A Strategic and Tactical Tool for ATFM Planning … · A Strategic and Tactical Tool for ATFM Planning based on Statistics and Probability ... airport management. Tactical planning

4th USA/Europe Air Traffic Management R&D Seminar Santa Fe (USA), December 3rd-7th, 2001

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A Strategic and Tactical Tool for ATFM Planning basedon Statistics and Probability Theory

Final paper for ATM-2001

Colin Goodchild, Miguel A. Vilaplana and Stefano Elefante

ATM Research GroupDepartment of Aerospace Engineering

University of GlasgowGlasgow G12 8QQ. United Kingdom

[email protected]

ABSTRACT

This paper presents a novel approach based on statisticsand probability theory to improve Air Traffic FlowManagement (ATFM) efficiency. This tool allows airtraffic controllers to organize a more efficient air trafficflow pattern for strategic and tactical planning.

Firstly, a procedure to establish a strategic arrivalschedule is developed. An implicit feature of thisprobabilistic procedure is that it takes into account theuncertainty in the arrival and departure times at a givenairport. The methodology has been applied at GlasgowInternational Airport to design a strategic schedule thatreduces either the probability of conflict of the arrivals orthe length of the landing slots necessitated by flights. Thebenefits that are expected through the application of thismethodology are a reduction of airborne delays and/or anincrease of the airport capacity. Thus a safer and moreefficient system is achieved.

Finally, a tactical arrival schedule is presented. This toolis designed to allow air traffic controllers to organise anair traffic flow pattern using a ground holding strategy.During the daily planning of air traffic flow unpredictableevents such as adverse weather conditions and systemfailures occur, necessitating airborne and ground-holddelays. These delays are used by controllers as a means ofavoiding 4D-status conflicts. Of the two methods, groundhold delays are preferred because they are safer, lessexpensive and cause even less pollution. In this paper amethod of estimating the duration of a ground-hold for agiven flight is developed. The proposed method is novelin the use of a real time stochastic analysis. The method isdemonstrated using Glasgow International Airport. Theresults presented show how a ground hold policy at adeparture airport can increase capacity and minimiseconflicts at a destination airport.

1. INTRODUCTION

This paper focuses on improving Air Traffic FlowManagement (ATFM) efficiency using a statistical andprobabilistic approach. ATFM aims to match the demandsof aircraft operators to airports and airspace capacity.

Air Traffic Flow Management (ATFM) is [1]:

“ (…) the process that allocates traffic flows to scarcecapacity resources (e.g. it meters arrival at capacityconstrained airports) (…) Traffic flow managementservices are designed to meter traffic to taxed capacityresources, both to assure that unsafe levels of trafficcongestion do not develop and to distribute the associatedmovement delays equitably among system users.”

ATFM is a service whose objective is to enable thethroughput of the traffic flow to or through areas whileguaranteeing a high level of safety. ATFM has the task ofallocating resources and facilities of airports and groundstructures. Two different types of ATFM services aimingat organising the traffic flows through airports can bedistinguished:

Strategic Planning: This service commences sevenmonths before the day under consideration up to twenty-four hours. Schedules and flight plans are computed forthe flights due to operate in a given network of airports. Asolution that aims at minimising airport congestion whilemaximising safety and reducing costs is sought.

Tactical Planning: This service is provided during theday of the operations. Its goal is to indicate to air trafficcontrollers where delays and failures are observed owingto adverse weather conditions, political issues etc. in orderthat necessary changes to the arrival and departureschedule can be made.

At present [2], the organisations in charge of air trafficflow management are the Central Flow Management Unit


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(CFMU) in Europe and the Air Traffic Control SystemCenter (ATCSCC) in the USA. In the USA the absence ofnational boundaries means that the administration of thetraffic flow is more straightforward than in Europe.The CFMU is mainly involved with tactical planning inorder to manage and organise the air traffic situation foren-route purposes (ATFM). The CFMU is not directlyinvolved with planning a strategic schedule, as this issueis mainly a concern for airport management. Tacticalplanning is usually given two hours before departureaccording to the expected ATM congestion (both en-routeand at the arrival airport). It is then revised according tothe actual situation (e.g. adverse weather condition, ATCcentre overloaded). Flights are only updated in the CFMUsystems when they take-off or when they enter a countrythrough an AFTN message issued by ATC. Currently,further developments are taking place in the collection ofactual flight information. The intention is that this willthen be distributed to airports and ATC centres in order tooptimise ATFM at short notice.

