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**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

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**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

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**Datalinked Clearances Control Tower Flight-Deck Automation**

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

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**Dallas Fort-Worth International Airport**

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**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 Workload

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**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

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**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

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**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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**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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**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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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**

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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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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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**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 cases

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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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