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7/30/2019 A Comparison of Aircraft Trajectory-based and Aggregate Queue-based Control of Airport Taxi Processes

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A comparison of aircraft trajectory-based and aggregatequeue-based control of airport taxi processes

Citation Hanbong Lee, I. Simaiakis, and H. Balakrishnan. A comparisonof aircraft trajectory-based and aggregate queue-based control ofairport taxi processes. Digital Avionics Systems Conference(DASC), 2010 IEEE/AIAA 29th. 2010. 1.B.3-1-1.B.3-15.Copyright 2010, IEEE

As Published http://dx.doi.org/10.1109/DASC.2010.5655526

Publisher Institute of Electrical and Electronics Engineers / American

Institute of Aeronautics and Astronautics / IEEE Aerospace andElectronic Systems Society

Version Final published version

Accessed Wed Mar 20 10:30:57 EDT 2013

Citable Link http://hdl.handle.net/1721.1/65943

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A COMPARISON OF AIRCRAFT TRAJECTORY-BASED AND AGGREGATE

QUEUE-BASED CONTROL OF AIRPORT TAXI PROCESSES

Hanbong Lee, Ioannis Simaiakis, and Hamsa Balakrishnan, Massachusetts Institute of Technology,

Cambridge, MA

AbstractThere is significant potential to decrease fuel

burn, emissions, and delays of aircraft at airports byoptimizing surface operations. A simple surfacetraffic optimization approach is to hold aircraft backat the gates based on aggregate information onsurface queues. Depending on the level of surfacesurveillance and onboard equipage, it may also bepossible to use a more complex approach, namely, tosimultaneously optimize the surface trajectories of alltaxiing aircraft. Using data from the DetroitMetropolitan Wayne County airport (DTW), this

paper compares the benefits of the two approaches,and finds that at a relatively uncongested airport suchas DTW, the aggregate queue-based approach onlyyields modest improvements in taxi-out time, whilethe trajectory-based approach yields a nearly 23%decrease in average taxi-out time (achieving theaverage unimpeded taxi-out time).

Introduction

Aircraft taxiing on the surface contributesignificantly to taxi delays, fuel burn and emissions at

busy airports. A promising approach to makingairports more efficient is to optimize the taxiwayoperations with the objective of minimizing the taxitimes, and thereby the associated fuel burn andemissions. Departing flights are held back at theirgates during congested time periods, therebyreducing taxi times without impacting the airportthroughput or the average flight delays. This tacticalscheduling method is called gate-holding.

In this paper, we investigate two differentapproaches for implementing the gate-holdingstrategy. The first method manages the traffic flow in

an aggregate manner by keeping track of thedeparting aircraft on the ground or the demand rate atthe runways. The second method optimizes thedeparting traffic taxi times on a flight-by-flight basisusing a detailed node-link model of the airport and aninteger programming-based optimization to decidethe optimal dispatching times. The two methods

differ in their modeling fidelity, and also in the costand complexity of preparation and implementation.They also differ in the design philosophy as theindividual aircraft-based approach assumes moreequipage and control authority than the aggregateapproach. However, both of them are implemented astactical tools aiming at mitigating the impact ofcongestion, and not as strategic scheduling tools.

The remainder of this paper is organized asfollowing. First, we describe an aggregate queue-based control approach. Then, we describe anindividual aircraft trajectory-based control approach,

which uses integer programming. The benefits of theindividual aircraft-based (integer programming) andthe aggregate queue-based approaches are evaluatedand compared, in order to assess the benefits ofautomating taxi processes, and of increasing the levelof control authority by establishing required times ofarrivals at multiple intersections on the airportsurface. The two methods are evaluated through asimulation study using a day of schedule data fromDetroit Metropolitan Wayne County airport (DTW).

Background

There have been several prior efforts focused onimproving the efficiency of airport surfaceoperations, and reducing taxi times and emissions. Aspart of the development of the Departure Planner,there was a comprehensive discussion about the airtraffic flow restrictions in the terminal area andpotential control points for surface operations [1].Based on the discussion, runways were considered asthe limiting factor for airport capacity [2], and taxi-out times were estimated using a queuing model[3, 4]. Such aggregate queue-based approaches canbe considered Eulerian models of surface operations.Simaiakis and Balakrishnan developed a predictivequeuing model to estimate the travel times of aircraftfrom gates to the departure runways by including theeffect of taxiway interactions. They also used thismodel to evaluate the potential reduction in taxitimes, fuel burn and emissions from queuemanagement strategies [5].


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There have also been several prior approaches tooptimizing surface operations for surface trajectory-based operations. These approaches are typicallyaimed at determining the optimal times for eachaircraft to reach significant control points along itstaxi route, while considering the movements of theother flights on the ground. Such individual aircraft-

based (orLagrangian) approaches include DynamicProgramming-based taxi route optimization usingDijkstra's algorithm [6], Time-Dependent ShortestPath techniques [7], and Mixed Integer LinearProgramming (MILP) formulations ([8-13]).

The integer programming model used in this paperfor the trajectory-based optimization of taxiwayoperations proposed in this paper is derived fromprior work by the authors, using data from DTWairport [13].

