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76:11 (2015) 131–139| www.jurnalteknologi.utm.my | eISSN 2180–3722 |
SECTOR COMPLEXITY MEASURES: A
Siti Mariam Abdul Rahmana*, Clark Borstb, Max Mulderb,
Rene van Paassenb
aFaculty of Mechanical Engineering, University Teknologi
MARA, 40450 Shah Alam, Selangor, Malaysia.
bControl and Operation Division, Delft University of
Technology, Delft, The Netherlands.
13 February 2015
Received in revised form
31 May 2015
30 June 2015
In developing a more advanced human-machine systems for future Air Traffic
Management (ATM) concepts requires a deep understanding of what constitutes operator
workload and how taskload and sector complexity can affect it. Many efforts have been
done in the past to measure and/or predict operator workload using sector complexity.
However, most sector complexity metrics that include sector design are calculated
according to a set of rules and subjective weightings, r endering them to be dependent of
sector. This research focuses on comparing the Solution Space Diagram (SSD) method with
a widely accepted complexity metric: D ynamic Density (DD). In essence, the SSD method
used in this research, observed aircraft restrictions and oppor tunities to resolve traffic
conflicts in bo th the sp eed and heading dimensions. It is hypothesized that the more area
covered on the solution space, that is, the fewer options the controller has to resolve
conflicts, the more difficult the task and the higher the workload experienced by the
controller. To compare sector complexity measures in terms of their transferability in
capturing dynamic complexity across different sectors, a human-in-the-loop experiment
using two distinct sectors has been designed and conducted. Based on the experiments, i t
is revealed that the SSD metric has a higher correlation with the controllers' workload ratings
than the number of aircraft and the un-weighted NASA DD metric. Although linear
regression analysis improved the correlation between the workload ratings and the
weighted DD metric as compared to the SSD metric, the DD metric proved to be more
sensitive to changes in sector layout than the SSD metric. This result would indicate that the
SSD metric is better able to capture controller workload than the DD metric, when tuning for
a specific sector layout is no t feasible.
Keywords: Air traffic control, sector complexity, solution space diagram
© 2015 Penerbit UTM Press. All rights reserved
Air Traffic Controllers (ATCOs) are responsible for the
supervision of a safety, efficiency and orderly flow of
air traffic. Current Air Traffic Control (ATC) uses
conventional technology (e.g., radar and Radio
Telephony (RT) communication) and little automation
support exists in supervising air traffic. Although more
aspects of air transportation are being automated
over time, the task of supervising air traffic is still
performed by human controllers and is therefore
limited by human performance constraints .
Without counter-measures, the rise in projected air
traffic  would inevitably result in a further increase
in the workload of Air Traffic Controllers (ATCOs). The
latter is often cited as one of the main impediments
to the growth of air transport [3,4,5].
Consequently, a more objective measure of sector
complexity is needed in order to determine the level
of task demand load imposed on the controller. In
order to successfully construct an objective measure,
a more comprehensive understanding of controller’s
task demand load, is required. A long and ongoing
research in this area suggests the importance of
132 Siti Mariam Abdul Rahman et. al. / Jurnal Teknologi (Sciences & Engineering) 76:11 (2015) 131–139
exploring ATC sector complexity in understanding its
relation to workload [6-10].
1.1 Taskload-Workload Relation
In normal ATC practice, there is a maximum number
of aircraft that can be contained simultaneously in
each particular sector. Whenever traffic demand
exceeds sector capacity, two solutions are available,
either more controllers can be assigned to the sector,
or a single sector can be divided into two or more
sectors, each of which is assigned to its own team of
controllers. These concepts of manageable number
of aircraft per sector will be less relevant with more
complex air-traffic situations. Thus, a need to forecast
complexity and a method to reduce complexity by
enabling varying degree of automation or assistance
provided to controller when an air-traffic situation
becomes more complex is foreseen.
