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AIAA Aviation Technology, Integration, and Operations Conference, Atlanta, Georgia, U.S.A., June 2018
1
An extended analysis of sequencing arrivals
at three major European airports
Raphaël Christien, Eric Hoffman, Aymeric Trzmiel, Karim Zeghal
EUROCONTROL Experimental Centre, Brétigny-sur-Orge, France
This paper presents an analysis of the sequencing of arrival flights at three major European airports
representative of different types of operation with more than 24000 aircraft pairs. The motivation is to better
understand and characterise how sequencing is performed in dense and complex environments during peak
periods. The analysis, purely data driven, focuses on the dynamic of spacing over time, investigating in
particular convergence and reactionary aspects. The two main results are: (1) progressive convergence of the
spacing with a deviation up to ±2.5min at 10min to final, and ±50s at 5min to final; and (2) noticeable
reactionary effect with a queue additional time up to 3min at 10min to final and 50s at 5min to final. These
values may reflect the level of difficulty and sensitivity of sequencing during peak periods in such dense and
complex environments. Future work will involve analysing high and late reactionary situations, investigating
how this approach may help identifying improvement areas, and assessing the impact of a change for future
operations.
Keywords: arrival sequencing, aircraft spacing, approach control, data analysis.
This study has been conducted as part of the European SESAR2020 programme (PJ01-02).
I. Introduction
his paper presents an analysis of the sequencing of arrival flights at three European airports representative of
different types of operation (Frankfurt Main, London Heathrow and Madrid Barajas). The motivation is to
better understand and characterise how sequencing is performed in dense and complex environments.
The analysis relies on a method purely data driven recently introduced [1][2] that focuses on the dynamic of
spacing over time between consecutive aircraft, investigating in particular convergence and stability aspects. The
paper presents an extension towards the assessment of the reactionary aspect (propagation of spacing deviation
between aircraft). The analysis considers peak periods during which significant sequencing takes place, using nearly
three months of data with in total more than 24000 aircraft pairs.
The paper is organised as follows: after a review of related studies and an overview of the method, it will go
through the data processing required to compute the spacing and additional time indicators. The analysis of the
sequencing will then be presented after a typical case illustration.
II. State of the art
A comprehensive framework has been developed by the Performance Review Unit (PRU) of EUROCONTROL to
characterise the performances of the arrival management process [3][4][5]. Two key elements introduced are the
notions of unimpeded time and additional time in the arrival sequencing and metering area, an area of 40NM
(extended to 100NM in some analyses) from the airport. The unimpeded time is the transit time in the area in non-
congested conditions. The additional time is the difference between the actual transit time and the unimpeded time. It
represents the extra time generated by the arrival management and “is a proxy for the level of inefficiency (holding,
sequencing) of the inbound traffic flow during times when the airport is congested.” This indicator is used (together
with other indicators such as the flow management delay) in particular to compare the performance of the main
airports in Europe and in the U.S.A.[6].
T
AIAA Aviation Technology, Integration, and Operations Conference, Atlanta, Georgia, U.S.A., June 2018
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The work presented here builds on these notions of unimpeded time and additional time in an area around the
airport, and aims at characterising further how the sequencing is performed. Similar types of indicators were also used
at the level of individual flights, such as terminal area transition time deviation, to detect any potential perturbations
and assess the resilience of scheduled Performance-Based Navigation arrival operations [7].
When assessing the impact of new concepts in relation with sequencing, detailed analyses have been conducted
[8][9][10].They consider different dimensions such as human factor (e.g. workload, radio communications,
instructions), flight efficiency (e.g. distance and time flown) and effectiveness (e.g. achieved spacing on final) using
simulation data (human in the loop or model based). To highlight the geographically based nature of the sequencing
activity, in particular late versus early sequencing actions, we introduced an analysis of instructions and eye fixations
as a function of the distance from the final point [10].
All these studies aimed at assessing the impact of a new concept and considered the observable actions for
sequencing. Although they informed on the sequencing activity of the controller, the dynamic of the spacing is not
considered as an element of the analysis. Furthermore, the need for operators related data, in particular instructions,
makes uneasy the analysis of current (live) operations. From a control theory perspective, the spacing variable is the
key element that should enable the understanding of the human behaviour. Here, we are not aiming at building a
mathematical model of the approach controller, however as stated in [11], “control theory is a good foundation for
developing the intuition and judgment needed for smart cognitive systems engineering”.
