Jason Atkin and Edmund Burke

1. Competing for the Edelman Prize: Enhanced Runway Sequencing and Pushback Time Allocation at Heathrow Jason Atkin and Edmund Burke LANCS Advisory Board 2011

2. Overview • Heathrow airport • Take-off Sequencing • Problem 1: Sequencing at the runway • Sequencing constraints within the holding area at the end of the runway • Problem 2: Allocating pushback times • Sequencing while at the stands • Consideration of the cul-de-sac problem • Summary

3. London Heathrow Airport Terminal 5 is HERE Problem 1: at the holding area (in green) Problem 2: at the stands (around the white terminals) Red: taxiways Two runways, shown in white

4. Take-off Sequencing • Sequence-dependent separations • Wake vortex • Lighter aircraft following heavier aircraft is bad • Routes and speed • Maintain in-flight separation

5. Problem 1 : Sequencing at the holding area

6. Departure Problem Objective: To find a take-off order that meets real world constraints while: • Breaking as few take-off timeslots (CTOTs) as possible • Reducing the delay suffered by aircraft • Controlling the workload of pilots and controllers • Being as ‘fair’ as possible

7. Departure Problem Real world constraints: • Must be achievable within the holding point • Must always maintain safe separations • Aircraft must be able to get to the runway on time • Aircraft preparation time

8. Runway Controller • Must solve this problem in real-time • Identify good take-off orders • Ensure the order can be achieved • Must talk to pilots and control local airspace • Has imperfect knowledge of the situation • Knowledge of all aircraft in the holding point • Limited knowledge of what will arrive next • Could a Decision Support System help? • Is any improvement possible? • Could a DSS solve the problem quickly enough?

9. Decision Support System • Aim: • Suggest an achievable, sensible schedule with low delay and low workload that misses as few CTOTs as possible • CTOT is a 15 minute take-off time-slot • Respond quickly to changing situations • Inputs: • Positions of any aircraft in the holding area • Predictions for aircraft on taxi-ways • Knowledge of currently planned take-off order • Output: • Suggested take-off order

10. Solution Method • Can be considered to be working on two levels: • Investigate possible take-off orders • Evaluate the worth of a specific take-off order • Take-off order search: • Use meta-heuristic search • Seeking a good permutation of the aircraft to take-off • Take-off order evaluation: • Is the schedule achievable? • How good is the solution?

11. Tabu Search • Solution is a take-off order • Different types of moves are available: • Shift 1 to 5 aircraft earlier or later in the schedule • Swap the positions of 2 aircraft • Randomise the order of a group of 3 to 5 aircraft • Sample the neighbourhood – check 50 neighbours • Evaluate each schedule • What paths must aircraft follow? • Can the reordering be done? • Predict take-off times • Determine a schedule cost • Move to lowest cost, achievable, non-tabu schedule • Mark the reverse move as tabu for 10 moves A B C D E F G H I J

12. Schedule Evaluation • Given a potential schedule, evaluate its worth • Four stages: • Allocate paths through the holding area • Determine whether required overtaking is achievable • Predict take-off times • Must be achievable • Must be safe • Determine a cost for the schedule • CTOT slots missed • Total delay for aircraft • Reordering delay (unfairness)

13. The Holding Point Example good routes: ADIN, CEGJN, BFHKL Slower (but good) routes: ADIMN, BFHKLOP Short-cuts, if necessary: ADI, CEGJI

14. Take-off Time Prediction Assumes an aircraft will take off as early as it can. Various constraints upon earliest time: • All separations from earlier aircraft must be maintained • Start of CTOT slot (if there is one) must be respected • Must allow time to get to the runway: Estimated taxi time to holding point + traversal time of holding point (depending on path) (May be increased if it has to wait for another aircraft!) • Must allow preparation time for aircraft

15. Objective Function Given predicted take-off times, determine a total cost for the schedule. Weighted sum of : • Number of CTOT slots missed • Exceptionally high cost! • Increasing cost as amount of missed time increases • Non-linear, large misses are exceptionally penalised • Total delay for aircraft • Calculated as time from HP arrival to take-off • Reordering delay (unfairness) • Square of deviations from ‘first come first served’ Note: Path assignment and feasibility check covers the sensible and achievable objectives

16. Simulation (1) • This is a dynamic problem • Simulation is required to understand later effects of decisions made • Simulating using real, historic data • Details of aircraft • Weight class, speed group, departure route • Times of leaving stand and arriving at holding area • Predict arrival entrance based upon allocated stand • Can model uncertainty, as prediction errors • Abstract simulation of the taxiways • Modelled as an arrival time at the holding area

17. Simulation (2) Inputs, current problem to solve: Positions of aircraft in holding area Arrival times of aircraft on taxiways Previously allocated paths and take-off order Details of aircraft that have already taken-off Initialise time to start of dataset Add all aircraft that have left their stands Update prediction errors (uncertainty) Uncertainty handler Solve the current problem Tabu Search Heuristic allocation of paths Heuristic feasibility check Take-off time prediction Objective function evaluation Update data for proposed solution: Estimated traversal times/take-off times Current holding point positions Allocated traversal paths Outputs of search: Desired take-off order * Allocated traversal paths to aircraft * New predicted positions of aircraft Advance time, update states Remove old aircraft