Aggregate Queue-Based ApproachThis section builds on and extends earlier workon queuing modeling of the airport departure process[5], by considering the case of airports for which therunways are best modeled as independent servers.The taxi-out time of an aircraft is represented as thesum of three components, namely, the unimpededtaxi-out time, the time spent in the departure queue,and the congestion delay due to ramp and taxiwayinteractions. This representation attempts to modelthe main characteristics of the departure process,namely: Aircraft pushback from their gates according

to the pushback schedule, enter the ramp and then thetaxiway system, and taxi to the departure queue,which is formed at the threshold of the departurerunway(s). As they taxi from the gate to the runway,aircraft interact with each other. For example, aircraftqueue to gain access to a confined part of the ramp, tocross an active runway, to enter a taxiway segment inwhich another aircraft is taxiing, or they getredirected through longer routes to avoid congestedareas. We cumulatively denote these spatiallydistributed queues and delays, which occur whileaircraft traverse the airport surface from their gates

towards the departure queue, as ramp and taxiwayinteractions. After the aircraft reach the departurequeue, they line up to await takeoff. We model thedeparture process as a server, with the departurerunways serving the departing aircraft in a First-Come-First-Serve (FCFS) manner. A schematic ofthe departure process is depicted in Figure 1.

Figure 1. Conceptual Queuing Model of the

Departure ProcessMathematically, the taxi-out time () can be very

simply represented as the sum of three terms:

= unimped + taxiway + dep.queue

In prior work [5,14], we showed how the threeterms comprising the taxi-out time, namely theunimpeded taxi-out time (unimped), the taxiway-relateddelay (taxiway), and the queuing at the runways(dep.queue) could be determined for Boston LoganInternational Airport (BOS) and Newark LibertyInternational Airport (EWR). While we showed thatthe runway service process at both BOS and EWRcould be modeled as a single-server process, DTWtypically uses two runways for departures 21R (or3L), and 22L (or 4R) under VMC. They areoperationally independent; and have distinctdeparture queues. The runway demand tends to beunbalanced, and the two runways tend to serveaircraft of different weight categories. For thesereasons, the fidelity of the model is enhanced bymodeling them as two separate servers and not as asingle one with capacity the sum of the capacities oftwo single runways, as shown in Figure 2.

Figure 2. Queuing Model of DTW Departure

Process.

Model Inputs and Outputs

We define the following quantities:

P(t): the number of aircraft pushing backduring time period t, which is obtainedfrom the pushback schedule.


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N(t): the number of departing aircraft onthe surface at the beginning of period t.

N(t) reflects the congestion from departingaircraft on the ground.

N1(t): the number of departing aircraft onthe surface at the beginning of period tdeparting from runway 21R.N1(t) reflectsthe departure demand of runway 21R.

N2(t): the number of departing aircraft onthe surface at the beginning of period tdeparting from runway 22L. N2(t) reflectsthe departure demand of runway 22L.

Q1(t), Q2(t): the number of aircraft waitingin the departure queue of runway 21R and22L, respectively, at the beginning ofperiod t. The departure queue is defined asthe queue, which is formed at the thresholdof the departure runway, where the aircraft

queue for takeoff.R(t): the number of departing aircraft

taxiing in the ramp and the taxiways at thebeginning of period t (i.e., the number ofdepartures on the surface that have notreached the departure queues).

R1(t), R2(t): the number of departingaircraft taxiing in the ramp and thetaxiways at the beginning of period twithdestination runway 21R and 22L,respectively.

C1(t), C2(t): the (departure) capacity ofdeparture runway 21R and 22Lrespectively, in period t.

T(t): the total number of takeoffs duringperiod t.

T1(t), T2(t): the number of takeoffs duringperiod t from runway 21R and 22L,respectively.

Using the above notation, the following relationsare satisfied:

N(t) = Q(t) + R(t)

N(t) = N(t1) + P(t1) T(t1)N(t) = N1(t) + N2(t)

R(t) = R1(t) + R2(t)

Ni(t) = Qi(t) + Ri(t)

Ti(t) = min(Ci(t),Qi(t)),i 1,2{ }

Unimpeded Taxi Time Estimation

The unimpeded taxi-out time is defined as thetaxi-out time under optimal operating conditions,when neither congestion, weather, nor other factorsdelay the aircraft during its movement from gate totakeoff [15]. In other words the unimpeded taxi timeconsists of the free-flow travel time of the aircraft

from its gate until its takeoff roll, in addition to otherevents necessary for a departure, such as towing fromthe gate, engine-start, communications with the ATC,etc., under optimal operating conditions. Theunimpeded taxi time therefore depends primarily onthe start and the end points of each aircrafts taxiroute, but also on the airline (due to differences inprocedures, etc.) It can also depend on the stuffing ofthe ATC, the pilot and the aircraft. In order toaccount for the most significant factors impacting theunimpeded taxi time, the unimpeded taxi time isusually calculated as a function of:

The airline ([4], [5] and [15]) whichreflects the starting point (gate location) ofeach aircraft at most airports in the US,since most major airlines own/lease agroup of gates at an airport.

The runway configuration ([4], [5])reflects differences between the locationand the number of the departure runways.

The weather conditions ([4], [5]), sincevisual vs. instrumental weather conditionscan significantly impact the speed of the

flow of aircraft through the airport.

In the case of DTW, we have to modify the setof explanatory variables, since the airline informationdoes not entirely capture the gate location (Delta/Northwest operates out of all gates of McNamaraterminal, which is one mile long). We therefore usethe gate as a surrogate for the start point of each taxiroute. Gates are separated in 17 groups of 3-20 gates,depending on their traffic density, location andairline, and unimpeded taxi times are calculated foreach gate group. In order to represent the end point ofthe taxi route of an aircraft, we use the runwayassignment information. For runway configurationscomprising more than one runway for departures, wecalculate two unimpeded taxi times for each gategroup: one for each departure runway. In this paper,we focus on the most frequently used runwayconfiguration in 2007 (22R, 27L | 21R, 22L), whichhas two departure runways (22L, 21R). We estimate


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two unimpeded taxi times for each gate group,estimating 34 unimpeded taxi times for this runwayconfiguration under VMC.