Numerous analysis of the spacing have been performed in the context of airborne spacing when studying the
performances of different algorithms or of the flight crews [12][13][14][15][16]. Typical analyses involved in
particular the relation between spacing accuracy (control error) and number of speed changes/variations (control
effort) as well as the impact of the resulting speed profile on the rest on the chain of aircraft (reactionary effect). In all
these cases, however, the situation was such that the spacing could be defined as both aircraft followed known paths.
The issue being that, in the general case, the spacing variable is hard to formally define and measure, or even does
not exist. In vectoring for instance, while it is straightforward to measure the spacing at a final common point, it is
unclear how to define the spacing between two aircraft being vectored on different paths but whose resume paths to
the common point are unknown in advance. In this case, the spacing is part of the cognitive process of the approach
controller and is not accessible.
III. Method
The method introduced is purely data driven and does not make any assumption in terms of sequencing
techniques used (e.g. vectoring, tromboning) or controller working methods. It proposes a definition of spacing
between two aircraft at all times in the area considered. No assumption is made regarding aircraft path/navigation:
aircraft may be following same or predefined trajectories, or may be on open vectors.
The method relies on the combination of two existing notions. Firstly, the constant time delay introduced by
NASA to define a spacing deviation for aircraft following same trajectories [12][13]; it considers the past positions
of the leader aircraft with a given delay corresponding to the required spacing. This notion will be generalised to any
aircraft trajectories. Secondly, the unimpeded time introduced by the PRU to define the additional transit time in the
area considered [3][4][5]; it considers the minimum flying time at the entry point of the area, obtained from recorded
data during non-congested periods. This notion will be generalised to any point in the area.
Let us consider a pair of consecutive landing aircraft denoted leader and trailer, with s their required time
spacing
1
. Using the constant time delay principle, the spacing deviation (or spacing error) at time t is defined by
considering the current position of trailer at time t, and the past position of leader at time t – s. Since aircraft do not
necessarily follow the same trajectory, we have to consider a reference point common to both trajectories typically
the final approach fix. The spacing can be defined by considering, for each aircraft, its flying time to this reference
point as if the aircraft was flying the shortest/fastest possible trajectory. This time will be denoted minimum (flying)
time.
1
To simplify the interpretation of the spacing deviation curves, we decided to set the final spacing deviation to zero, considering
that the required spacing was the final one. An analysis of the achieved spacing at major European airports may be found in [17].
AIAA Aviation Technology, Integration, and Operations Conference, Atlanta, Georgia, U.S.A., June 2018
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Precisely, we define the spacing deviation at time t as the difference between the minimum time from the
position of trailer at time t, and the minimum time from the position of leader at time t – s (cf. next figure):
spacing deviation (t) = min time (trailer (t)) – min time (leader (t – s))
Figure 1: Spacing deviation definition
Assuming a representative set of trajectories covering non-congested periods, the minimum time from a given
point to a fix common point (e.g. final approach fix) is the minimum time along all trajectories passing through this
point to the fix common point. Practically, this implies to compute first all the minimum times for the area
considered, typically under the form of grid.
With a spacing defined at all times, the sequencing can be formulated as a problem of manual control: the
objective is to set the spacing deviation to zero for all aircraft pairs in the sequence. The intrinsic difficulty, beyond
the handling of multiple pairs, is the interdependency of these pairs with potential reactionary effect. Indeed, during
peak periods, every aircraft may be at the same time the trailer of a pair and the leader of the following pair. Hence,
any action on an aircraft may impose to adjust the spacing on the rest of the sequence. This is typically the case
when creating spacing to integrate two flows of aircraft. To limit this reactionary effect (and manage their
workload), controllers tend to perform a progressive convergence by adjusting the spacing more accurately as
aircraft get close to the runway, leaving a loose spacing when further away and even creating some buffer (extra
spacing) to anticipate integration of aircraft.
Considering the aircraft are set by default on their shortest/fastest paths, the control action is to delay the trailer
by acting on lateral (path stretching) and/or on longitudinal (speed reduction) dimensions. The control effort can
thus be reflected by the additional time (delay) applied on each trailer aircraft. Generalising the PRU notion,
assuming flown trajectories available, this value can be defined, at any time, as the difference between actual
remaining flying time and minimum flying time. This additional time can be split in two parts: the “individual” part
related to the spacing deviation of the considered pair
2
, and the “queue” part related to the “individual” part of all the
preceding pairs in the sequence
3
. This “queue” part will be propagated later to the considered pair and will reflect
the reactionary effect. Hence, for any time t:
total additional time (t) = individual additional time (t) + queue additional time (t)
where:
individual additional time (t) = – spacing deviation (t) if spacing deviation (t) ≥ 0, otherwise 0
2
There will be no individual additional time when spacing is larger than required.
