Integrated Taxiing and Take-Off Scheduling for Optimization of Airport Surface Operations

1. Integrated Taxiing and Take-Off Scheduling for Optimization of Airport Surface Operations H.-S. Jacob Tsao, Wenbin Wei, Agus Pratama and Suseon Yang College of Engineering, San Jose State University, San Jose, California, USA Posted at http://www.engr.sjsu.edu/jtsao/papers/ISDSI-2009-airport.ppt

2. Optimization of Airport Surface Operations • Background and Motivation • US Air Transportation • Necessity to Optimize Airport Surface Operations • A Wide Spectrum of Decision-Support Problems • Salient Features of the Optimization Problem • An optimization Architecture, reported separately • Our Focus on Control: taxiway and take-off scheduling • Solution Approach to Efficient, Fair and Safe Control (of Aircraft Movements) • Decision Variables, Objective and Constraints • Implementation and Numerical Results • Conclusion

3. Tower Automation Datalinked Clearances Control Tower Flight-Deck Automation 3/18/2008 3

4. Dallas Fort-Worth International Airport

5. Background and Motivation • US Air Transportation • Runways being the bottlenecks, at airport & AIRSPACE • No more space for airport expansion: planning horizon • Noise concerns, where there is space for new runways • Market driven: 10 departures at same time • Carrier gaming: false departure-time forecasts for FCFS • Human factors: controller and pilot • CONGESTION • Necessity to Optimize Airport Operations, Despite • Sobering from the “excess era” of the 1990’s: frequent flights, small planes; high and volatile fuel prices

6. Current Airport Surface Operations • Air Traffic Controllers plan and control aircraft movements, real-time and primarily manually • Priority: • Safety is the primary concern. • Fairness is secondary. • Efficiency is tertiary. • Result: • Congestion on taxiways and runway entrances: delays and ripple/cascading effects • Stop-and-go movements: wasted fuel, unnecessary emissions, noise, etc.

7. Decision Support: Problem Features • Salient Features of the Operations Optimization • Crux: Runways being the primary bottlenecks • Aircraft sequencing: • large safety air-separation required for small following large • Air-separation also dependent on direction aftet take-off • Air carrier marketing and hub-and-spoke network structure • Stochasticity/Uncertainty: • Time of readiness for departure or time of arrival • Air carrier gaming: false forecasts of readiness time for departure for First Come First Serve (FCFS) control policy • Pushback from gate as soon as ready for FCFS & “fairness” • Resulting congestion on the taxiways • Human Factors: Controller and Pilot Workload

8. Decision Problems: Needs & Our Focus • An overall optimization architecture, as context • Instructions for 4-D trajectories for efficient, fair and, of course, safe control (of aircraft movements), • In presence of • Human-Factors limitations • Stochasticity/uncertainty • With the assistance of • Operational procedures • Mathematical optimization and algorithms • Advanced Technologies • Control difficulty and inefficiency as Input to longer-term planning

9. Problem Statement: Integrated Taxiway and Take-Scheduling • Existing Literature: • Little on optimization architecture for ASO • Component problems, treated mostly as independent • Taxiway scheduling by Smeltink et al. [2004] • Aircraft sequencing for take-off optimization, e.g., Anagnostakis [2001] • Our Contribution, Thanks to NASA Support • Architecture, reported separately • “Derived” from salient features of ASO optimization: runways as the bottlenecks, uncertainty, human factors, fairness, etc. • Operational procedures, advanced technologies and mathematical algorithms, integrated also with strategic planning • Integrated Taxiway and take-off scheduling

10. Solution Approach to Efficient Control (of Aircraft Movement) • 4-D trajectories: continuous time and continuous space • Control decisions about discrete times of aircraft reaching discrete intersections on taxiways • Transforming an complex optimal-control problem to a mathematical programming problem • Decisions embellished to build 4-D trajectories • Anticipation of deviation from instructions due to human factors before implementation of technologies for Instruction adherence • Reduce stochasticity/uncertainty for better resource utilization

11. General Strategies and Requirements • Runway bottlenecks: a small queue to avoid spoilage, due to human factors • Stochasticity/Uncertainty: • penalty for inaccuracy of forecast departure readiness times • Inclusion of only aircraft ready for near-ready for departure (i.e., pushback) from gate • smooth travel and gate-hold to avoid taxiway congestion • Fairness • Safety, of course, and Other Requirements

12. Input • Airport Configuration • A planning horizon • Flight schedule • One route per aircraft, departing or arriving • Air-separation required between any pair of aircraft, depending on their sizes and the directions (i.e., “departure fixes”) after take-off • Optional: Locations of aircraft already on tarmac (i.e., taxiway or runway entrances)