For each aircraft in the set (gate group, runway),the taxi-out time is represented as a function of thetakeoff queue of the particular runway, where thetakeoff queue is defined as the number of aircrafttaking off from the same runway while the flight istaxiing. The unimpeded taxi time is the estimatedvalue of this function when the takeoff queue is zero,that is, when there are no other aircraft taking offfrom the same runway.

Runway Service Process ModelOf central importance for queuing models of the

departure process is a model of the runway serviceprocess, since the runway is the main bottleneck ofthe departure process ([2]). In prior work, we

demonstrated the use of two runway models for theprediction of taxi-out times ([5], [14]). These modelsaimed at deriving the statistical characteristics of therunway departure process from operational data,through the observation of runway performanceunder heavy loading.

In this work, we take a different approach and weuse a runway service model based on the aircraft typeseparation requirements, as listed in Table 1. Themain reason for this modeling choice is that the airportof DTW is very rarely heavily congested [16] and thismakes it difficult to use the techniques of [5], [14] to

infer the runway service process characteristics.

Table 1. Minimum Time Separations (in Seconds)

Between Departures on the Same Runway

Leading

Aircraft

Trailing Aircraft

Heavy B757 Large Small

Heavy 120 120 120 120

B757 90 60 90 90

Large 90 60 60 60

Small 60 60 60 60

Figure 3 shows the 15-minute throughput ofrunway 21R as a function of the number of taxiing

departures assigned to depart from runway 21R (i.e.,N1(t)). We observe that there is no area of thethroughput saturation, which would allow us toobserve the capacity of the runway. In contrast, thethroughput of runway 22L seems to saturate ataround 13 aircraft/15 minutes (Figure 4).

We can use the separation requirements listed inTable 1 the fleet mix of the departures using runways21R and 22L, and the method outlined in [17] 1 tocalculate the capacity of the two runways. This wouldresult in the capacities listed in Table 2, which areconsistent with Figure 3 and Figure 4: Runway 22L iscalculated to have the same capacity as the one that

can be inferred from Figure 3. The calculatedcapacity of runway 21R (14 AC/ 15 min) standsslightly higher from the red line. It is plausible that isclose to the actual capacity of runway 21R, but is notachieved under the current demand levels. Therefore,the separation requirements of Table 1 appear toadequately model the DTW runway service process.

Figure 3. Departure Throughput of Runway 21R

(in Takeoffs/15 Min) as a Function of Departure

Demand

Figure 4. Departure Throughput of Runway 22L

(in Takeoffs/15 Min) as a Function of Departure

Demand

1 The calculation routine is applied assuming zero buffer time anddeparture-only scenarios.


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Table 2. Expected Capacity from Fleet Mix and

Separation Requirements

Runway Capacity (departures/ 15 min)

21 R 14

22 L 13

Taxiway Delay Model

The last component of the airport modeldepicted in Figure 2 represents ramp and taxiwayinteractions. For modeling this delay, we follow thesame approach as in [5]. The delay incurred becauseof the aircraft interacting on the ramp and taxiways,taxiway, is proportional to the number of aircraft in theramp and taxiway area,R(t).

taxiway = R(t)

The parameter is empirically estimated fromthe available data, validated and tested as describedin [5]. Its value is estimated to be 0.265.

Departure Queue-Based Control Protocol

The departure queue-based control protocol is anextension of the idea of N-Control, which wasdescribed in [5]. It is based on controlling the demandof every runway,Ni(t), at any time, t, so that it neverexceeds the number (denotedNi

*) that is necessary tosustain the capacity of the runway. The pushbacktimes are modified so as to achieve, and not exceed,

Ni* departures on the surface bound for runway i. If

the number of aircraft requesting to push back wouldincrease Ni(t) further, those aircraft are held at theirgate and form a virtual departure queue, Vi.Therefore, at each time tand for each runway i:

IfNi(t) Ni*,o If the virtual departure queue (set of

aircraft that have requested clearanceto pushback), Vi, is not empty, clearaircraft in the queue for pushback inFCFS order.

IfNi(t) > Ni*, for any aircraft that requestspushback,

o If there is another aircraft (arrival)waiting to use the gate, cleardeparture for pushback, in FCFSorder

o Else add the aircraft to the virtualdeparture queue.

In other words, whenNi(t) >Ni*, we regulate the

pushback time of an aircraft unless it may delay anarrival that is waiting to use the gate. In order tomaintain fairness, aircraft that request pushbackclearance and are not cleared immediately form aFCFS-virtual departure queue. When the congestioneases and Ni(t)Ni

*, we allow the aircraft in thevirtual departure queue to pushback in the order thatthey requested pushback clearance. This approachenables reductions in fuel burn and emissions,without decreasing departure throughput.

We note that the parameterNi* may differ for

each runway, it depends on the throughput of therunway and the average delay that aircraft incur ontheir way to the runway i. If, for example, aircraftthat are bound for one runway take much longer to

reach the runway threshold than the ones using theother runway, the demand (Ni(t)) for the former couldreach high numbers without necessarily implyingcongestion. On the other hand, if the runwaythreshold is close to the gates, then a highNi(t) wouldimply a long departure queue. Analogously, there aretwo virtual departure queues, one for each departurerunway. Each of them gets populated with aircraftheld at the gate when the demand for the runway theyare heading toward exceedsNi

*.

A more integrated approach would be tocoordinate the utilization of the runways to maximize

the efficiency of the departure runway process.However, runway assignments are a complicatedfunction of the aircrafts route, airspace restrictions,airline preferences, aircraft type, etc., and are beyondthe scope of this paper.

The proposed queue-based control approachreflects a tactical response to the accumulation ofdepartures on the surface, and requires minimalmodifications to current procedures. In the nextsection, we investigate a more complex approach thatseeks to regulate the exact trajectory of each aircraft

on the surface, by simultaneously considering thetrajectories of all other flights.

