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

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 2

3

Flight-DeckAutomation

ControlTower

DatalinkedClearances

Tower Automation

3/18/2008

3

Dallas Fort-Worth International Airport

4

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

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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.

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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 Workload7

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

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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 9

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 10

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

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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)

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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

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iutijux

iut

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

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The Objective Function: Math Details

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Min

arrdep ici

ii

AiAi

riqqiuiu

ARTAXItttWttDRPUSHtW iiuiuiuig iik

iik,1

iik1

)()()-(

(0)

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

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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

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Constraints: Math Details

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iARTAXIi1iu

t arrAi (1)

iDRPUSHi1iu

t depAi (2)

irii GDPLtGDPE , dep

GDPAi (3)

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.

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Constraints: Math Details

20

,maxmin

1ij

ij

ij

ij

ij iliuiuiliu

TttTt

ikjAi ,...,1, (4)

10

uAi

ijux 0, uAjNu (5.1)

10

uAj

ijux 0, uAiNu (5.2)

Mxtt ijuiuju )1( }{\,, iAjAiNu uu (5.3)

Mxtt ojujuiu )1( }{\,, jAiAjNu uu (5.4)

Mxtt ioujuiu )1( }{\,, iAjAiNu uu (5.5)

ijuiju xy }{\,, 00 iAjAiNu uu (6.1)

ojujiu xy }{\,, jAiAjNu uu (6.2)

1 ijuoju yx }{\,, jAiAjNu uu (6.3)

ioujiu xy }{\,, iAjAiNu uu (6.4)

1 ijuiou yx }{\,, iAjAiNu uu (6.5)

1 kiuijukju yxy },{\},{\,, jiAkiAjAiNu uuu (6.6)

,0 ijviju yy ji RRvuijAjAi ),(,,, (7)

0 ijviju yy ji RuvRvuitsvuijAjAi ),(&),()(..),(,,, (8)

MyttvuD

Dtt ijuiuiv

sepiuju )1()(

),( , }{\,, iAjAiNu uu (9)

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.

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Constraints: Math Details

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Mxttrrkrk ijqiqjq )1(

01

,

1,...,1,0,)()(..,,, rDepDep ckrjitsijAjAi (10)

rrcrrc iqriq tt , )(; irAi Dep (11)

MxSttirrcrrc ijqij

riq

rjq )1()(

0 , rjitsijAjAi DepDep )()(..,,, (12)

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:

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Constraints: Math Details

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Mxttrrrcrrc ijq

riqjq )1(

0 rjitsijAjAi DepDep )()(..,,, (13)

rkkr iqiq tt 1,

1,...,1,0),(, rDep ckirAi (14)

dep

kkuAk

iiu A

DRPUSHtPDRPUSHt

k

dep

i

)()1(

1

1

, DepAi (15)

Rtiu qii

Dep RRuAi , and iArr RuAi , (16.1)

Rt ri DepAi (16.2)

}1,0{, ijuiju yx ijAjAiNu uu ,,, 00 (16.3)

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

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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

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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 cases27

qW

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

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