ENRI Int. Workshop on ATM/CNS. Tokyo, Japan. (EIWAC 2010)[EN­029]Fluctuation Scaling in the Air Traffic Controller
Communication Activities+★

Yanjun Wang★*, Minghua Hu★, Vu Duong*Nanjing University of Aeronautics & Astronautics, Nanjing, China

Telecom-ParisTech, Paris, France*
EUROCONTROL, Bretigny-sur-Orge, France{yanjun.wang.ext, vu.duong}@eurocontrol.int

Abstract: In this paper we report the phenomenon of fluctuation scaling in air traffic controller communication activities.
Taylor’s power law has long been observed in a wide range of disciplines, ranging from ecology through physics to socialscience, to characterize the fluctuation scaling of the system. In ATM system, which is a typical human-centered system,
controller communication activities play a vital role in system’s safety and efficiency. We analyze controller communication
activities from a complex system point of view: ATCOSIM controller communication data has been analyzed with a humandynamics approach and the result shows that the variance of the controller’s communication activities has a linear
relationship with the average of the activities, which can also be described as Taylor’s power law with the exponent α = 1 .
The ensemble fluctuation scaling found here may help a better understanding the dynamics of ATM system, so that to close
the gap between the physical part and human part of ATM complex system.
Keywords: human factors; air traffic controller; fluctuation scaling; Taylor’s power law
describe the mental cost of the controller to accomplish theATC tasks, it is still unable to be predicted due to its
unknown dynamic property [1]. In ATM system, voicecommunication was the primary means used by controller,
to control air traffic prior to the emerging of digital data
communication between controller and aircraft, i.e.
Controller Pilot Data Link Communication (CPDLC).
However, it is still the only channel for information flow
between pilots and controllers in most control centers.
Under such circumstance, controller voice communications
activities still have direct impact on the whole systemevolution. In the past, communication events wereextensively used to measure workload [2-4]. We assume
that the communication activity encapsulates both cognitiveefforts and physical efforts of the controllers to accomplish
the mission of ensuring traffic safety and efficiency.
Therefore, the analysis of the controller communication
activities is of great importance.

1. INTRODUCTION
Air Traffic Management (ATM) system has been
progressed with the introduction of new technologies
together with the enhancements from the methods
employed by the operators, the air transport system hassignificantly improved its capability, safety and efficiency.
But how to meet the continuous growth of traffic demand
however is still an urgent and practical task being faced by
the researchers and the engineers of the field. Thetechnologies and the methodologies not only improve thesystem capability but also increase the system complexity.
Large number of parts of the system being interconnected
keeps the structure of the whole system unportrayable.
Prediction and control of the system is quite difficult due tothe linear or non-linear interaction between the elements.
For instance, although the local sector behavior may beclear, the global picture of the system could be still
unknown. The understanding of the mechanism by which
the ATM system evolves has becoming the central questionof this field.

One may think that it is impossible to develop a generalmodel of controllers communications due to the uniquesector structure, the dynamical changed traffic, and theindividual knowledge and experience. Our analysis here
presents that the intellectual challenge could be the physicalunderstanding of the rules by which the air traffic controller
control the traffic. A few qualitative mechanisms used by
the controller to mitigate cognitive complexity have beenfound in [5]. In the other fields, the quantitative study ofhuman has discovered amazing results on human activities.
Instead of the presumed randomly occurred human actions,
there is increasing evidences showing that there exist

Modeling the ATM system from a complex systemapproach may be an efficient way to analyze the wholesystem and the subsystems. The air traffic controller is themain human part of the system, whose behavior has direct
influence on the system performance. As an important partof the ATM system, air traffic controller has been long wellstudied . Efforts have been made into the understanding of
the workload and taskload of the controllers. Although
workload metric is widely used in many ATC centers to143

Y. Wang, M. Hu, and V. Duongthe database. Because the simulations took place more thanten years ago, it is impossible to find the information on
traffic and airspace corresponding to the communicationdata.

similar activity patterns among human daily activities,
includinghumancorrespondences[6] ， emailcommunication [7], human printing behavior [8], and online
films rating[9], and human mobility [10]. These findings
suggest that there is a universal law that governs humanactivities[11].

The general information of the whole fifty exercises isshown in table 1. We still have the detailed information oneach exercise, while it is not given here.