Taxi Trajectory Optimization

In this section, we describe an IntegerProgramming formulation to control individualflights on the airport surface and determine the


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optimal surface trajectories for them. Details of theformulation can be found in [13].

The airport taxiway system is modeled as anetwork of links and nodes. In the node-link model,nodes represent significant control points on theairport surface, such as gate locations, runway entryand exit points, intersections of taxiways, and holdingspots for clearance. The model also includes linksthat connect adjacent nodes, representing taxiwaysegments between two points on the surface. Time isinitially discretized into 5 sec intervals [13]. A 5 sectime interval ensures that every intersection in thetaxi route is captured without missing any significantevents. Using the node-link model, the taxiwayoperations planning procedure can be formulated asan integer programming formulation.

Consider a set of arrivals, Fa, and a set ofdepartures,Fd. It is assumed that every aircraftfhas a

preferred taxi routePf, consisting of a sequence of thesegments P(f,i) for a node i on the route. The firstsegment of a departing aircraft's path begins at itsgate; the last segment terminates at the departure

runway. That is, for any departing flightdFf , P(f,

1) andP(f,Nf) represent a gate and a departure runwayqueue, respectively. In contrast, the taxi route for anarriving aircraft starts at the exit point of the arrivalrunway and ends at the assigned gate. Each flight alsohas a set of feasible times to arrive at link j,

],[ jfj

f

j

f TTT = , for all fPj .

Decision VariablesThe binary decision variable w

jf,t is used to

decide if flightfarrives at link (or node)jby time t. Itis defined as

wf,tj =

1, if flightfarrives at link (or node)j by time t;

0, otherwise.

Objective Function

The objective of taxiway operationsoptimization is to determine the pushback times ofdeparture flights and to control the taxiwaymovements of all flights on the surface such that the

total delay cost is minimized. A large penalty isimposed on the delay cost either if a departing flightmisses its scheduled runway departure time, or if theflight is cancelled for that time period.

Given a set of scheduled pushback times (theearliest times that flights can leave the gate) and

scheduled times of arrival at the departure runway (rf)for departing aircraft, the objective is to find surfacetrajectories and pushback times for all flights suchthat the total taxi-out cost is minimized, where cf

on isthe unit operating cost on the ground when theengines of flight f are running. In addition, a largepenalty (P1) is enforced when the aircraft does not

arrive at the runway before its scheduled departuretime. In addition, if a departing flight arrives at theassigned runway earlier than the scheduled takeofftime, this can cause congestion in the departurerunway queue, increasing congestion at the runwaythreshold. It is therefore desirable that aircraft arriveat the runway as close as possible to their scheduledtimes of runway arrival. The cost function fordepartures can be written as follows:

Q(Departures)= cfqueue max[rf t(wf,t

k wf,t1k ), 0

tTfk,k=P( f,Nf)

]

fFd

+c fon rf t(wf,t

k wf,t1k )

tTfk,k=P( f,2)

+P1 *max[ t(wf,tk wf,t1

k ) rf, 0]tTf

k,k=P( f,Nf )

In the function above, cfqueue is the cost per unit

time when flight f arrives at the departure runwayqueue earlier than its scheduled departure time. It isassumed that cf

queue = cfon.

The taxi cost function for arrivals is simpler. Thetaxi-in time is defined as the time between landing onthe runway and reaching the assigned gate. In thismodel, the cost per unit taxi time for arrivals is

assumed to be twice that of departures ( onf

on

f dacc 2= ),

reflecting a greater sense of urgency for arrivals. Thetotal cost for arrivals is expressed as

Q(Arrivals) = c fon { t(wf,t

k wf,t1k ) df

tTfk,k=P( f,Nf )

}fFa

where df represents the time when arriving flight fexits the runway after landing.

We also consider the case in which a flight iscancelled for that time interval, i.e., moved to thenext planning horizon. This concept is incorporatedin the problem formulation by adopting additionalvariablesxf and adding another term to the objectivefunction, as shown below.

=otherwise.0,

cancelled;isflightif1, fxf


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=ad FFf

fx

*Ptions)Q(Cancella 2

where P2 is a penalty when flight fis cancelled. Themagnitude of the penalty is determined by the totalcost generated by cancelling the flight for thatplanning period, and is much higher than the cost oftaxi delays.

The overall objective of the IP model is tominimize the total cost for departures, arrivals, andtemporarily cancelled flights subject to severaloperational constraints, as described below [12].

Operational ConstraintsFirst, we have to meet the flight schedules while

optimizing the taxiway operations. These includescheduled takeoff times for departures and landingtimes for arrivals. While the takeoff times ofdepartures are relaxed by applying a penalty in theobjective function, arrivals touch down at the

scheduled landing times and exit the runway asscheduled. Next, the arrivals should reach the gateswithin a reasonable taxi-in time range. On the otherhand, departing aircraft should leave the gate beforethe latest allowable time of gate-occupancy,considering the gate utilization of the next flight.Taxiing aircraft are constrained to move forward tothe next link along their routes within a reasonableamount of time in order to avoid gridlock situations.

Because of the tactical nature of the operations,the taxiway schedule is typically updated every 15 to

30 minutes using a rolling horizon. Therefore, after

the first time horizon of optimization, eachsubsequent time horizon needs to consider the flightsof which schedules were already optimized in theprevious time frame. We assume that the taxischedules of the flights planned in an earlier iteration(denoted frozen flights) are fixed in the currentoptimization. To ensure that each aircraft does not

conflict with others on the taxiways, the IP constrainsthe feasible trajectories of aircraft by taking intoaccount the trajectories of the frozen flights, byadding an additional parameter j

tgy , , defined as:

yg,tj =

1, if a frozen flightgtravels on linkj at time t;

0, otherwise.