3
May also include deviations related to other factors than arrival sequencing (e.g. interaction with departures).
AIAA Aviation Technology, Integration, and Operations Conference, Atlanta, Georgia, U.S.A., June 2018
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IV. Data collection and preparation
A. Data collection
The case study is based on a dataset for three major European airports: Madrid Barajas (LEMD), Frankfurt Main
(EDDF) and London Heathrow (EGLL), from the 1st of January to the 18th of March 2017 (78 days). The dataset
contains about 130000 arrival flights (37485, 43927 and 47491 for LEMD, EDDF and EGLL respectively), and
consists in position reports, updated at an average rate of 30s (interpolated linearly at 5s).
We consider a geographical focus area of 80NM radius around each airport to encompass the sequencing area.
To ensure enough representative data, only major flows will be considered, making up of more than 80% of the
dataset. We retain typical arrival flights that enter and exit the focus area. In particular, this excludes go-arounds,
flights with exceptionally short or long flying time within the area, and aircraft not flying over the final approach fix
(or without data close enough to the runway). This makes the filtered sample sizes to be: 26196, 30748 and 35981
flights respectively for LEMD, EDDF and EGLL
The following figure shows a random sample of about 1000 flights for each airport within the focus area.
Figure 2: Trajectory samples within focus area
B. Data construction: minimum time
As presented in section III, minimum times are computed in all the cells of a 2D mesh covering the focus area on
the basis of all the recorded data. These minimum times are computed per flow (defined as a pair of entry point and
landing runway), for each airport. Note that other factors may be considered to refine the estimation like heading,
speed, altitude, aircraft type, wind.
The selected cells size shall not be too large to allow for accurate trajectory deviations assessment. It shall not be
too small, as the number of flights per cell will be insufficient to ensure reliable estimates (as a rule of thumb, 10
flights per cell can be considered as a minimum). For this case study, square cells of 1NM width were found to
provide an appropriate trade-off. The cells minimum times are used to fit thin plate splines [17] for each associated
flow: this allows smoother, continuous minimum times estimation from area entry to final approach fix to be
performed, reducing the cells boundary aliasing effect.
The result of this computation is shown on the figure below, for each airport, with one map per configuration
(only one shown here per terrain). The colors depict the minimum time to final, from red (20 minutes) to blue (lower
than 1 minute), with overlaid maps and iso-contours per flow (sampled with a one minute time step).
AIAA Aviation Technology, Integration, and Operations Conference, Atlanta, Georgia, U.S.A., June 2018
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Figure 3: Minimum time per flow
C. Data selection: peak hours
We focus the analysis on peak periods during which significant sequencing is expected to take place. The
identification of the peak periods is based on the additional time measured at 80NM. We consider periods with an
average additional time per hour greater than the 3rd quartile value per airport (see boxplots figure below). This
corresponds to average values of 5, 4 and 12 minutes for LEMD, EDDF and EGLL respectively (upper part of the
boxes on the figure below). Since the peak periods are based on different levels of congestion per airport, direct
comparison would not be relevant. Flights landing during these periods are considered for the analysis. At this stage
of the data preparation process, the dataset consists of 13509, 12016 and 13771 flights for LEMD, EDDF and EGLL
respectively.
Figure 4: Average additional time per hour
D. Data selection: aircraft pairs
We further focus the analysis on aircraft pairs considered to be close enough to require sequencing: we selected
pairs with a final spacing lower than 200 seconds at the final approach fix. This makes the aircraft pairs sample sizes
to be: 7664, 5656 and 11593 respectively for LEMD, EDDF and EGLL, making a total of more than 24000 pairs.
These sample sizes are considered sufficiently large to be representative.
AIAA Aviation Technology, Integration, and Operations Conference, Atlanta, Georgia, U.S.A., June 2018
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V. Typical case example
This section focuses on a single pair of successive aircraft landing on the same runway to illustrate the notions of
spacing deviation and additional time (total, individual and queue).