As stated in [3], the problem of assigning to aircraft thenecessary ground hold time so that total delay cost isminimised will here after be referred to as the groundholding problem (GHP). Two different versions of GHPcan be distinguished according to the moment in whichthe decisions are taken: static and dynamic. In the firstcase, the ground and airborne holds are established onceat the beginning of the day. In the second case the amountof ground hold and airborne delay is assigned during thecourse of the day taking into account new informationavailable real time. The parameters involved in the GHPcan be modelled either as deterministic or as randomvariables giving respectively a deterministic or aprobabilistic version of GHP.

There has been much research concerning GHP, however[4] is the first author to have given a methodical and aregular description of the GHP problem. [5] proposed adynamic programming algorithm to solve the singleairport static probabilistic GHP once the probabilitydensity function (PDF) of the capacity of the airportinvolved is known. The first systematic attempt toexamine a network of airports is given by [6], where astatic deterministic multi airport GHP is analysed. In [7] amulti airport probabilistic formulation for the static anddynamic GHP is given. In this model different possiblescenarios of airport capacities are introduced giving aprobabilistic GHP.

This paper is novel as it presents and introduces a newapproach to ATFM at both the strategic and tacticalplanning that aims:• either to reduce the probability of conflict between

aircraft arriving at a given airport, which will decrease thelikelihood of airborne delay. Thus the benefits expected bythe implementation of this approach are a reduction of the

costs for the airlines, an improvement of the safety ofairports operations and even a reduce pollution.• or to reduce the length of the slots required by flights,

which will increase the airport capacity.

• or a combination of these two options.

The core of this new approach is to model arrival time ofaircraft as real random variables in order to solve:

• strategic planning.• tactical planning (single airport dynamic probabilistic

GHP).

Owing to unpredictable events, changes may be requiredto the planned schedule at very short notice. As shown,the daily schedule planning is called tactical planning.Presuming the availability of a data link support betweenaircraft and airport a tactical planning methodology, basedon a dynamic probabilistic GHP, is shown in this paper.The methodology proposes that the aircraft, throughout itsflight, relays its current position to the arrival airport. Thisdata will then be computed real-time by the system topropose a new tactical planning. Ground hold and airbornedelay will be then allocated and finally communicated toaircraft and airports.

2. MATHEMATICAL MODEL

2.1. Nomenclature

∆= is defined to beR set of real numbersT set of the points belonging to a time periodF set of flightsA departure airportB arrival airportP generic pointd(⋅,⋅) euclidean distanceΩΩ experimentζ outcome of the experiment

ast Scheduled Arrival Timedst Scheduled Departure Time

da Arrival Delayta Arrival Timett Travelling Timev Velocity

set in which the arrival delay is defined

set in which the arrival time is defined

set in which the departure time is defined

set in which the travelling time is defined

set in which the velocity is defined

For the definition and further details of airport capacity see

[8] and [9].


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2.2. Arrival Time as a Real Random Variable

According to [10], a random variable “… consists of anexperiment ΩΩ with a probability measure P[.] defined onsample space S and a function that assigns a real numberto each outcome in the sample space of the experimentΩΩ”.In this section the arrival time of an aircraft is defined as areal random variable:

⊆∈⊆

+=∆

a

a

aa

d

t

dt Ras

as tt

where :

ast

∆= Scheduled Arrival Time of a given flight

. This is a

deterministic variable having as domain the set of the realnumber R.

da ∆= Arrival Delay for a given flight. This is modelled as

a real random variable defined in the set . This choicehas been made due to the intrinsic unpredictabilityaffecting delays. For an aircraft operating a given flight,an arrival delay (positive or negative) can be observed. Toeach outcome ζ∈ of the experiment ΩΩ, a real number

da(ζ)∈R is assigned.

ta ∆= Arrival Time for a selected flight. This variable is

the sum of a deterministic and of a real random variable.The result gives a real random variable defined in the set

.

For clarity, all random variable will be written in boldfaceletters ta, da. All sets, in which random variable aredefined, will be typefaced with the following style ,

.

2.3. Building Probability Density Function (PDF)

Real random variables have been introduced to model theATFM issue. To build the Probability Density Functions(PDFs) of these random variables, real data provided bythe Civil Aviation Authority CAA are used. The dataprovide the real and the scheduled arrival times for everyflight landing in Glasgow International Airport between 1st

April 1998 and 30th of September 1998.

The experiment ΩΩ is defined in the following step:

ζ = difference between actual landing time and scheduledarrival time

Throughout this paper the word flight refers to a regular

scheduled service between the departure and arrivalairport.

The random variable da is defined by:

da(ζ) ∆= ζ

The PDF of da⊆ is computed as histogram of therelative frequency of occurrences. This histogram isconsidered equivalent to the PDF by applying the Law oflarge numbers [11]:

If the experiment ΩΩ is repeated n times and the event aoccurs na times, then, with a high degree of certainty, therelative frequency na/n of the occurrence of a is close top=Pr(a),

n

na a≅)Pr(

provided n sufficiently large.