Figure 1 Taskload and workload relation Hilburn and
A number of factors affect controller’s workload
including but not limited to airspace complexity,
traffic complexity, interface complexity and
controller’s level of skills and experience. To enable
air traffic growth while ensuring the safety of air
traffic, we need a better understanding of where the
workload comes from. There is one main distinction
generally made between task demand load (in this
paper referred to as ‘taskload') and mental workload
(in this paper referred to as ‘workload'). Taskload
refers to the objective demands of a task, whereas
workload addresses the subjective demand
experienced by the operator in the performance of
a task. In the effort to distinguish between taskload
and workload, Hilburn and Jorna  defined that
system-related factors such as airspace demands,
interface demands and other task demands
contribute to taskload, while operator-centered
factors like skill, strategy, experience and so on
determine workload. This is illustrated in Figure 1.
Also, perceived operator workload is highly
dynamic, thereby, it is not only dependent on
contextual factors (such as traffic state, weather
conditions, sector layout and etc.), but also
dependent on the operator's own actions. That is, an
operator can influence his own workload by the
decisions he makes and be totally unaware of how
he actually influenced his own future workload (or
task complexity). This conform to a study on
occurrences of Short Term Conflict Alert (STCA)
warnings, which highlighted that a large number of
these alerts do not occur in isolation, but were linked
to earlier alerts .
2.0 SECTOR COMPLEXITY MEASURES
In the effort to balance air traffic growth demand
and airspace capacity, describing airspace sector
complexity is indeed important. Many efforts have
been done in the past to measure and/or predict
operator workload using sector complexity [4,7,9,
13,14]. Measures such as counting the number of
aircraft, or Static Density (SD), which uses the number
of aircraft per-sector basis [4,7], in many experiments,
present the highest correlation with ATCO subjective
taskload ratings [9,10]. However, it has significant
shortcomings in its ability to accurately measure and
predict sector complexity [8,9] due to its inability to
illustrate sufficiently the dynamics of the behavior of
aircraft in the sector. Thus, the SD method alone is
unable to represent the maximum number of aircraft
that is manageable by a controller.
Another sector complexity measure such as the
Dynamic Density (DD) incorporates the dynamic
behavior of aircraft in the sector. The DD metric takes
into account “the collective effort of all factors or
variables that contribute to sector-level ATC
complexity or difficulty at any point of time" .
However, the calculation of the DD is based on the
weights gathered from regression methods on
samples of traffic data and comparing them to
subjective taskload ratings. As a result, the DD metric
represents a complexity measure that incorporates
both subjective and objective workload
measurements. The method is therefore both sector-
dependent and controller-dependent. However,
most sector complexity metrics that include sector
design are calculated according to a set of rules and
subjective weightings, rendering them to be
dependent of both sector and individual controllers.
Other notions of sector complexity measure using
visualization techniques have also been proposed
through complexity maps such as the Input-Output
(IO) approach by Lee et al. , the Lyapunov
Exponents (LE) approach by Puechmorel and
Delahaye  and a medium-term multi-sector
planning tool called the Tactical Load Smoother
(TLS), which was realized during the Programme for
Harmonised Air-Traffic Management Research in
Eurocontrol (PHARE) project . However, these
complexity maps all have the shortcomings of either
being controller dependent (IO approach) or both
controller and sector dependent (TLS tool approach)
or having a computational challenge (LE approach),
which is critical for application to high density
The long and still ongoing research attempts in this
133 Siti Mariam Abdul Rahman et. al. / Jurnal Teknologi (Sciences & Engineering) 76:11 (2015) 131–139
area confirm the importance of exploring ATC sector
complexity metrics in understanding its relation to
ATCO workload. Clearly, there is a need for an
objective metric that can be used to predict
taskload in a controller-independent fashion, and
also that can be used to compare the complexity of
sectors in a quantitative way.
3.0 SOLUTION SPACE DIAGRAM APPROACH
In this paper, approach based on the investigations
of problems using the solution space based analysis
was incorporated. Initial work by Van Dam et al. 
has introduced the application of a Solution Space
Display in aircraft separation problems from the pilots'
perspective. Hermes et al. , d'Engelbronner et al.
 and Mercado Velasco et al.  then continued
the idea of using the Solution Space in aircraft
separation from the perspective of the ATCO. A high
correlation was shown to exist between derived
metrics from the Solution Space, and the subjective
workload reported by ATCOs [17,18]. This research will
continue expanding the Solution Space by utilizing
the solution space method in sector complexity
exploration and also relating workload to sector
Figure 2 The example of SSD unsafe area. (a) SSD with
multiple no-go beams. (b) The unsafe area (Awhole).