A. Spacing deviation
The following figure presents on the left part the trajectories of the leader (pink) and trailer (blue) aircraft
(superimposed most of the time). The yellow trajectories are typical trajectories flown in the approach area. The
second (middle) graph shows the corresponding time to final and minimum time to final for both aircraft: the
difference of both y-values gives the spacing deviation at a given flight time to final, as reported on the right graph.
Figure 5: 2D trajectories (left), minimum times to final (middle) and spacing deviation (right)
It can be seen that the spacing deviation starts with a negative value (e.g. about -1 minute at 15 minutes to final),
showing that the trailer aircraft is does not have the spacing with the leader aircraft
4
and some additional time (+1
minute on the trailer aircraft) is required to create spacing. The spacing deviation converges from its negative value
toward zero in the 15 to 7 minutes to final. This convergence starts at a slow pace from 15 to about 9 minutes to
final (trailer aircraft flying at a slower speed than the leader) and gets faster from 9 to 7 minutes (path
stretching/trombone area). It diverges up to about 30s of positive “extra” spacing deviation: this occurs when the
trailer enters the path stretching area, while the past position of the leader is not there yet. In this case, this
divergence could be symptom of traffic in front of the leader aircraft, and the trailer aircraft gets more additional
time to allow for the leader adjustment toward its own leader. The spacing deviation converges then again, when the
leader gets some path stretching too, reducing the “extra” spacing toward the final spacing.
B. Additional time
The following figure presents total, individual and queue additional times (cf. section III) from 15 to 0 minutes
to final for the trailer aircraft.
The individual additional time curves is symmetrical to the spacing deviation curve above by definition, after
replacing the positive (“too large”) spacing deviation values by zero. The queue additional time that will be
propagated toward the trailer aircraft is significantly higher than the individual one (e.g. max of 4 minutes at 15
minutes to final vs. 1 minute).
On this example, the spacing is sufficient (i.e. greater or equal to the final spacing) between the leader and the
trailer aircraft from 6 minutes to final (individual additional time green curve at zero) while there is still some queue
additional time to be propagated to the trailer (e.g. about 30s at 4 minutes to final). This is typically a reactionary
effect produced by the additional time on the preceding pairs.
4
A negative value larger than a required spacing may reflect a swap in the natural sequence order.
AIAA Aviation Technology, Integration, and Operations Conference, Atlanta, Georgia, U.S.A., June 2018
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Figure 6: Total, individual and queue additional times
VI. Analysis of sequencing
The analysis of sequencing will consider two aspects: convergence using spacing deviation, and reactionary
using queue additional time, as introduced in sections III and IV. It starts at 15min to final to encompass the
sequencing area, although we acknowledge that depending on the environment, sequencing may start closer to the
runway (e.g. at around 10min for EGLL). It should be recalled that since the peak periods are based on different
levels of congestion per airport, direct comparison would not be relevant.
A. Spacing deviation
The following figure illustrates the spacing deviations with light gray curves samples (1000 random cases per
airport), 90% containment (lower curve corresponds to the 5% percentile and the upper curve to the 95% percentile)
and a median curve (black line).
Figure 7: Spacing deviation
The median curves for all airports are all aligned with the zero deviation, suggesting a form of symmetry between
the positive and negative spacing deviation values, also suggested on the containment curves. For LEMD and EGLL,
the containment curves follow a pretty linear rate. For EDDF, such a linear part exists in the 10-5 minutes to final;
while in the 15-10 minutes range, the curves are relatively flat (no spacing evolution). It can be observed that, at
10min to final, the spacing deviation (90% containment) is about ±2.5min for EDDF, ±2min for EGLL and ±1min for
LEMD. At 5min to final, these values decrease to ±42s, ±48s and ±30s for EDDF, EGLL and LEMD respectively,
showing the convergence toward zero.
AIAA Aviation Technology, Integration, and Operations Conference, Atlanta, Georgia, U.S.A., June 2018
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Overall, the variations of the spacing deviation reflect the progressive nature of the convergence from 10min
down to final. This is typically the case for LEMD and EGLL; EDDF shows a convergence in a smaller range (5min)
which may result from tromboning and the turn to final. The deviation span at 10min-15min reflects the traffic
presentation (level of smoothing/bunching) and the ordering of the aircraft (level of swap between flights).