Suppose this experiment ΩΩ is performed n times, at agiven outcome ζ of the experiment the real randomvariable da⊆ associates a value da(ζ)∈R. Inconclusion, the Probability Density Function (PDF) f(x)for a given x is computed as ratio between the number oftrials such as x≤ da(ζ)≤ x+∆x and the total number of trialsn.

n

xnxxf

)()(

∆≅∆

Provided n sufficiently large and ∆x sufficiently small.

2.4. Strategic planning

Let ( ) nR∈dsn

d,s2,

ds1 tt,t be the departure scheduled time of

a set of flights 1,2,…n∈F. Let an

a2

a1 ttt ,, ⊆ n be

the arrival times of F.The task is to compute the shifting times

( ) 1nR −− ∈n)1n(,23,12 TTT to satisfy the conditions

=>+

=>+=>+

−− n)n(n)n( 11

2323

1212

T Pr

T Pr

TPr

a1-n

an

a2

a3

a1

a2

tt

tt

tt

where T12, T23, … T(n-1)n∈Rn-1 are the required unknownsrepresenting the time to shift the random variable

an

a2 tt , ⊆

. The term TPr ijaj

ai tt >+ expresses

the probability one random variable is greater than theother one.

To compute the unknowns T12,T23,…T(n-1)n∈Rn-1, thisprobability is imposed by fixing the terms:

12,,

23,…

(n-1)n∈[0,1]n-1


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Denoting by zij=ait - a

jt , the following equivalence is

derived:

Pr aj

ai tt > ⇔ 0Pr >ijz

With the previous position the difference between two

real random variables ait , a

jt is leaded in the study of only

one real random variable zij.

∫+∞

∞−

+= )dtt(z)z( jjijij aj

aiij ttz ff

where ( )aj

ai t,ta

jai tt

f is the joint PDF of the real random

variables ait ⊆

and ajt ⊆

.

Suppose that ait ⊆

and ajt ⊆

are independent real

random variables.

iijititjjtjijtijz dt )z-(t)(t )dt(t)t(z)z( aj

ai

aj

aiij ∫∫

+∞

∞−

+∞

∞−

=+= fffff

This is an important result as the integral shown above isvery similar to the well-known integral of convolution.

Solving the following system formed by n-1 separatedequations with the n-1 unknowns T12, T23,…T(n-1)n∈Rn-1,the required shifting times are calculated.

=+

=+

=+

−∞

∞+

∞

∞

∞+

∞

∞

+∞

∞

∫ ∫

∫ ∫

∫ ∫

n)1n(

T

-

1)n-(nnnn1)n-(n

23

T

-

2333323

12

T

-

1222212

1)n-(n

23

12

dz)dt(t)t(z

dz)dt(t)t(z

dz)dt(t)t(z

-tt

-tt

-tt

an

a1-n

a3

a2

a2

a1

ff

ff

ff

Delays can be presented as stochastic processes as theyare time dependent. The aircraft scheduled to land at

R∈ast has a delay da⊆ , this scheduled time can be

changed into a new scheduled time R∈'ast . Thus, in

general another delay da’⊆ is defined.

The task of this section is to present a methodology for

strategic scheduling and thus scheduled times R∈ast

will be affected by changes. These adjustments of thescheduled times will be small when they are comparedwith the whole interval time required by PDFs. Hence,delays are hypothesised stationary random variables:

( ) ( )

∈⊆∈∀

+=R

R

as

as

as

t

T

Tttaaa ddd

With this hypothesis, the same delays da⊆ are

observed even if the departure times ast ∈R are changed.

The old and new departure schedule is shown in the Table1 while the old and the new arrival schedule is shown inTable 2.

Old departingscheduling

New departingscheduling

Aircraft 1 ds1t d

s1t Aircraft 2 d

s2t ds2t +T12

… … …

Aircraft n

dsnt d

snt +∑=

−

n

k 21)k(kT

Table 1: Old and new departure schedule

Old arrivalscheduling

New arrivalscheduling

Aircraft 1 as1t a

s1t Aircraft 2 a

s2t as2t +T12

… … …

Aircraft n

asnt a

snt +∑=

−

n

k 21)k(kT

Table 2: Old and new arrival scheduling

2.5. Travelling Time as a Real Random Variable,Velocity as a Two Dimensional Real Random Variable

The real random variable travelling time is defined asdifference between the arrival time and the scheduleddeparture time.