This paper investigates whether the solution space
area of a two-dimensional ATC separation problem
can be used to assess the inherent difficulty of ATC
situation more accurately and objectively than
current metrics. The metrics based on the SSD
method consider the SSD area percentage measures
(both individual and/ or average SSD area
properties) in order to quantify the level of sector
complexity. Figure 2 (a) illustrates an example of the
SSD of an aircraft, with seven other aircraft within the
area. The unsafe area within minimum and maximum
velocity-heading band of the respective aircraft
(such as in Figure 2 (b)) is referred in this paper as
Awhole. It defines all possible velocity vectors for the
controlled aircraft that could lead to future
separation violation. Another area property
investigated is the mean area affected (Am ean). The
Amean percentage affected is the Atotal affected for
all aircraft in the sector divided by the number of
aircraft. This will give an overview of the complexity
metric for the whole sector.
To more thoroughly investigate the applicability and
potential advantages of the SSD metric, it is crucial to
compare it with a widely accepted complexity
metric: DD. In this paper, the number of aircraft and
the DD metric are compared to the SSD metric in
terms of their correlations to controller workload.
As the study described in this paper relies on
correlation analysis between the controller's
workload ratings with the complexity metrics, the first
step includes collecting subjective workload ratings
throughout the experiment at regular time intervals to
capture a workload profile for each controller.
Secondly, based on the recorded aircraft
parameters, such as such as position, speed, and
heading, the SSD and un-weighted DD metrics can
be computed after a run. Linear regression analysis
will then be performed to gather weighting
coefficients corresponding to a number of Dynamic
Variables (DV) to produce the weighted NASA DD
metric that improves the correlations per individual.
With all the information gathered, the comparison
study between the number of aircraft and also both
the un-weighted and weighted NASA DD with the
SSD can be facilitated.
4.1 Subjects And Tasks
In the experiment, the participating eight male
subjects with age between 29 and 51 (μ = 35.63, σ =
8.18), have all received an extensive ATC
introductory course. As such, all subjects have a
similar basic experience level in ATM. The subjects
were instructed to clear aircraft to their designated
sector exit points and keep aircraft separated by at
least 5 NM.
All traffic was situated at FL290 and the function to
change the altitude of aircraft was not enabled.
Thus, the participants could only use heading and/or
speed clearances to control aircraft. To support the
controllers in their task, aircraft were color coded to
indicate their course deviations and when they were
in conflict. The unselected aircraft, which were
headed towards their assigned exit point, were
colored in green, whereas unselected and deviating
aircraft were colored in gray. Further, a selected
aircraft was colored in white and would display an
inner circle, indicating the 5 NM protected zone, and
a green circle that indicated the current speed and
a magenta circle and line, indicating the intended
speed and heading clearance (Figure 3 (b)). In safely
separating aircraft, a predicted loss of separation
within 3 minutes (simulated-time) would trigger an
aural alert and the involved aircraft in the conflict
would be colored in red. Figure 3 shows an example
of the simulator presented to the subjects.
Only aircraft, which were inside the controlled
134 Siti Mariam Abdul Rahman et. al. / Jurnal Teknologi (Sciences & Engineering) 76:11 (2015) 131–139
sector, could be given a speed and/or heading
command. To control an aircraft, subjects first had to
select an aircraft. Then, by dragging the heading line
with the mouse to a new heading and/or scrolling
the mouse scroll wheel up or down for speed
change, the state of the aircraft could be changed.
To confirm and implement a speed and/or heading
change, the enter key had to be pressed.
Figure 3 (a) Experiment Simulator. (b) Aircraft control area.
During the experiment, the participants were asked
to rate their perceived workload every 60 seconds.
An automated stimulus provided a scale on the
display that triggered the participants to rate their
workload by means of clicking between 0 (low
workload) and 100 (high workload). A mouse click on
a scale that appeared on the same display (Figure 3)
is presumed to provide subjects with a more direct
and less intrusive workload rating measure than
typing a number on a keyboard. The scale is also
much finer grained, allowing the slightest change in
workload to be captured.
