 2022 .

[34]  Lucio Bianco,et al.  Flow Control of Congested Networks , 1987, NATO ASI Series.

[35]  C. Daganzo.  THE CELL TRANSMISSION MODEL.. , 1994 .

[36]  Dengfeng Sun,et al.  Traffic Flow Management Using Aggregate Flow Models and the Development of Disaggregation Methods , 2009 .

[37]  Parimal Kopardekar,et al.  Airspace Restriction Planner for Sector Congestion Management , 2005 .

[38]  Joseph L. Rios,et al.  Massively Parallel Dantzig-Wolfe Decomposition Applied to Traffic Flow Scheduling , 2010, J. Aerosp. Comput. Inf. Commun..

[39]  Hanif D. Sherali,et al.  An Airspace-Planning and Collaborative Decision-Making Model: Part II - Cost Model, Data Considerations, and Computations , 2006, Transp. Sci..

[40]  Banavar Sridhar,et al.  Modeling and Optimization in Traffic Flow Management , 2008, Proceedings of the IEEE.

[41]  Daniel Pérez Palomar,et al.  Alternative Distributed Algorithms for Network Utility Maximization: Framework and Applications , 2007, IEEE Transactions on Automatic Control.

[42]  Michael O. Ball,et al.  Ground Delay Program Planning under Uncertainty Based on the Ration-by-Distance Principle , 2007, Transp. Sci..

[43]  Amedeo R. Odoni,et al.  The Multi-Airport Ground-Holding Problem in Air Traffic Control , 1992, Oper. Res..

[44]  Michael O. Ball,et al.  Collaborative decision making in air traffic management current and future research directions , 2001 .

[45]  David J. Lovell,et al.  EXAMINING THE TEMPORAL EVOLUTION OF PROPAGATED DELAYS AT INDIVIDUAL AIRPORTS : CASE STUDIES , 2007 .

[46]  Banavar Sridhar,et al.  Integration of Traffic Flow Management Decisions , 2002 .

[47]  P. I. Richards.  Shock Waves on the Highway , 1956 .

[48]  Michael S. Nolan,et al.  Fundamentals of Air Traffic Control , 1990 .

[49]  Karl D. Bilimoria,et al.  New Approach for Modeling, Analysis, and Control of Air Traffic Flow , 2002 .

[50]  P.T.R. Wang,et al.  Flight connections and their impacts on delay propagation , 2003, Digital Avionics Systems Conference, 2003. DASC '03. The 22nd.

[51]  Stephen P. Boyd,et al.  Simultaneous routing and resource allocation via dual decomposition , 2004, IEEE Transactions on Communications.

[52]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[53]  Banavar Sridhar,et al.  COMPARISON OF LINEAR DYNAMIC MODELS FOR AIR TRAFFIC FLOW MANAGEMENT , 2005 .

[54]  Amedeo R. Odoni,et al.  Strategic Flow Management for Air Traffic Control , 1993, Oper. Res..

[55]  Carlos F. Daganzo,et al.  THE CELL TRANSMISSION MODEL, PART II: NETWORK TRAFFIC , 1995 .

[56]  Michael O. Ball,et al.  A GENERAL APPROACH TO EQUITY IN TRAFFIC FLOW MANAGEMENT AND ITS APPLICATION TO MITIGATING EXEMPTION BIAS IN GROUND DELAY PROGRAMS , 2003 .

[57]  Dengfeng Sun,et al.  MILP control of aggregate Eulerian network airspace models , 2006, 2006 American Control Conference.

[58]  Alexandre M. Bayen,et al.  Adjoint-based control of a new eulerian network model of air traffic flow , 2006, IEEE Transactions on Control Systems Technology.

[59]  Hector A. Rosales-Macedo.  Nonlinear Programming: Theory and Algorithms (2nd Edition) , 1993 .

[60]  Giovanni Andreatta,et al.  Multiairport Ground Holding Problem: A Computational Evaluation of Exact Algorithms , 1998, Oper. Res..

[61]  Cynthia Barnhart,et al.  An Analysis of Passenger Delays Using Flight Operations and Passenger Booking Data , 2005 .

[62]  Steven Lake Waslander,et al.  Lump-Sum Markets for Air Traffic Flow Control With Competitive Airlines , 2008, Proceedings of the IEEE.

[63]  Eugene P. Gilbo,et al.  Airport capacity: representation, estimation, optimization , 1993, IEEE Trans. Control. Syst. Technol..

[64]  Heinz Erzberger,et al.  CTAS: Computer intelligence for air traffic control in the terminal area , 1992 .

[65]  Banavar Sridhar,et al.  Central East Pacific Flight Scheduling , 2007 .

[66]  E. Andrew Boyd,et al.  TRAFFIC FLOW MANAGEMENT MODELING WITH THE TIME ASSIGNMENT MODEL. , 1993 .

[67]  Banavar Sridhar,et al.  Relationship between Weather, Traffic and Delay Based on Empirical Methods , 2006 .

[68]  Tom E. Bishop,et al.  Blind Image Restoration Using a Block-Stationary Signal Model , 2006, 2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceedings.

[69]  Hanif D. Sherali,et al.  An Airspace Planning Model for Selecting Flight-plans Under Workload, Safety, and Equity Considerations , 2002, Transp. Sci..

[70]  Geoffrey D. Gosling.  Aviation System Performance Measures , 1999 .

[71]  Giorgio Romanin-Jacur,et al.  The Multiple Connections Multi-Airport Ground Holding Problem: Models and Algorithms , 1998, Transp. Sci..

[72]  T. Mexia,et al.  Author ' s personal copy , 2009 .

[73]  M. P. Helme,et al.  Reducing air traffic delay in a space-time network , 1992, [Proceedings] 1992 IEEE International Conference on Systems, Man, and Cybernetics.

[74]  Kathryn B. Laskey,et al.  Estimation of Delay Propagation in the National Aviation System Using Bayesian Networks , 2005 .

[75]  Hanif D. Sherali,et al.  An Airspace Planning and Collaborative Decision - Making Model: Part I - Probabilistic Conflicts, Workload, and Equity Considerations , 2003, Transp. Sci..

[76]  Giovanni Andreatta,et al.  Multi-Airport Ground Holding Problem: A Heuristic Approach Based on Priority Rules , 1997 .

[77]  Banavar Sridhar,et al.  Classification and Computation of Aggregate Delay Using Center-based Weather Impacted Traffic Index , 2007 .

[78]  Craig Wanke,et al.  Incremental, Probabilistic Decision Making for En Route Traffic Management , 2007 .

[79]  Michael O. Ball,et al.  Optimization and mediated bartering models for ground delay programs , 2006 .

[80]  Dengfeng Sun,et al.  Integration of an Aggregate Flow Model with a Traffic Flow Simulator , 2008 .

[81]  F. Tung,et al.  Navigation and control. , 1968 .

[82]  A. Robert Calderbank,et al.  Layering as Optimization Decomposition: A Mathematical Theory of Network Architectures , 2007, Proceedings of the IEEE.

[83]  Ravindra K. Ahuja,et al.  Network Flows: Theory, Algorithms, and Applications , 1993 .

[84]  A. Bayen,et al.  Multicommodity Eulerian-Lagrangian Large-Capacity Cell Transmission Model for En Route Traffic , 2008 .

[85]  Michael O. Ball,et al.  Ground Delay Programs: Optimizing over the Included Flight Set Based on Distance , 2004 .

[86]  Kevin Ross,et al.  Solving High Fidelity, Large-Scale Traffic Flow Management Problems in Reduced Time , 2008 .