∈⊆⊆

−=∆

Rds

ds

t

t

a

t

at t

t

tt

dst

∆= Scheduled Departure Time of a given flight. This is

a deterministic variable having as domain the set of thereal number R.


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tt ∆= Travelling Time of a given flight. The differences

between the arrival and departure times of aircraftoperating a given flight are observed. A real randomvariable is defined assigning a real number to each ofthese observations.

is called the set where this random

variable is defined. To every outcome ζ∈ of the

experiment ΩΩ, a real number tt(ζ)∈R is assigned.

A set of Cartesian axes is defined as follows:

• the axis τ, whose unit vector is labeled with τ, is along-track direction of the aircraft

• the axis n, whose unit vector is labeled with n, is cross-track direction of the first aircraft

A P B

Figure 1: Cartesian axes

Velocity is defined as a two dimensional real randomvariable.

v ∆= (vττ,vn) v ⊆

v ∆= Velocity of the aircraft. This is a two dimensional

random variable. The measurements of the velocities infixed instant of times for given aircraft operating aselected flight are observed. A two dimensional realrandom variable is defined assigning a pair of realnumbers to each of these observations.

is called the set

where this random variable is defined. To every outcomeζ∈

, a pair of real number are assigned vτ(ζ)∈R,

vn(ζ)∈R.

For clarity, all multidimensional random variables will bewritten outlined in boldface letters v.

2.6. Velocity as stochastic process

The random variable velocity is defined by the experimentΩΩ.. The outcome ζ, of the experiment ΩΩ is here given:

ζ = measurement of aircraft velocity in a fixed instant oftime during a selected flight for a given aircraft.

A two dimensional real random variable v(ζ)⊆ is

defined for a given instant of time. If t1,t2,t3,…tn

(t1,t2,t3,…tn)∈Tn are instants of time at which theexperiment ΩΩ is performed, the outcome of ΩΩ will be theset of values v(ζ1,t1),v(ζ2,t2), v(ζ3,t3),…v(ζn,tn).Therefore, a function of two variables t and ζ is defined.For a fixed t, the two dimensional random variable speed

v(ζ)⊆ is obtained. This indicates the probability of

occurrence of a certain speed. For a specific ζ, the timefunction v(t) indicating the time-record of the speedduring the flight is obtained. Hence, the family of randomvariables v(ζ,t) ⊆

xT is defined to be a stochasticprocess.

2.7. Velocity as a stationary stochastic process

An aircraft which goes from the point A(Ax,Ay)∈R2 to thepoint B(Bx,By)∈R2 is given. Let v(ζ;t)⊆

xT be thestochastic process velocity of this aircraft. The marginalPDFs of the two dimensional random variable velocityv(ζ;t)⊆

xT along and across track are defined as:

( )( ) ( )( ) nn, dvt;v,vt;v

tv

velocity has

aircraft

Pr ∫∞+

∞−ττ

τ

τ==

nvvvv ffττ

( )( ) ( )( ) τ

∞+

∞−τ∫ τ

==

dvt;v,vt;v

tv

velocity has

aircraft

Pr n,n

n

nn vvvv ff

Without considering taking off and landing time (wherespeed is affected by substantial changes), the hypothesisthat the speed is time dependent is not necessary. For agiven instant of time during aircraft cruise, a velocitydistribution indicating the probability of occurrences of agiven speed can be computed. Therefore, the stochasticprocess velocity v(ζ,t) ⊆

xT is assumed to be stationary.

v(ζ,t) = v(ζ) ( ) ( )( ) ( ) T∈∀

ζ=ζζ=ζ

⇔ tt;

t;

nn vv

vv ττττ

Hypothesising the stochastic process v(ζ;t)⊆ xT be

stationary v(ζ)⊆ , the PDFs, (each of them being

calculated for different instant times) are assumed to beidentical, see Figure 2.

Figure 2: PDF of the along track velocity

τ

n

B

t1

( )( )t;vt τττvf

( )1tvτ

…

t2 tn

( )2tvτ ( )ntvτ

t

A


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2.8. Considerations to build the PDF of the along trackvelocity

Due to the lack of data regarding the experiments definingthe random variable velocity v(ζ)⊆

, the PDF of thevelocity along the track is obtained through atransformation of variables from related experiments fromwhich data are available. Thus, considering the workdescribed [12], the PDF of the random variable travellingtime will be transformed into the PDF of the velocityalong the track assuming certain simplifying hypothesis.The PDF of the travelling time is obtained using the dataprovided by the CAA.