4.2 Complexity Measures
The complexity measures consisted of two DD metrics
and the SSD area metric. Both DD metrics were
measured every 60 seconds to match with the
workload rating instances. The first DD metric, NASA
DD Metric 1 (NASA1) is based on research
conducted by Chatterji and Sridhar . For further
details on the Dynamic Variables (DV) and
calculation methods, readers are encouraged to
refer to Chatterji and Sridhar . The metric consisted
of 16 DV and it is calculated as follows:
DD = WiDVi
The second DD metric, NASA DD Metric 2 (NASA2)
calculation based on research by Laudeman et al.
 and Sridhar et al. . For further details on the DV
and calculation methods, readers are encouraged
to refer to Laudeman et al.  and Sridhar et al. .
The metric consisted of 8 DV, excluding traffic density
(TD) and it is calculated as follows:
DD = WiDVi
The original NASA DD metrics represented in
previous researches [6,7,8] were constructed based
on a 3-Dimensional (3D) airspace model. In gathering
airspace and traffic factor to produce NASA DD
metrics from a 2-Dimensional (2D) airspace model as
used in this research, several DV were canceled out
from both NASA1 and NASA2 metric. These DV are
relevant to changes in altitude measures (DV 2 and
DV 4 for NASA1 metric and DV 3 for NASA2 metric)
and also related to vertical proximities (DV 8, DV 9
and DV 10 for NASA1 metric).
The SSD area properties were calculated using the
mean of SSD area (Amean) of all aircraft within the
sector (referred in this paper as SSD). It is gathered
using the following equation with Awhole representing
the total area within minimum and maximum
velocity-heading band of each individual aircraft
within the sector and n being the number of aircraft
within the sector. The SSD area properties were
measured every 60 seconds to match with the
workload rating instances.
135 Siti Mariam Abdul Rahman et. al. / Jurnal Teknologi (Sciences & Engineering) 76:11 (2015) 131–139
Amean = 1
4.3 Sector Layout
The experiment scenarios were constructed based
on the ‘clearance to exit point task' with one type of
aircraft on one flight level. There were three streams
of incoming aircraft entering the sector. Apart from
these three main similarities in sector designs, a
number of differences were designed in both sectors
in order to produce two different sectors. This is
crucial in order to be able to test the metrics
sensitivity to sector design. Figure 4 shows an
example of the two sector designs used in this
The sector design variables can be observed from
Figure 4 and the settings are detailed as follows:
1. Sector 1 has three crossing points, while Sector 2
has two crossing points.
2. Sector 1 has mixed combinations of the intercept
angle of traffic routes of approximately 45°, 90°
and 120°. Whereas Sector 2 has two
approximately 90° crossing angles.
3. The two sectors had a different pattern in crossing
point clusters. That is, Sector 1 had more clustered
crossing points near the sector border, whereas
Sector 2 had a less clustered intersection points
with the two crossing points having ample
spacing between them.
4. Both sector also had a different pattern in the
clustering of entry and exit points. Sector 1 has all
exit points on the right hand side of the sector,
whereas Sector 2 has entry and exit points at both
sides of the sector.
5. Different sector shapes were designed for both
sectors. Sector 1 has a more odd polygon shape,
whereas Sector 2 has a more regular polygon
6. The two sectors had different sector area
properties. Sector 1 has an area of approximately
30% less than Sector 2. Sector 1 has a total area of
7000nm2, whereas Sector 2 has a total area of
Figure 4 Sector design and the traffic flow assignment
5.0 RESULTS AND DISCUSSION
5.1 Un-weighted Correlation Analysis
The analysis of un-weighted NASA DD metrics was
made based on the assumption that all DV weighting
coefficient are equal and were all assigned as 1. The
un-weighted NASA DD metrics in this section were
calculated using Equation (1) and (2).
Based on the results of the correlation analysis
between workload rating and sector complexity
measures, SSD showed the highest correlation with
workload rating. Average number of aircraft is
second in line as a good sector complexity measure
which demonstrates that indeed the number of
aircraft is one of the most important sector
complexity variable that in influences controller's
(a) Sector 1
(b) Sector 2
136 Siti Mariam Abdul Rahman et. al. / Jurnal Teknologi (Sciences & Engineering) 76:11 (2015) 131–139
(a) Sector 1 (b) Sector 2
Figure 5 Un-weighted NASA1 based on different sectors
(a) Sector 1 (b) Sector 2
Figure 6 Un-weighted NASA2 based on different sectors
(a) Sector 1 (b) Sector 2
Figure 7 SSD area properties based on different sectors
Figure 5, 6 and 7 showed plots of un-weighted NASA
DD and SSD metric compared to workload rating
based on number of aircraft, respectively. The plots
were intended to illustrate how workload ratings
behave towards number of aircraft and also how un-
weighted NASA DD and SSD metric behave in
responds to the same number of aircraft.