One of the strategies to restrict overtaking flights(which is infeasible in reality) is to limit the linkcapacities to a single aircraft. Long links havingcapacities of greater than one aircraft are divided intoseveral pieces by dummy nodes. However, thischange increases the number of nodes and links in themodel, thereby increasing the number of variablesand constraints. Maximum and minimum taxi speedlimits are taken into account in the model in the formof the minimum and maximum travel times on eachlink. Additional constraints are introduced to preventhead-on collisions at intersection points [13].

Problem Formulation

Incorporating these objective terms andconstraints described above, the IP formulation forflight-by-flight taxiway operations optimization can

be expressed as follows.


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1.B.3-8

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1.B.3-9

1, 2007). On this date, there were 675 departures and661 arrivals, respectively. Overnight hours betweenmidnight and 5:45AM were excluded because mostflights during this period were cargo flights, andtraffic demand was low. 656 departures and 638arrivals between 5:45AM and midnight wereconsidered in the optimization. The average taxi-out

time (from BTS) was 18.4 minutes.

Simulation Environment for Trajectory-Based

Optimization

As mentioned above, the integer programmingapproach requires a node-link model that mimics theactual airport taxiway layout for the optimization.The node-link model (Figure 6) consists of 715 nodesthat represent significant control points on the airportsurface and 863 links that connect adjacent nodes, inaddition to 101 dummy nodes. The model contains158 gates utilized by 46 airlines, and parking areas

for general aviation and cargo flights.

Figure 6. Node-Link Model for DTW

Based on surface surveillance data from DTW,the maximum taxi speed is limited to 7 knots on theramp area and to 18 knots on taxiways. Whencrossing an active runway, a flight is constrained towait for at least one minute for clearance; in addition,if there is a flight arriving or departing on thatrunway, a taxiing aircraft waits for at least twominutes before crossing the runway. Taxi routes

between gates and runways on the surface are alsodefined based on surface movement observations andNOTAMs at DTW.

A departure flight can stay at its gate for a while,although it is ready to start taxiing. We assume thatthis gate-holding is allowed to be up to 25 minutes,

taking gate utilization into consideration. It is alsoassumed that the time needed to complete all theevents for preparing taxiing between brake releaseand actual movement with its own power is 5minutes, as evidenced by our observations at BOS.

The data set for the simulations includes flightcall signs, aircraft types, pushback times, takeofftimes, runways, and gates, which are used as inputs inthe integer programming based optimization. Thepushback times from BTS are used as the earliestpushback times for departing flights. The arrival timeat the departure runway is computed using the traveltime (travel) from the gate to the runway threshold, asderived from the queing model:

travel =unimped +taxiway

For departure runway operations, appropriateinter-departure times are enforced for safety,depending on the weight classes of the successivedepartures, while maintaining the first-come, first-served (FCFS) order of departing flights. Theminimum separation requirements to avoid the waketurbulence are given in Table 1. The takeoff times areadjusted from the runway arrival times of the aircraft,considering these separation rules. For arrivals, thelanding times from BTS are used to take theinteraction with departures on the surface intoaccount.

Simulation Environment for Queue-Based

ControlThe simulation environment for the aggregate

queuing control is much simpler, but consistent withthat of the trajectory-based optimization. The module,implemented in MATLAB, runs in discrete timeincrements of 10 seconds and processes all flights asdescribed previously. The pushback times from BTSare used as the earliest pushback times for departingflights. The pushback schedule is the same times asthe ones used for the trajectory-based optimization.

Simulation of Current Operations

The model of Figure 2 was built and calibratedfor the purposes of demonstrating the expectedbenefits from controlling the runways demand N1(t)and N2(t). Before we show the results of this queuemanagement technique, we compare the results ofsimulating the operations of August 1, 2007 as theytook place. The simulation results yield the same


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1.B.3-10

average taxi-out time (18.4 min) as the BTS data.Figure 7 and Figure 8 show the results of makingpredictions using the pushback schedule from August1, 2007, along with observed data for the twodeparture runways. The top subplot shows theobserved and predicted number of takeoffs in a 15-minute interval, and the bottom one shows the

average taxi-out times of the flights that depart in thecorresponding 15-minute interval.

Figure 7. Prediction of Departure Throughput

and Average Taxi-Out Times (in Min) for Runway

21R

Figure 8. Prediction of Departure Throughput

and Average Taxi-Out Times (in Min) for Runway

22L

We note that the model predictions match theobservations reasonably well. We also compute theroot mean square error (RMSE), the root mean squarepercentage error (RMSPE), the mean error (ME), andthe mean percentage error (MPE) between theobserved measurements and the average of the results(see Table 3).

Table 3. Evaluation of Model Predictions

RMSError

RMS% Error

MeanError

Mean% Error

21R Departures 1.63 0.55 1.09 0.309

22L Departures 1.72 0.65 1.21 0.371

21RTaxi-out times 6.03 0.30 3.58 0.184

22LTaxi-out times

4.58 0.26 3.17 0.178

Implementation of the Aggregate Queue-Based

Control

The model of departure operations developedso far allow us to estimate the potential benefits ofthe proposed queue-based control. We modify thesimulation so as to ensure that N1(t) and N2(t) stay

within N1*

andN2*

, provided there is gate availability.Critical to the results of the simulation is the choiceof the design parameters N1

*and N2*: If they are too

high, they will result in non-significant taxi-out timereductions. If they are too low they will implysignificant delays ([5]). Here,N1

*andN2* were chosen

after simulating the results of different choices andcombinations. First, we define:

dj : the additional delay because of gate-holding for flight j. It is calculated as thesum of taxi time and the gate hold time,

ghj, in the controlled case minus the taxi

time of flightj at the base case

j : the taxi time reduction for flightj. It iscalculated as the taxi time of flight j in thebase case minus the taxi time in thecontrolled case.