The departure and arrival airports are supposed to beplaced in A and B. For a given journey, a travelling time

( )ζtABt ∈R is observed. The temporal mean of the

velocity ( )ζτv is computed through the following

equation (see Figure 3):

( ) ( )( )

( )( )( )

∈ζ∈ζ∈

ζ=ζ

τ

τ

R

R

R

v

t

d

t

dv t

ABtAB

BA,BA,

Figure 3: For a given journey ( )ζτv is observed

Observing this temporal mean n times a random variableis built that represents the distribution of the mean of thevelocity.

( )

⊆⊆

∈==

ττ

ττ

v

t

BA

tBA

tv tABt

AB

tAB

R),d(),d(

g

Supposing that ττττ vv = , then vττ is a real random

variable defined not directly for each experimentaloutcome. Alternatively vττ is defined indirectly via the real

random variable tABt ⊆

and the function g( tABt ).

2.9. Applied Tactical Planning based on a dynamicprobabilistic GHP

The velocity along the track vττ(ζ)⊆ is computed

through the ratio between the travelling time ⊆tABt

of the route AB and the euclidean distance d(A,B)∈Rbetween the point A and the point B

⊆∈

⊆=

tAB

tAB t

BA

v

tBA

v R),(d),(d

ττ

ττ

The travelling time ⊆tPBt of the aircraft for the route

PB is:

⊆⊆

∈=

tPB

tPB

t

v

BP

vBP

t ττττ

R),(d),(d

Substituting the velocity vττ(ζ)⊆ , the travelling time

⊆tPBt of the route PB can be expressed as travelling

time ⊆tABt of the route AB

⊆⊆

∈∈=

tPB

tAB

tAB

tPB

t

t

BABP

tBABP

t

RR ),(d,),(d

),(d

),(d

The arrival time ⊆a

PBt in B once the aircraft has

departed from P is:

=+= tPB

dPB

aPB ttt

⊆⊆

∈∈

+=

dPB

tAB

tAB

dPB

t

t

BA

BP

tBABP

tR

R

),(d

),(d

),(d

),(d

If the departure time from P is known the random variable⊆dPBt simplifies in a mere scalar ( ) R∈ζd

PBt . In a

real implementation of this methodology, the departuretime from P can be known though a data-link messagebetween aircraft and ground.

A B

P

t

( )ζτvvτ(t)

d(A,B)


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( )

⊆∈∈

∈⊆

+ζ=

tAB

aPB

tAB

aPB

t

BA

BP

t

tBABP

t

R

R

R

),d(

),d(

t

),(d

),(dt

dPB

dPB

This formula solves the arrival time in the destinationairport B once is know the departure time of the aircraft inP. Note the departure time from P is equal to the arrivaltime in P.The parameters involved are the eucledian distancesd(P,B)∈R, d(A,B)∈R, the real random variable travelling

time ⊆tABt and the departure time from P R∈d

PBt .

Applying the Fundamental Theorem of transformation ofvariables [10], the PDF of the arrival time in the

destination airport B ⊆a

PBt is derived by:

( ) ( )

−=

),d(

),d(tt

),d(

),d(t d

PBtPB

aPB BP

BABP

BAtAB

aPB tt

ff

In conclusion, the PDF ( )aPBta

PBtf of the arrival time in B is

given using only:

• the PDF of the travelling time of the route AB

⊆tABt which is known through real-data.

• the departure time from P, R∈dPBt which is

supposed to be known through a data-link message.

3. RESULTS

3.1. Strategic planning

Probability Density Functions (PDFs) of the delay arebuilt using real data covering the period commencing 1st

April 1998 up to 30th September 1998. There follows ananalysis of the British Airways flight from Birmingham(UK), scheduled to arrive at Glasgow InternationalAirport (UK) at 8:25 a.m.. In Figure 4 samples of thedelays da(ζ1),d

a(ζ2),…da(ζ130)∈R130 are shown. Thesedelays are the difference between the real landing timeand the scheduled arrival time, observed over 130consecutive days, using real data.

The origin of the PDF is set at the scheduled arrival time,for the studied flight at 8:25 a.m. The points placed beforezero show flights coming earlier than planned while themeasurements positioned after the origin show delays.The vertical axis gives the probability that a fixed delayoccurred. Given the fact that this is a short haul flight,arrival times (PDF) are very close each other.

Figure 4: Samples of the delays for British Airways

In Figure 5 the PDF ( )adadf is displayed.

Figure 5: PDF of the delays of British Airways

In Figure 6 the PDF of Air Canada flight flying fromToronto (CA) to Glasgow (UK) scheduled to arrive at8:00 a.m. is displayed. Owing to the length of the journey,the arrival times are effected by a higher uncertainty.