18. Uncertainty • Modelled as estimation errors • When will an aircraft leave its stand? • Add aircraft to system as they leave stands • Preparation/ready time? (pre-flight checks) • Estimate based on weight class • Taxi time through the holding point? • Estimate based upon weight class and route • Taxi time to the holding point? • Estimate remaining taxi time

19. Uncertainty Effects • Ready time uncertainty • A safe (high) estimate has shown the best results • Rarely constraining due to (often large) taxi-time • Holding point traversal time/speed • A fairly large (safe) estimate works well • If underestimated, delays can be introduced • Holding point arrival time accuracy • By far, the element which most affects results! • Makes delay/CTOT compliance worse and/or increases the amount of late rescheduling • Estimation errors affect predicted arrival order too • Overestimation causes unnecessary delays • Results used a much greater error than would be expected in real life: In actuality, the DSS should do better

20. Example Results Comparison of manual, first come first served and automatically generated take-off orders.

21. Results: Delay Key Results: Delay decreased, so it is worth considering. Holding area structure affects schedule delay.

22. CTOT compliance Key Result: CTOT compliance is also good!

23. Key Results • Solution system can solve the problem fast enough (heuristic / meta-heuristic elements) • Simulation predicts system does as well as the controllers when only considering aircraft in holding point • Simulation predicts improvements in slot compliance and delay if taxiing aircraft are included, even with great uncertainty

24. Problem 2 : Sequencing at the stands, to assign pushback times

25. Aims • Ultimate aim: Reduce environmental impact of departures from London Heathrow • Previous research: Improve sequencing at the runway • Has limits to what is achievable • Delay will accumulate when stand release rate (aircraft ready rate) exceeds runway capacity • This research: Reduce engine running time by absorbing necessary delay at the stand • Part of Collaborative Decision Making at London Heathrow

26. Method • Stage 1: Predict a good take-off sequence, consider contention • Predict take-off times, determine consequent delay • Determine ideal pushback time from ideal maximum runway hold • Includes slack for uncertain timings / alternative sequences • Stage 2: Find consistent set of pushback times, close to ideal times • Consider contention around the stands • Use minimum and maximum runway hold values • A non-linear minimisation problem, for equity reasons • Predictive Runway sequencing is harder part

27. Sequencing at stands • Sequencing at holding area removes many uncertainties compared with at the stands • When will aircraft be ready to push back? • Input from Collaborative Decision Making system • Airlines provide the information • How much delay will occur in the cul-de-sac? • Model the contention in cul-de-sacs • How long will taxi operation take? • Expected to be reliably predictable • How long will runway queue be? • Dependent on take-off sequence - modelled

28. Cul-de-sac Contention A K B J C I D H E F G • Two types of contention: • Blocked from pushing back while another aircraft is pushing back • Blocked from leaving cul-de-sac until an aircraft nearer to the end does so

29. Earliest pushback time (from airline) Pushback time (Assume = TSAT) Cul-de-sac time Leave cul-de-sac Reach holding area (Holding area time) Take off Stand delay (contention) Pushback duration Taxi duration Holding area delay(queueing for runway) Departure system Contention at the cul-de-sac can delay the taxi operation, delaying arrival at the holding area and hence take-off

30. Take-off sequencing • Cul-de-sac delay can delay pushback • Thus delaying holding area arrival • And earliest take-off time • So can affect take-off sequences • Cul-de-sac separations • Minimum separations between cul-de-sac times • Have to consider cul-de-sac time • Similar objectives to previous problem • non-linear delay cost (power 1.5 or 2) • Avoids excessive penalty for any one aircraft • Cannot rely upon holding area structure to help

31. Take-off SequencingSolution Method Stage 1 • Branch and bound algorithm within rolling window (rolling from first to last) • Variable window size, multiple passes • Optimally sequence aircraft within window • Fix sequence/times before window • Ignore aircraft after window • Predict take-off time as aircraft added • Assigns a feasible (not optimal) cul-de-sac time, as aircraft is added • Two (linked) sequencing problems A B C D E F G H I J

32. Stage 2 - Problem • Decompose by contention • Sub-problem sizes are up to 9 aircraft • Small enough to solve optimally • For each aircraft: • Know earliest cul-de-sac time (from earliest pushback time) • Know latest cul-de-sac time (latest time which will allow predicted take-off time to be achieved) • Know ‘ideal’ cul-de-sac time – absorb all delay beyond ‘Ideal Runway Hold’ as stand hold • Minimise a cost for deviation from ideal • Non-linear (power 1.1) to favour equity • Bigger cost for late pushback than early pushback

33. Stage 2 - Solution • Branch-and-bound solution method • Add aircraft to a potential cul-de-sac sequence one at a time, in increasing cul-de-sac time order • Reduce window sizes by contention • Get bounds on the cost for window sizes • Prune if cost too great • Optimally assign times • Issued times have to lie on minute boundaries • Very few possibilities/combinations • Optimal solutions to decomposed sub-problems in milliseconds

34. Comparative results • Both systems involve take-off sequencing • Experiments were performed using the same data => can compare the results • Sequencing at the runway holding area • vs at the stands • vs the manual results • Consider: • Overall delay – direct comparison, assuming correct sequence prediction • Proportion of delay absorbed as stand hold

36. Results Summary • Two systems give similar results • Can schedule as well at the stands as at the runway • Planning horizon at holding area can help (to a certain degree) • Window size at stands is important • TSAT allocation system allows significant further delay to be absorbed as stand hold

37. Any questions?