Based on Figure 5, NASA1 plots did not show a
pattern that is closely related to workload rating.
Other sector complexity measures such as NASA2
(Figure 6) and SSD (Figure 7) showed a more
resembling pattern that of the workload rating.
5.2 Weighted Correlation Analysis
In this section, the un-weighted NASA DD metric were
fixed to the workload rating data, using the linear
regression method, resulting in a fitted weighted
NASA DD metric. In principle, the weighted NASA DD
metric should correlate better than the un-weighted
137 Siti Mariam Abdul Rahman et. al. / Jurnal Teknologi (Sciences & Engineering) 76:11 (2015) 131–139
ones. The regression analysis was conducted based
on different sector. This is done in order to investigate
whether the weighted NASA DD metric is consistently
better than the SSD regardless of different sector.
Also, in the subsequent section, analysis on the
transferability of the weighted NASA DD metric across
different sector design.
First, linear regression analysis were conducted on
the basis of different sectors. Based on the analysis, a
number of significant variables were identified.
Variables that computed regression weights were
small and non significant were removed from the
equation that was used to compute the end DD. The
weighted NASA DD metrics were constructed based
on the coefficient individual contribution (b-value),
representing the weighting factor for each DV. By
replacing the significant b-value into equation (1)
and (2), the NASA DD model can be defined as
follows with the corresponding DV detailed in earlier
1) Sector 1:
NASA11.134 1.191*DV10.738 *DV 37.301*DV 60.534 *DV11 0.0003*DV 14
1.189 *DV15 0.0003 *DV 16
NASA2 0.466 0.111*DV10.111 *DV 20.023 *DV 5TD
2) Sector 2:
NASA1 0.761*DV 39.902*DV 53.043 *DV 61.750 *DV 7
NASA2 0.844 0.098 *DV10.036 *DV 50.012 *DV 6TD
For both sectors, the NASA1 DD metric are defined
as having different significant DV, which are included
in the end DD equation. In Sector 1, the significant
DV are focused more to the variables related to
aircraft horizontal proximity (DV 6), speed (DV 14 and
DV 15) and intercept angle (DV 16), whereas in
Sector 2, only variable concerning horizontal
proximity (DV 5 to DV 7) are found to be significant. It
is also concluded that the number of aircraft has
shown a significant effect for Sector 1, but not in
For the NASA2 DD metric, the speed change
variable (DV 2) showed to be significant in Sector 1,
but not in Sector 2. However, in both sectors, variable
concerning heading change (DV 1) and horizontal
proximity (DV 5) were found to be significant.
Differences in variables that influence the NASA DD
model for both sector showed that different sector
design demand for different weighted NASA DD
The correlation between the resulting weighted DD
and workload rating were gathered again using
Kendall's tau correlation coefficient. Based on the
result, NASA1 for Sector 1 and NASA2 for Sector 2
have higher correlation than SSD. It is observed that
weighted NASA1 showed an increase in correlation
on both sector if compared to un-weighted NASA1.
However weighted NASA2 showed a lower
correlation in Sector 1 and a higher correlation in
Sector 2 compared to un-weighted NASA2.
(a) Sector 1 (b) Sector 2
Figure 8 Weighted NASA1 based on different sectors.
138 Siti Mariam Abdul Rahman et. al. / Jurnal Teknologi (Sciences & Engineering) 76:11 (2015) 131–139
(a) Sector 1 (b) Sector 2
Figure 9 Weighted NASA2 based on different sectors.
Figure 8 and 9 showed weighted NASA DD with
workload rating also against the number of aircraft.
This can be compared with the initial un-weighted
NASA DD from Figure 5 and 6 where the plots of
weighted NASA1 and NASA2 have improved to a
plot that better matches the workload rating in Figure
8 and 9.