It is possible to have a closer look at the spacing deviation by identifying typical patterns through statistical
clustering. We selected a robust clustering technique (Partitioning Around Medoids, [19]) that partitions all the
spacing curves into clusters in which each curve belongs to the cluster with the nearest mean, serving as a typical
representative. We decided to select three distinct clusters per airport. On the figure below, the typical pattern
associated to each cluster is represented by a thick colored line. Three typical patterns are observed for all airports: the
“spacing obtained” patterns, starting and staying close to zero (middle curves for all airports, light green); the “less
spacing needed” upper patterns, starting above zero (dark blue); the “more spacing needed” lower patterns (light
blue).
Figure 8: Spacing deviation, typical patterns
All patterns get close to zero deviation from 5 to 0 minutes to final for all airports. The “spacing obtained”
patterns for the different airports are pretty similar: the spacing is kept close to the final spacing value. On the “less
spacing needed” patterns, LEMD has a spacing reduction around 1 minute, and shows a relatively linear convergence
from 15 to 5 minutes to final. EDDF has a spacing reduction around 2 minutes, and is reducing it in the 7-5 minute
range. EGLL has a spacing reduction around 2.5 minutes and is reducing it linearly from 15 minutes to about 5
minutes to final. The “more spacing needed” patterns show a pretty symmetrical shape to their “less spacing needed”
counterparts for all airports.
B. Additional times
The two following figures (top and middle) illustrate the individual and queue additional times, with gray dot
sample measures (1000 random cases per airport), a 90% containment area (lower curve corresponds to the 5%
percentile; upper curve corresponds to the 95% percentile) and a median thicker curve. The following figure (bottom)
focuses on the median values of the three additional times (total, queue and individual).
Focusing on the median curves, it can be seen that the values at 10min to final are around 15s, 30s, and 17s for
LEMD, EDDF and EGLL respectively, and at 5min, around 7s for all airports: the pairwise spacing is usually
acquired at that time. Note: a link can be made between the upper containment curve and the lower, negative spacing
deviation containment (cf. Figure 7) curve, with similar values: this is a consequence of the individual additional time
definition.
It can be noticed that the queue additional times are significantly higher than the individual additional times: at
10min to final, the median queue values are 1min, 2.35min and 2.75min, and at 5min to final, 28s, 50s and 43s for
LEMD, EDDF and EGLL respectively. This suggests that, while the pairwise spacing is established (and kept), there
is some sequencing effort even at a closer distance to the runway, due to the propagation of the individual additional
time applied on the preceding pairs. One source for that late propagation may be the late integration of multiple
arrival flows.
AIAA Aviation Technology, Integration, and Operations Conference, Atlanta, Georgia, U.S.A., June 2018
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Figure 9: Individual, queue and total additional times
VII. Conclusion
This paper presented an analysis of the sequencing at three European airports representative of different types of
operation (Frankfurt Main, London Heathrow and Madrid Barajas) during peak periods. The analysis focused on the
dynamic of spacing over time, investigating in particular convergence and reactionary aspects. The computation of
the spacing relies on a model purely data driven, calibrated on and applied to more than 24000 aircraft pairs.
The convergence aspect was assessed using spacing deviation (difference between current and final spacing).
Depending on the airport, the values (90% containment) are in the order of ±1min to ±2.5min at 10min to final, and
±30s to ±50s at 5min to final. These values reflect the level of bunching that has to be resorbed and the progressive
nature of the convergence of spacing.
AIAA Aviation Technology, Integration, and Operations Conference, Atlanta, Georgia, U.S.A., June 2018
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The reactionary aspect was assessed using additional time (delaying action) applied on the trailer aircraft of a
given pair, dissociating the “individual” part of the pair, from the “queue” part of all preceding pairs. Depending on
the airport, the individual values (median) are in the order of 15s to 30s at 10min to final, and 7s at 5min to final. The
queue values are significantly higher, in the order of 1min to 3min at 10min to final, and 30s to 50s at 5min to final. In
particular, the noticeable result is the high value of queue additional time close to the runway compared to the
individual additional time (30s-50s vs 7s at 5min to final). This may reflect the level of reactionary effect in dense and
complex environments.
Future work will involve analysing high and late reactionary situations. It will also involve applying the analysis
to other airports, and beyond, investigating how this approach may help identifying best practices, potential
inefficiencies and improvement areas, and assessing the impact of a change for future operations.
VIII. References
[1] R. Christien, E. Hoffman, A. Trzmiel, K. Zeghal, “Toward the characterisation of sequencing arrivals”, 12
th
USA/Europe Air Traffic
Management R&D Seminar, Seattle, USA, June 2017.