Figure 6: PDF of the delays of Air Canada

Studying PDFs of different flights arriving at GlasgowInternational Airport, long distant flights show that areeffected by a greater uncertainty than short distanceflights. This is caused by variable factors ( e.g. wind, AirTraffic Centre overloaded etc.) encountered on the route.Using Glasgow International Airport as an example, thetime interval between 8:00 a.m. until 8:25 a.m. isanlaysed. As shown in Table 3, four aircraft are scheduledto land. This interval is chosen both because it is one ofthe busiest period during the day and because a longjourney flight is involved. In Table 3, the flights and theirscheduled arrival time 4R∈a

s4as3

as2

as1 t,t,t,t

are listed.

0 40 80 140Sample

-50

0

150

Del

ay (

min

)-20 0 20 60 100 140

Delay (min)

0

0.1

Pro

babi

lity

-20 0 50 100 150Delay (min)

0

0.1

Pro

babi

lity


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no Flight Label DepartureScheduled

ArrivalTime(a.m.)

1 Aer Lingus AE Dublin as1t =8:00

2 Air Canada AC Toronto as2t =8:00

3 British

AirwaysBA Birmingham a

s3t =8:25

4 European

Air CharterEAC Bournemouth a

s4t =8:25

Table 3: Current scheduling

In Figure 7 the total distribution of the arrival time iscomputed. For a fixed instant time in time, this PDF givesthe probability that at least one of the four aircraft iscoming. Two main peaks are distinguishable, indicatingtwo intervals time with high probability of arrivals.

Figure 7: Total distribution of the arrivals according tothe current scheduling

Although from the scheduling an interval commencing at8:00 a.m. until 8:25 a.m. is considered, Figure 7 showsaircraft landing even later, so a longer time period must beconsidered. Define Arrival Slot (AS) as “The shortesttime period in which 90% of the flights arrive.”. Asshown in Figure 8 in the current scheduling AS=56 isminutes long. According to the current aeronauticallegislation, the minimum aircraft time separation in thelanding procedure is 3 minutes. In order to guarantee sucha temporal distance during peak hours, operators allocateairborne and ground hold delays. Probability of Conflict(PC) is defined as “The probability of at least two aircraftarriving within a time difference of 3 minutes”. The higherthe probability of conflict, the higher the likelihood ofairborne delay having to be allocated, since if a conflict isdeemed to occur, the air traffic controllers would have toissue separation instructions to the aircraft in order toachieve the adequate time spacing at the runway. Thus,the probability of conflict should be reduced to increaseefficiency, reduce cost and improve the levels of safety.As shown in Figure 8, PC in the current scheduling isequal to 35.4%.

Figure 8: Current situation

In Table 4 two new strategic schedules are proposedgiving the option of:• decrease of airborne delay by 15.3% reducing the

Probability of Conflict (PC) by the same quantity. SeeFigure 9.• improve the airport capacity by 14.3% reducing the

Arrival Slot (AS) of the same quantity. See Figure 10.• a combination of the two options above described.

NEW STRATEGIC SCHEDULE

Flight Fixed AS=56minPC=30.0%

Reduction by 15.3%

Fixed PC=35.4%AS=48min

Reduction by 14.3%

AE 8:00 a.m. 8:00 a.m.

EAC 8:07 a.m. 8:09 a.m.

AC 8:28 a.m. 8:12 a.m.

BA 8:33 a.m. 8:18 a.m.

Table 4: Proposed new scheduling

Figure 9: Strategic Planning: fixed AS

Figure 10: Strategic Planning: fixed PC

8:00 8:50 9:40 10:30Time (a.m.)

0

0.05

Pro

babi

lity

PC=35.4%

AS=56 min

6min

AE EACBA

AC

Time

Pro

babi

lity

PC=30.0%Reduction by 15.3%

AS=56min

AE EACBA

AC

Time

Pro

babi

lity

AS=48minReduction by 14.3%

PC=35.4%

AE BA

AC

EAC

Time

Pro

babi

lity


- 9 -

3.2. Tactical Planning based on a dynamicprobabilistic GHP

When the Air Canada (AC) flight arrives at a pointlocated P=1000 Km away from Glasgow International

Airport, the aircraft transmits the time ( ) R∈ζdPBt to the

arrival airport placed in B. The traffic manager codes thisdata into the computer updating the PDF of the delay andthus the PDF of the arrival time.

Figure 11: Air Canada transmits its position

If the flight arrives early at the point placed P=1000 Kmaway from the airport, it will be allocated as first in thearrival order while if it is late it will be placed as the lastone. In all the intermediate situations, depending of theamount of the delay, it will be allocated between theflights.