The decision criterion here was formulated as anoptimization problem:

min (dj j )j=1

M

s.t

dj 5,j Mghj 25,j M

The decision variables are N1*and N2

*. M is the

set of flights. The constraint dj 5 ensures that noflight will get an additional delay of more than 5minutes because of this control scheme. Analogously


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1.B.3-11

the constraintghj 25 ensures that no flight is held atthe gate for longer than 25 minutes, in line with theindividual trajectory-based optimization. Thedecision criteria are listed in Table 4.

Table 4. Queue Control Parameters.

Runway Ni*

21 R 15

22 L 17

Using the design parameters listed in Table 4 forN1

*andN2*, we use the surface model to simulate the

expected taxi-time reductions, delays and gateholding times resulting from the queue controlprotocol.

Results

In the simulation results, the taxi-out time of aflight is defined as the difference between thecontrolled pushback time at the gate and the actualwheels-off time on the departure runway. The gate-holding time is defined as the controlled pushbacktime obtained by the control method minus theearliest (scheduled) pushback time. The time intervalused for the simulations was August 1 2007, 5:45AMto midnight. We first report the results of the aircrafttrajectory-based optimization. Then, we report theresults of aggregate queue-based control andsubsequently, we compare the results of the two

methods.

Trajectory-Based Optimization

The proposed integer programming methodcomputes the optimal pushback times and therequired time of arrivals (RTAs) at significant controlpoints on the taxiways to minimize the taxi-out timesof the aircraft and meet the scheduled takeoff times.This optimization model also determines the gate

arrival times for arriving aircraft to minimize the taxi-in times of arrivals, although they are not comparedwith the aggregate queue approach, which does notco-optimize taxiing-in flights.

Benefit of Gate Holding StrategyThe simulation results show an average gate-

holding time of 4.1 min and an average taxi-out timeof 14.3 min. This result can be compared with thecurrent operations, where aircraft push back whenready: The average observed taxi-out time was 18.4min. By deploying trajectory-based optimization the

taxi-out time can be reduced by 23% on average.Figure 9 shows the average taxi-out times (on

the left y-axis) and the corresponding number offlights on the surface (on the right y-axis) during 15min time intervals for the cases of the currentoperations (light color bar) and the trajectory-basedoptimization simulation (dark color bar). In thegraph, we observe that the amount of taxi timesavings is large when the traffic density is high as ina peak period such as 1:30PM~2:15PM,3:14PM~3:45PM, 7PM~7:45PM, and 9PM~10PM.The gate holding strategy is more effective under

congestion, as expected.

Figure 9. Taxi-Out Times with/Without Gate Holding and the Number of Flights for Each Optimization


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1.B.3-12

Aggregate Queue-Based Control

The simulation results of the queue-basedcontrol show a much smaller gate-holding time and amuch smaller reduction in taxi-out time. In summary,the average taxi-out time gets reduced by 0.1 minute.The average gate-hold time is 0.15 minutes. Theaverage additional delay because of this gate holding

scheme is 0.04 minutes.

We observe the operational impact of the controlstrategy in Figures 10 and 11, which show thedemand of the two runways, N1(t) and N2(t), in thebaseline and the controlled case, as simulated. Wenote that for the time periods in whichN1(t) andN2(t)take values lower than the specified thresholds inTable 4, the base case and the controlled case areidentical. One such time period is 6 AM until 10 AM.Queue-based control is not applied, and the pilots arefree to push back and taxi as usually.

Benefit of Gate Holding StrategyWhen congestion on the ground builds up,

demand for the two runways builds up and eventuallyexceeds the specified thresholdNi

*. The times periodswhen this happens are 10 to 10.30 am, 2 to 2.15 pm,3.30 to 3.45 pm, 7.30 to 8pm and 9.15 pm to 9.45pm, as can be seen in Figures 10 and 11.

Figure 10. Runway 21R Queue Management

Figure 11. Runway 22L Queue Management

They are essentially all the high demand periods.During these time periods, the total number of flightsthat get held at their gates is 37. For these flights, theaverage gate hold time is 2.6 minutes. The additionaldelay for these flights is 1.5 minutes.

Flights incur additional delay for two reasons:

As taxi speeds and routes are notcontrolled, their time of arrival at therunway is not specified. Thus, they mayarrive at the runway after the runwayserver becomes available.

The aircraft that get held at their gate mayget overtaken by other aircraft. In this way,they get behind in the departure queue.

Comparison of the Two Approaches

The aggregate queue based approach attempts toavoid congestion and thus the long taxi times thatexcessive queuing would cause. On the other hand,the taxi trajectory optimization attempts to optimizeall flights with the objective of achieving free flow ofaircraft on the ground (unimpeded taxi times). Thetwo methods are fundamentally very different: Theyhave different objectives, which lead to differentresults. That was part of the reason that we built twodifferent models in order to evaluate them.

Consistency of the ModelsFor a meaningful results comparison, we need

the two models to be consistent in their assumptions.

This consistency is ensured in the following ways:

The runway server component is identicalin the two models.

The unimpeded taxi time results areconsistent with the derived speeds ofaircraft in the ramp and the taxiways. Thisensures that in both models, the free flowspeed is the same.

For both control strategies, the maximumgate holding time is fixed at 25 minutes.

The expected runway arrival time used inthe trajectory-based optimization wasderived using the travel time from gate torunway of the queuing model. This, incombination with the identical separationrequirements, ensures that both modelsaim at adhering to the same runwayschedule.