[2] R. Christien, E. Hoffman, A. Trzmiel, K. Zeghal, “An analysis of sequencing arrivals at three European airports”, Joint AIAA and Royal
Aeronautical Society, Modelling and Simulation in Flight Simulation conference, London, U.K., December 2017.
[3] ATM Airport Performance (ATMAP) Framework, Measuring Airport Airside and Nearby Airspace Performance, Performance Review
Commission, EUROCONTROL, December 2009.
[4] Performance Review Report, An Assessment of Air Traffic Management in Europe during the Calendar Year 2016, Performance Review
Commission, EUROCONTROL, June 2017.
[5] EUROCONTROL Performance Review Unit web site http://ansperformance.eu
[6] Comparison of Air Traffic Management-Related Operational Performance: U.S./Europe, EUROCONTROL (on behalf of the EU) - FAA,
June 2014.
[7] J. Jung, S. A. Verma, S. J. Zelinski, T. E. Kozon, L. Sturre, “Assessing Resilience of Scheduled Performance-Based Navigation Arrival
Operations”, 11
th
USA/Europe Air Traffic Management R&D Seminar, Lisbon, Portugal, June 2015.
[8] T. J. Callantine, P. U. Lee, J. Mercer, T. Prevôt, E. Palmer, “Air and ground simulation of terminal-area FMS arrivals with airborne spacing
and merging”, 6
th
USA/Europe Air Traffic Management R&D Seminar, Baltimore, Maryland, USA, June 2005.
[9] J. E. Robinson III and J. Thipphavong, W. C. Johnson, “Enabling Performance-Based Navigation Arrivals: Development and Simulation
Testing of the Terminal Sequencing and Spacing System”, 11
th
USA/Europe Air Traffic Management R&D Seminar, Lisbon, Portugal, June
2015.
[10] I. Grimaud, E. Hoffman, L. Rognin, K. Zeghal, Spacing instructions in approach: Benefits and limits from an air traffic controller
perspective, 6
th
USA/Europe Air Traffic Management R&D Seminar, Baltimore, Maryland, USA, June 2005.
[11] M. Mulder, M. M. Van Paassen, J. M. Flach, and R. J. Jagacinski, “Fundamentals of Manual Control Theory,” in The Occupational
Ergonomics Handbook (Second Edition) – Fundamentals and Assessment Tools for Occupational Ergonomics, W. S. Marras and W.
Karwowski, Eds. CRC Press, Taylor & Francis, London, 2005, pp. 12.1–12.26, ISBN 0849319374.
[12] Sorensen, J.A., Goka, T., "Analysis of in-trail following dynamics of CDTI-equipped aircraft", Journal of Guidance, Control and Dynamics,
vol. 6, pp 162-169, 1983.
[13] Kelly, J.R., Abbott, T.S., “In-trail spacing dynamics of multiple CDTI-equipped aircraft queues”; NASA, TM-85699, 1984.
[14] K. Krishnamurthy, B. Barmore, F. Bussink, “Airborne precision spacing in merging terminal arrival routes: a fast-time simulation study”,
6
th
USA/Europe Air Traffic Management R&D Seminar, Baltimore, Maryland, USA, June 2005.
[15] E. Alonso, G.L. Slater, “Control Design and Implementation for the Self-Separation of In-Trail Aircraft”, AIAA Aviation, Technology,
Integration, and Operations Conference (ATIO), Arlington, Virginia, USA, September 2005.
[16] D. Ivanescu, C. Shaw, E. Hoffman, K. Zeghal, “Towards Performance Requirements for Airborne Spacing: a Sensitivity Analysis of
Spacing Accuracy”, 6
th
AIAA Aviation Technology, Integration and Operations Conference (ATIO), Wichita, Kansas, USA, September
2006.
[17] G. Van Baren , C. Chalon-Morgan, V. Treve, The current practice of separation delivery at major European airports, 11
th
USA/Europe Air
Traffic Management R&D Seminar, Lisbon, Portugal, June 2015.
[18] P.J. Green, B.W. Silverman. Nonparametric Regression and Generalized Linear Models, A roughness penalty approach, Eds. Chapman &
Hall/CRC, 1993.
[19] Reynolds, A., Richards, G., de la Iglesia, B. and Rayward-Smith, V. Clustering rules: A comparison of partitioning and hierarchical
clustering algorithms; Journal of Mathematical Modelling and Algorithms 5, 475–504 (http://dx.doi.org/10.1007/s10852-005-9022-1).
1992.
