School of Computer Science
Competing for the Edelman
Prize: Enhanced Runway
Sequencing and Pushback
Time Allocation at Heathrow
Jason Atkin and Edmund Burke
LANCS Advisory Board 2011
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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
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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
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Take-off Sequencing
• Sequence-dependent separations
• Wake vortex
TOT
– Lighter aircraft following heavier aircraft is bad
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• Routes and speed
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– Maintain in-flight separation
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Wt.
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Dir.
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Problem 1 : Sequencing at the
holding area
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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
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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
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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?
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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
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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?
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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
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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
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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)
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The Holding Point
Example good routes: ADIN, CEGJN, BFHKL
Slower (but good) routes: ADIMN, BFHKLOP
Short-cuts, if necessary: ADI, CEGJI
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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
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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
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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
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Simulation (2)
Initialise time to start of dataset
Add all aircraft that have left their stands
Update prediction errors (uncertainty)
Solve the current problem
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
Uncertainty handler
Tabu Search
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
Heuristic allocation of paths
Heuristic feasibility check
Take-off time prediction
Objective function evaluation
Outputs of search:
Desired take-off order
* Allocated traversal paths to
aircraft
* New predicted positions of
aircraft
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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
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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
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Example Results
Comparison of manual, first come first served and
automatically generated take-off orders.
Delay (s)
Manual, real times
CTOTs
missed
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Manual, predicted times
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130313
First come first served
94
408249
Tabu Search, Deterministic
3.7
83339
Tabu Search, Uncertain
4.1
91634
117894
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Results: Delay
Key Results:
Delay decreased, so it is worth considering.
Holding area structure affects schedule delay.
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CTOT compliance
Key Result: CTOT compliance is also good!
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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
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Problem 2 : Sequencing at the
stands, to assign pushback times
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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
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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
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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
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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
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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
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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
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Cul-de-sac separations
– Minimum separations between cul-de-sac times
– Have to consider cul-de-sac time
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Similar objectives to previous problem
– non-linear delay cost (power 1.5 or 2)
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Avoids excessive penalty for any one aircraft
Cannot rely upon holding area structure to help
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Take-off Sequencing
Solution 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-desac time, as aircraft is added
• Two (linked) sequencing problems
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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
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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
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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
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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
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Any questions?
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