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1.B.3-13

For both simulations, we consider the 656departures between 5:45 AM and midnightof August 1, 2007. The earliest pushbacktimes of the flights are the actual pushbacktimes of this day.

Finally, arriving traffic on the ground isregarded as a fixed source of delay in theaggregate queue based control model. Incontrast, the taxi time of arriving traffic isan explicit objective in the integeroptimization model.

One important difference between theassumptions of two control methods is that thetrajectory-based optimization assumes knowledge ofthe pushback schedule in every fifteen-minuteinterval, and also assumes the ability to control RTAsat every node on the airport surface. This means thatthe aircraft must give exact ready-to-push times atthe beginning of the fifteen-minute interval that theyplan to pushback. This renders this method muchmore proactive, as the optimizer can optimize all theflights of the fifteen minute interval together. On theother hand, the queue based control method does notmake any assumption about the ready-to-push timeof a departure.

Overall ResultsWith the aircraft trajectory based approach, 585

flights, or 89% of all departures, are held back at thegates. The IP model tends to get the maximumbenefit of the gate-holding strategy, since it can

control the trajectory of each flight in detail (seeTable 5). The average gate holding time of flightsthat experience gate holding is 4.9 min, whereas theaverage gate holding time is 4.1 min. For theaggregate queue-based control, the total number offlights that get held at the gate is only 37. For theseflights, the gate average holding time is only 2.6minutes on average. The longest gate-holding time is8.2 minutes.

Table 5. Comparison of the Simulation Results

AircraftTrajectory

Optimization

QueueBased

Control

Avg. gate-holding time (min) 4.1 0.2

Avg. taxi-out time (min) 14.3 18.3

Avg. taxi-in time (min) 10.5 -

Avg. additional delay (min) 0 0.04

Number of flights held at the gate 585 37

Avg. gate-holding time of flightsheld (min)

4.9 2.6

The discrepancy between the results of the twostrategies stems from their different objectives: Thetaxi trajectory optimization brings taxi times down tothe unimpeded ones by coordinating all the trafficsimultaneously, and by controlling RTAs at all nodes,whereas the queue control simply reduces taxi timesby stopping the build-up of excessive queues. DTW

is though a relatively uncongested airport, thedemand for the runways rarely saturate, as it can beseen in Figure 3 and Figure 4, and therefore queue-based control has very little impact [18].Interestingly, if all departures taxied with theirunimpeded taxi times in the queue control model(=unimped), the average taxi out time would be 14.3minutes. This would be the lower bound of theaverage taxi-out time of this control strategy. It isworth noting (but not unexpected) that the taxitrajectory optimization achieves the lower bound ofthe queue based control: The airport is relatively

uncongested, so all taxiway conflicts are resolvedwithout aircraft incurring delays.

Congested PeriodsSince the aggregate queue based control strategy

is effective only during the congested periods, wealso compare the taxi-out times and gate hold timesfrom the two approaches during these periods. Wefocus on two time periods: 3:15~3:29 PM and9:15~9:29 PM, the two most congested periods of thesimulation date. During these 15 min periods, thenumber of flights that are scheduled to push back was24 and 25 flights respectively.

During both time intervals, the aircraft trajectorybased optimization holds the departures back at thegate, and releases them one by one so as to avoidunnecessary delays. In contrast, for the aggregatequeue-based approach, the control protocol isreactive rather than proactive. Most of the flightsrequesting push back at these intervals are released attheir requested pushback time. This results incongestion building up on the ground;N1(t) andN2(t)exceeding the control thresholds N1

* and N2*; and

flights getting held at their gate during the following

time periods, 3:30~3:44 PM and 9:30~9:44PM.During the 3:15~3:29 PM period, with aircraft

trajectory-based optimization, all the flights exceptfor one flight getting rerouted to a long taxi route areheld at their gates between 100 seconds and 10minutes. The average gate-holding time for theseflights is 5.7 min, and this is equal to the average taxi


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1.B.3-14

time reduction for them. With queue-based control,none of the flights get held back during the 3:15~3:29PM period and all push back at their requested time.However, 9 flights get held at their gate during the3:30~3:44PM for 3.9 minutes in average.

During the 9:15~9:29PM period, with aircrafttrajectory-based optimization, all flights are held attheir gates. The gate holding times range from 30seconds to 11 minutes. The average taxi-out timereduction for these flights is 6.3 min, which equalsthe average gate-holding time. This reduction is 2min larger than the average taxi time reduction of thewhole time interval. With queue based control, only 4flights get held back during the 9:15PM~9:29PMperiod for 1.3 minutes in average. However, 9 flightsget held at their gate during the 9:30PM~9:44PM for2.6 minutes in average.

Optimization without Taxi Conformance

We also consider an operational environment inwhich the pushback schedule is designed assumingthe ability to control surface trajectories, but wherethe aircraft do not have the equipment and therequirement to meet RTAs at nodes on the surface.One could argue that there may be still some benefitfrom such a scenario, since the optimization maypresent better a better schedule, even if the pilots donot fully adhere to its implementation.

In order to explore this scenario, we use thetaxiway-based optimized pushback schedule as theinput to the queuing model. The results of the

simulation show that the suggested gate-holds (onaverage 4.1 min) would achieve an average taxi-outtime reduction of only 0.4 min, but at the cost of anaverage additional delay of 4.17 min. Similar delayswould result from very aggressive queue control:ChoosingN1

*andN2* at 8 and 10 respectively, would

result in average additional delay of 4.17 min.However, the average gate-holding time (for suchaggressive queue control) would be 4.97 min, and theaverage taxi-out time reduction 0.85 min.

