School of Computer Science
1
Competing for the Edelman Prize: Enhanced Runway
Sequencing and Pushback Time Allocation at Heathrow
Jason Atkin and Edmund Burke
LANCS Advisory Board 2011
School of Computer Science
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
School of Computer Science
3
London Heathrow Airport
Problem 1: at the holding area (in green)Problem 2: at the stands (around the white terminals)
Red: taxiwaysTwo runways, shown in white
Terminal 5 is HERE
School of Computer Science
4
Take-off Sequencing• Sequence-dependent separations• Wake vortex
– Lighter aircraft following heavier aircraft is bad
• Routes and speed
– Maintain in-flight separation
TOT Wt. Dir.
1 M N
2 H S
3 H N
4
5 M S
6
7 M S
8 H N
9 H S
School of Computer Science
5
Problem 1 : Sequencing at the holding area
School of Computer ScienceDeparture 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
School of Computer Science
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
Departure Problem
School of Computer ScienceRunway 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?
School of Computer ScienceDecision 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
School of Computer ScienceSolution 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?
School of Computer ScienceTabu 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
School of Computer ScienceSchedule 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)
School of Computer ScienceThe Holding Point
Example good routes: ADIN, CEGJN, BFHKL
Slower (but good) routes: ADIMN, BFHKLOP
Short-cuts, if necessary: ADI, CEGJI
School of Computer ScienceTake-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
School of Computer ScienceObjective 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
School of Computer ScienceSimulation (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
School of Computer Science
Inputs, current problem to solve:Positions of aircraft in holding areaArrival times of aircraft on taxiwaysPreviously allocated paths and take-off orderDetails of aircraft that have already taken-off
Simulation (2)Initialise time to start of dataset
Add all aircraft that have left their stands
Update prediction errors (uncertainty)
Solve the current problem
Update data for proposed solution: Estimated traversal times/take-off times Current holding point positions Allocated traversal paths
Advance time, update states
Remove old aircraft
Uncertainty handler
Tabu SearchHeuristic allocation of pathsHeuristic feasibility checkTake-off time predictionObjective function evaluation
Outputs of search:Desired take-off order* Allocated traversal paths to aircraft* New predicted positions of aircraft
School of Computer ScienceUncertainty
• 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
School of Computer ScienceUncertainty 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
School of Computer ScienceExample Results
CTOTs missed
Delay (s)
Manual, real times 6 117894
Manual, predicted times 15 130313
First come first served 94 408249
Tabu Search, Deterministic
3.7 83339
Tabu Search, Uncertain 4.1 91634
Comparison of manual, first come first served and automatically generated take-off orders.
School of Computer Science
21
Results: Delay
Key Results: Delay decreased, so it is worth considering.
Holding area structure affects schedule delay.
School of Computer Science
22
CTOT compliance
Key Result: CTOT compliance is also good!
School of Computer ScienceKey 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
School of Computer Science
24
Problem 2 : Sequencing at the stands, to assign pushback times
School of Computer Science
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
School of Computer Science
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
School of Computer Science
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
School of Computer Science
28
Cul-de-sac Contention
• Two types of contention:
1. Blocked from pushing back while another aircraft is pushing back
2. Blocked from leaving cul-de-sac until an aircraft nearer to the end does so
A
B
C
D
K
J
I
H
E
F
G
School of Computer Science
29
Departure system
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)
Contention at the cul-de-sac can delay the taxi operation, delaying arrival at the holding area and hence take-off
School of Computer Science
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
School of Computer Science
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
School of Computer Science
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
School of Computer Science
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
School of Computer Science
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
School of Computer Science
35
School of Computer Science
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
School of Computer Science
37
Any questions?
Top Related