Through the tactical planning, the airport managers canhave control over flights using data link capabilities.Suggestions to pilots to increase, decrease or keep thesame velocity can be given. To reduce complexity, theexample to be considered will not use the feed backcapability. To study the affect of the data link, it is enoughto run the program again simulating the new data.

Updating the information, the PDFs of the arrival time forgiven flights seem compressed, as shown in Figure 12.The uncertainty is clearly reduced so there is moreaccuracy in predicting the arrival time. The closer theaircraft is to the airport minor uncertainty effects ETA. InFigure 11 the PDFs for the Air Canada flight whenrecalculated using the updated information from a pointP=1000 Km away from Glasgow International Airport isshown.

Figure 12: Transformed PDF of delays for Air Canada

The task now is how to allocate the landing of Air Canadaflight between the others when the time of reaching thepoint P=1000 Km away from Glasgow InternationalAirport is known. Four cases are analysed as shown inFigure 13:

1. The aircraft comes very early and lands first, beforethe Aer Lingus (AE) flight.

2. The aircraft is nearly on time. To optimise efficiencyit is scheduled to land in the second position after theAer Lingus (AE) flight.

3. The aircraft is nearly on time. To optimise efficiencyit is scheduled to land in the third position after theEuropean Air Charter (EAC) flight.

4. The aircraft is delayed. It lands last after the BritishAirways (BA) flight.

Figure 13: Tactical planning

To estimate the advantages of this real time system, theprobability that each of the arrival order occurs iscomputed. For instance, it is not likely that Air Canadaarrives before Aer Lingus. Although both flights areplanned to land at 8:00 a.m., the mean delay of AirCanada is 20 minutes while Aer Lingus usually arrives 3minutes earlier.If the Air Canada flight arrives at the transmitting point(in this case the point P placed 1000 Km away fromGlasgow International airport) before ( ) 34:6td

PB <ζ a.m.,

there is a high probability that the aircraft will arrive earlyand thus it will be accommodate as the first in the landingorder. If the Air Canada flight arrives at the transmittingpoint between 6:34 a.m. and 6:45 a.m., it will be thesecond in the arrival order having a high probability ofarriving after Aer Lingus. European Air Charter will thenbe shifted into the third position and ground hold delaywill be allocated to it.

If the Air Canada flight arrives before Aer, no groundhold has to be imposed upon the other flights as they arealready planned to arrive simultaneously. As shown inTable 5, the probability of this happening is 1.9%. If theflight from Toronto arrives at the point P located 1000Km away from the airport between 6:34 a.m. and 6:47a.m., there is a probability of 25.2% that the Air Canada

-40 0 40 100Delay (min)

0

0.15

Pro

babi

lity

PC=35.4%

AE EAC BA

AC

AC

AS=56min

Time

Pro

babi

lity

1000 Km

A P B

( )ζdPBt


- 10 -

and Aer Lingus flights will arrive at the same time (seeFigure 11 and Table 5). To avoid collision, the other lastthree flights require to be shifted as many minutes as AirCanada arrives at that point after 6:34 a.m. (see Table 6).For instance, if it crosses that point at 6:40 a.m., a groundhold delay of 6 minutes has to be imposed to the otherflights

Figure 11: Tactical planning: Air Canada arrives beforeAer Lingus

Arrival orderProbability

of theEvent

TimeCondition

AC…AE,EAC,BA 1.9% dPBt <6:34

AC,AE,EAC,BA 25.2% 6:34≤ dPBt <6:47

AE,AC,EAC,BA 24.9% 6:47≤ dPBt <6:55

AE,EAC,AC,BA 18.0% 6:55≤ dPBt <7:05

AE,EAC,BA…AC 30.0% dPBt ≥7:05

Table 5: Probability and time condition

There is a probability of 24.9% corresponding to theevent: “Air Canada arrives between Aer Lingus andEuropean Air Charter” (see Table 5). In this situation,ground hold delay would be imposed only on the last twoflights. The amount of delay is equal to the differencebetween the arrival time of Air Canada to the referencepoint and 6:47 a.m (see Table 6).

In 18.0% of cases, Air Canada will be arrive betweenEuropean Air Charter and British Airways. In thiscircumstance ground hold delay will be imposed only tothe last flight. In the last rows of Table 6 no ground holdis required as Air Canada arrives in the last position afterBritish Airways.

Remember that only the flights until 8:25 a.m. areanalysed excluding all those which are planned to comelater. To estimate the improvements achieved in term ofreduction of PC with this methodology all the flights with

which the Air Canada arrival could conflict have to beincluded. In term of the Arrival Slot (AS) a reductionmean by 32.1 % is achieved, note that in this circumstancethe ground hold cost has to be taken into account.