As already mentioned, taxiway-based

optimization achieves free flow taxi times. Thiscorresponds to having very few aircraft on theground, which are being routed to the runway atspeeds necessary to meet the runway schedule. Therest can wait at their gates. However, if the aircraft donot have to conform to the given taxi speeds, theywill end arriving at the runways at non-scheduledtimes and the runway will occasionally get starved.

The runways will be under-utilized and the aircraftwill end up getting delayed. On the other hand,implementing aggregate queue based control withappropriately chosenN1

*andN2* values will maintain

pressure on the runways.

Conclusions

Aggregate queue-based control is a simplestrategy that can be implemented with minormodifications of the current operational proceduresand very little automation equipment. It has beenshown that it can achieve significant emissionsreductions in congested airports. However, theexample of DTW shows that modest taxi timescannot be reduced with such aggregate reactive tools.

On the other hand, trajectory-based optimizationrequires significant computing infrastructure andautomation, and careful model preparation and data

processing, to successfully design, implement andoptimize a network model of an airport. Moresignificantly, it requires significant modifications ofcurrent procedures: in a potential implementation,ATC would require exact ready-to-push times frompilots at the beginning of each 15-minute interval. Inaddition, pilots would be required to adhere to taxispeeds and given arrival times at different controlpoints (taxi conformance), otherwise trajectory-basedoptimization (without the required actuation) couldhave adverse effects. The results from this work showthat for an uncongested airport the aircraft trajectory-

based optimization can achieve free flow of aircraft,thereby minimizing taxi-out times.

The next steps for this research would include acomparison of the two methods at a more congestedairport, and the modification of the queue-basedcontrol so as to account for near-future demand whenmaking decisions. This would allow us to comparesuch hybrid control strategies and generalize ourresults to other airports.

References

[1] Feron, Eric, R. John Hansman, Amedeo R. Odoni,Ruben B. Cots, Bertrand Delcaire, Xiaodan Feng,William D. Hall, Husni R. Idris, Alp Muharremoglu,and Nicolas Pujet, December 1997, The DeparturePlanner: A conceptual discussion, Technical report,Cambridge, MA, Massachusetts Institute ofTechnology.


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[2] Idris, Husni R., Bertrand Delcaire, IoannisAnagnostakis, William D. Hall, Nicolas Pujet, EricFeron, R. John Hansman, John-Paul Clarke, andAmedeo R. Odoni, August 1998, Identification offlow constraint and control points in departureoperations at airport systems, AIAA Guidance,Navigation, and Control Conference and Exhibit.

[3] Idris, Husni R., John-Paul Clarke, Rani Bhuva,and Laura Kang, September 2001, Queuing Modelfor Taxi-Out Time Estimation, ATC Quarterly.

[4] Pujet, Nicolas, Bertrand Delcaire, and Eric Feron,1999, Input-output modeling and control of thedeparture process of congested airports, Portland,OR, AIAA Guidance, Navigation, and ControlConference and Exhibit, pp. 1835-1852.

[5] Simaiakis, Ioannis, Hamsa Balakrishnan, August2009, Queuing Models of Airport DepartureProcesses for Emissions Reduction, AIAA Guidance,

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[6] Cheng, Victor H. L., August 2003, AirportSurface Operation Collaborative AutomationConcept, Austin, TX, Proceedings of the AIAAGuidance, Navigation, and Control.

[7] Trani, Antonio A., Hojong Baik, Julio Martinez,and Vineet Kamat, November 2000, A NewParadigm to Model Aircraft Operations at Airports:The Virginia Tech Airport SIMulation Model(VTASIM), FAA Headquarters Auditorium,NEXTOR Fourth Annual Research Symposium.

[8] Visser, H. G., P. C. Roling, 2003, Optimal AirportSurface Traffic Planning Using Mixed Integer LinearProgramming, AIAA Aviation Technology,Integration and Operations (ATIO) Conference.

[9] Smeltink, J. W., M. J. Soomer, P. R. de Waal, andR. D. van der Mei, January 2005, An OptimisationModel for Airport Taxi Scheduling, Lunteren, TheNetherlands, Thirtieth Conference on theMathematics of Operations Research.

[10] Rathinam, Sivakumar, Justin Montoya, andYoon C. Jung, September 16, 2008, An OptimizationModel for Reducing Aircraft Taxi Times at the Dallas

Fort Worth International Airport, Anchorage, AK,26th International Congress of the AeronauticalSciences.

[11] Gupta, Gautam, Waqar Malik, and Yoon C.Jung, September 2009, A Mixed Integer LinearProgram for Airport Departure Scheduling, HiltonHead, SC, AIAA Aviation Technology, Integration,and Operations (ATIO) Conference.

[12] Balakrishnan, Hamsa, Yoon C. Jung, August2007, A Framework for Coordinated SurfaceOperations Planning at Dallas-Fort WorthInternational Airport, AIAA Guidance, Navigation,and Control Conference.

[13] Lee, Hanbong, Hamsa Balakrishnan, September2010, Optimization of Airport Taxiway Operations atDetroit Metropolitan Airport (DTW), AIAA AviationTechnology, Integration and Operations (ATIO)Conference.

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[15] Simaiakis, Ioannis, Nikolas Pyrgiotis, September2010, An Analytical Queuing Model of AirportDeparture Processes for Taxi Out Time Prediction,AIAA Aviation Technology, Integration andOperations (ATIO) Conference.

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Transportation.[17] de Neufville, Richard, Amedeo Odoni, 2003,Airport Systems: Planning, Design and Management,McGraw-Hill.

[18] Simaiakis, Ioannis, Hamsa Balakrishnan, 2010,Impact of Congestion on Taxi times, Fuel Burn andEmissions at Major Airports, TransportationResearch Record.

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