13. Decision Variables • Time epoch of aircraft i reaching intersection u , not continuous 4-D trajectories • Implied and implicit are sequence of take-off at a runway and sequence of reaching an intersection • Adjacency binary variable =1 if and only aircraft j follows immediately aircraft i at intersection u • needed to formulate safety-separation requirements of aircraft on the ground and in the air: • Other derived variables, e.g., binary predecessor variables

14. The Objective Function • To minimize the total, across all aircraft within scope, weighted sum of • Waiting time at the runway entrance: lowest weight, to encourage use of the small queue and to avoid spoilage of take-off slots • Waiting time at the gate: medium weight, to implement gate-hold when no room for waiting at the runway entrance • Time spent on the taxiway: highest weight, to discourage crowding up the taxiway

15. The Objective Function: Math Details

16. Constraint Categories • Consistency between times reaching intersections and flight adjacency for each intersection • Smooth Travel: min and max speed • Modeling the slots of a small queue as nodes with connecting links of 0 length • Safety separation, on the ground and in the air • Fairness • Other movement-logic and operational constraints

17. Constraints • C1: An arriving aircraft starts taxiing off the runway exit immediately after landing, • C2: The time at which a departing aircraft i reaches the first node of its route is no earlier than its time of readiness for pushback. • C3: To satisfy the requirement imposed by air traffic control, e.g., the National Ground Delay Program dictating a time window for departure of a flight in order to cope with congestion at another airport or in the airspace

18. Constraints: Math Details

19. Constraints (Cont’d) • C4: To ensure smooth travel, we require that the speed of an aircraft be within a given range. • C5: Definition of Immediate Predecessors: • C6: Definition of Predecessors: • C7: In terms of and , the following constraint prevents overtaking: • C8: The following constraint prevents head-on collision of two aircraft in a link (u,v): • C9: Aircraft must be separated for safety.

20. Constraints: Math Details

21. Constraints (Cont’d) • C10: The small queue at a runway has a limited capacity, and the capacity can be modeled as a sequence of virtual links that have zero length. • C11: We impose the following constraint to ensure that the release time for departing aircraft i is no sooner than when it reaches the runway entrance, • C12: Departing aircraft must be safely separated in the air.

22. Constraints: Math Details

23. Constraints (Cont’d) • C13: If an aircraft is released for take-off at a particular time at the runway entrance, i.e., the last artificial node (or queueing slot) of the assigned runway, its immediate follower cannot reach the runway entrance any earlier. • C14: To ensure that the time at which a departing aircraft i reaches queueing slot k+1 is not earlier the time at which it reaches queueing slot k, • C15: Finally, we impose the following fairness constraint • C16: Binary and non-negativity constraints:

24. Constraints: Math Details

25. Implementation • Dallas Fort-Worth International Airport (DFW) • One quarter of DFW only • One departure runway and one arrival runway • Demand: 15 to 20 flights in 30 minutes • 1101 binary variables; 132 real-valued variables • 7538 integer functional constraints; 219 real ones • Some key parameters • Weight for wait at small queue: 0.5 • Weight for wait at gate: 0.75 • Weight for time spent on taxiway: 1 • Implemented with ILOG-CPLEX on a laptop

26. Numerical Results • Numerical Results: Very Promising • Aircraft take-off sequencing achieved: e.g., s-l-s-l-s-l re-sequenced to s-s-s-l-l-l • from same terminal area; on same route; to same runway • in sequence of time of departure-readiness (i.e., readiness for “pushback”) • as long as delays to aircraft do not exceed preset criteria • The small runway queue always filled first and then followed by gate-holding; smooth travel on taxiway • Computation time: optimality of mixed-integer linear program reached in minutes, although the optimal integer solution is found in a fraction of time

27. Numerical Results (Cont’d) • Sources of computational requirement: contention • Primary: schedule intensity • Secondary: route diversity • Computation time to reach optimality of program • 15 flights randomly over 30-minute span: one second or less • 15 flights clustered over 6-minute span: 30 seconds • 15 flights clustered over 3-minute span: 350 seconds • However, 99% optimality reached in 10% time. • Taxiing only, e.g., set to 0.01, requiring only 3 seconds for all cases

28. Conclusion • Promising decision-support for efficient, fair and safe airport surface operations • Future work, for next two years and beyond • Reordering • Runway crossings, but perimeter taxiway just implemented for one quadrant of DFW and to become a new standard, for safety, etc. • Deicing, but new technology for special liquid spray being tested to avoid the complexity • Larger network, e.g., full DFW; higher demand • Full-scale implementation, subject to NASA decision