5.3 Cross-Sector Transferability
In addition to the weighted NASA DD analysis, to
demonstrate that the weighting coefficient only
serves a certain sector, a cross analysis of NASA DD
metric between different sectors was carried out.
Cross-sector analysis was conducted by applying the
weighting coefficient gathered in Sector 1 to Sector 2
and vice versa. Based on the analysis, only NASA2 for
Sector 1 showed a higher correlation level than the
original correlation value. Others showed lower
correlation level. However, both NASA1 and NASA2
showed lower correlation than SSD metric sector
This paper compares the proposed metric, SSD with
known metrics such as the number of aircraft and
NASA DD metric gathered from research by
Laudeman et al. , Sridhar et al.  and Chatterji
and Sridhar . Multiple scenarios from two different
sectors were presented to the subjects with varying
incoming traffic sequences. This is to avoid scenario
recognition during the course of the experiment.
Analysis with regards to subject's behavior and
workload rating were initially conducted to observe
whether both sectors represent two sectors of
different complexity, which would enable cross-
sector transferability investigation on sector
complexity measures. It is gathered that both sector
indeed represent different levels of complexity,
based on significant differences gathered from both
subject's behavior and workload rating. It is also
gathered that the number of aircraft present in a
sector does not need to constitute the main factor
that determines controller workload. Other sector
complexity influencing variables, such as sector
volume, route design and also geographical location
of intercept points also contribute to the effect on
how much effort was needed to control the sector.
This is consistent with the concept of having different
maximum number of aircraft per sector basis.
Initial correlation analysis were conducted to
compare the SSD metric and un-weighted NASA DD
metric towards workload rating. The analysis is aimed
at having a neutral comparison between both un-
weighted NASA DD and the SSD metric without the
influence of any post-processing procedures. It is
observed that based on initial correlation analysis,
SSD is shown to have a higher level of correlation
than un-weighted NASA DD metric and number of
aircraft. This is found in analysis based on different
Weighted NASA DD metrics from a collection of
significant DV coupled together with weighting
coefficient were gathered through regression
analysis. Different sets of DV used to construct NASA
DD metric for different sector, were an indication of
differences in controller's strategy in handling traffic
within a sector. Thus, controller's individual differences
would highly influence the construction of the DD
metric. An improved correlation between weighted
NASA DD and workload rating were gathered
compared to un-weighted NASA DD. However, when
compared to SSD metric, only some weighted NASA
DD metric showed a better correlation than SSD
metric with workload rating.
It has been observed that when transferring a
certain NASA DD model to a different sector, it has
resulted in the metric not delivering the same level of
correlation as previously found. The cross-sector
analyses also reveal that both NASA DD metrics is
sensitive towards different sector.
The original NASA DD metric was constructed
based on a 3D airspace model with traffic samples
from 36 high and low sectors, respectively. Due to the
extent of data used in producing the metric, it is
139 Siti Mariam Abdul Rahman et. al. / Jurnal Teknologi (Sciences & Engineering) 76:11 (2015) 131–139
assumed that the NASA DD metric should be robust
enough to be used on other traffic samples.
However, the fact that the linear regression analysis
to produce the weighted NASA DD metric in this
experiment was gathered based on 2D airspace
model using limited number of participants over a
large number of variables, there could always be a
possibility of the model being overfitted and in the
end produce a poorer predictive performance.
Exaggeration of minor fl uctuations in the data could
have deteriorated the method's performance.
Nevertheless, the NASA DD metric should not be too
sensitive to a specific sample size and should perform
well on any sector design.
This paper presents the result of the investigation of
whether the SSD indeed presents a more reliable and
objective sector complexity measure as it managed
to show the same level of correlation under various
sector designs settings. Comparisons between
proposed SSD metrics and other known sector
complexity measures, namely the number of aircraft
and DD were conducted. From the experiment, it is
concluded that the proposed method indeed
represents a reliable and objective sector complexity
measure, which could function better than number
of aircraft, un-weighted NASA DD metric and in
certain conditions, than the weighted NASA DD
metric. The SSD metric, which can be use in real-time
situation without any post-processing procedures
also, appeared to be less sensitive than the NASA DD
metric, towards controller differences as to sector
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