Arrival orderGroundHold for

AE

GroundHold for

EAC

GroundHold for

BAAC…AE,EAC,BA 0 0 0AC,AE,EAC,BA d

PBt -6:34dPBt -6:34 d

PBt -6:34

AE,AC,EAC,BA 0 dPBt -6:47 d

PBt -6:47AE,EAC,AC,BA 0 0 d

PBt -6:55AE,EAC,BA…AC 0 0 0

Table 6: Amount of ground hold delay to assign

4. CONCLUSIONS AND FURTHERDEVELOPMENTS

This paper has presented a tool for the development of anoperational procedure for strategic and tactical planning. It isbased on Statistics and Probability theory and relies onhistorical data modelling the arrival times as real randomvariables.

This new procedure has been applied to improve thestrategic schedule of Glasgow International Airport usingCAA real data. It has been proved that the consequentialbenefits include the options of:• Reducing the Arrival Slot length (AS) by 14.3%

thereby increasing the airport capacity.• Reducing the Probability of Conflict (PC) by 15.3%

which will decrease airborne delay at the arrival airport,which will reduce fuel consumption both reducingoperators costs and environmental pollution.• A combination of the two options.

Furthermore the tactical planning procedure has beenpresented and tested always for Glasgow InternationalAirport. The results of the tests have indicated apromising mean reduction of the Arrival Slot (AS) equalsto 32.1%. The advantage of such a high percentage is asignificant improvement in the airport's capacity whereasthe disadvantage is an increase in expenses due to theallocation of ground hold delays.

5. REFERENCES

1. Kayton, M., Fried, W. R., Avionics navigationsystems, 2nd edition. 1997, New York: John Wiley &Sons, Inc.

2. Liang, D., Marnane, W., Bradford, S. Comparison ofUS and European Airports and Airspace to SupportConcept Validation. in 3rd USA/Europe Air TrafficManagement R&D Seminar. 2000. 13th-16th June ofNapoli, Italy.

Reduction by 35.7%.This event occurs with probability equals to 25.2%

PC=35.4%

AE EACBA

ACAC

AC

AS=36minTime

Pro

babi

lity


- 11 -

3. Vranas, P.B., Bertsimas, D.J., Odoni, A.R., The MultiAirport Ground Holding problem in air TrafficControl. Operations Research, 1994. 42(2): p. 249-261.

4. Odoni, A.R., The Flow Management Problem in AirTraffic Control. Flow control of congested networks,1987: p. 269-288.

5. Andreatta, G., Romanin-Jacur, G., Aircraft FlowManagement under Congestion. TransportationScience, 1987. 21: p. 249-253.

6. Vranas, P.B., The Multi-Airport Ground-HoldingProblem in Air traffic Control. 1994, MassachussetInsitute of Technology: Cambridge, Massachusset.

7. Vranas, P.B., Bertsimas, D.J., Odoni, A.R., DynamicGround-Holding Policies for a Network of Airports.Transportation Science, 1994. 28(4): p. 275-291.

8. Gilbo, E.P., Airport Capacity: Representation,Estimation, Optimization. IEEE Transactions onControl Systems Technology, 1993. 1(3): p. 144-154.

9. Gilbo, E.P., Optimizing Airport Capacity Utilizationin Air Traffic Flow Management Subject to Contraintsat Arrival and Departure Fixes. IEE Transaction onControl Systems Technology, 1997. 5(5): p. 490-505.

10. Yatess, R.D., Goodman, D. J., Probability andStochastic Processes. A Friendly introduction forElectrical and Computer Engineering. 1999: JohnWiley & Sons, Inc.

11. Papoulis, A., Probability, Random Variables, andStochastic Processes. 1981: McGraw-Hill.

12. Qiao, M., Morikawa, H., Moriyuki Mizumachi, M.,Dynamic Departure Regulations of Air Traffic FlowManagement. Electronics and Communications inJapan, 1998. 81(9): p. 68-76.

6. BIOGRAPHICAL NOTE

The authors are with the ATM Research Group of theDepartment of Aerospace Engineering at GlasgowUniversity. The ATM Research Group is supervised byDr. Colin Goodchild who is employed by the Universityand lectures in avionics. Miguel A. Vilaplana Ruiz andStefano Elefante are researchers that joined the ATMresearch group in 1997 and 1998 respectively. The group'sATM research focuses on mathematical modelling ofmethodologies that address the issues of the ICAO FANScommittee. The authors may be contacted directly viaemail ([email protected]).

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A Strategic and Tactical Tool for ATFM Planning … · A Strategic and Tactical Tool for ATFM Planning based on Statistics and Probability ... airport management. Tactical planning