Besides the human system, the Taylor’s power law has been
observed in many natural and human-driven systems,
ranging from ecology system through stock market tohuman dynamics, characterizing the fluctuation scaling
property of the system. The Taylor’s power law is named
after L. R. Taylor in recognition of his paper in 1961 [12].
Taylor’s law can be applied to describe many complex
systems in characterizing the relationship between thefluctuation in the activity of an element and the average
activity. The relationship is usually in the following from:

Table 1 Information on the 50 exercises in the ATCOSIM database
TOTAL

AVERAGE

Length of the exercise ( hh:mm:ss )59:18:37

1:11:10

Number of the flights (complete flights*)
identified in the exercise

3121(1966)

62.42 (40)

Number of the communication events(Unidentified) in the exercise

10078(1276)

201.56 (26)*Complete flight is the flight that receives both hand-in message andhand-out message.

fluctuation ≈ const. × averageα , where α ∈ [1/ 2,1]
Based on the data over which the averages are taken, theTaylor’s power law can be grouped into two categories:
Temporal Fluctuation Scaling (TFS) and Ensemble
Fluctuation Scaling (EFS) [13]. Models for the explanationof the origins of Taylor’s power laws can be found in [14],in this paper we report the ensemble fluctuation scaling in
the controller’s communication activity.

2.2 Definition
Communication activity is defined as the event that
controller press the push-to-talk button and hold in order tosend the transmissions to aircraft, disregarding the contentsof the transmissions. Particularly, each utterance in theATCOSIM data is a single communication eventrepresenting a complete communication activity. Emptytransmission is also seen as the complete communicationactivity.

The rest of the paper is organized as following: Section 2gives a description of the communication data on which wehave investigated, followed with the method with which wemanipulate the data. Section 3 shows the empirical resultsof the ensemble fluctuation scaling in the controller
communication activities. Possible explanation of thephenomena is also discussed. The paper ends withconclusion remarks in Section 4.

The purpose of this paper is to examine the ensemblefluctuation scaling in the controller communicationactivities. One may naturally relate the communication
activities to the traffic activities. A flight will receive atleast two messages (hand in and hand out) from thecontroller when it traverses the sector. The more flights
enter the sector, the more communication activities shouldbe. Of course, communication activities will fluctuate
according to the traffic situation. We simplify traffic
activity here as the cumulative number of the flights
entering the sector. The more communication activities aremade, the more fluctuation should be.

2. METHOD
2.1 Controller’s communication data
The controller communication data used in this study isfrom the ATCOSIM Air Traffic Control Simulation Speech
corpus of EUROCONTROL Experimental Centre. The aimof the ATCOSIM is to provide a speech database of
non-prompted and clean ATC operator speech. It consists often hours communication data, which were recorded during
ATC real-time simulations[15]. These simulations wereconducted between 20/01/1997 and 14/02/1997, with theaim to evaluate the concept of RVSM (reduced VerticalSeparation Minimum) in Europe. For the purpose ofATCOSIM, only controllers’ voice was recorded andanalyzed. Considering the traffic initialization phase withlittle speech, the first half-hour of traffic was not recorded.
Hence, each record consists of circa one hour ofcommunication data. Both speech signal data andtranscription of the utterance, together with the complete
annotation and meta-data for all utterances, can be found in

2.3 Data processing
In order to correlate the communication activities andtraffic activities, it is essential to acquire the traffic
information associated with the communication data.
According to the regulation of controller-pilot voicecommunication, both the flight call-sign and the types of
the communication could be identified based on theanalysis of the content of the speech data. Unidentified
communication events are labeled with empty flight number.
Two important types of the communication are also
identified: hand-in and hand-out. The hand-incommunication to the flight indicates that and this time theflight enters the sector, while the hand-out communication
gives the time of the flight leaves the sector. Flights withboth hand in communication and hand out communication

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(EIWAC 2010)

are the complete flights. There is around 10% of thecommunication events are labeled with empty flightnumber.

3. EFS in ATCO communication
3.1 Ensemble Fluctuation Scaling
We note that each exercise consists of different amount ofthe traffic. The minimum number of the flights in theexercises is 44 in the exercise GM2_01, while themaximum number of the flights is 73 in ZF2_05. In orderto calculate the mean and the standard deviation of thecommunication activities, we set the exercise start time as
the start point and the algorithm will terminate when thenumber of the flights reaches 44. In the Fig. 2, we show theempirical results on the number of the communication
activities with the number of the flights. As can be seenfrom the figure, both the average and the standard deviationof the communication activities grow quickly as the numberof the flights increases.

In order to illustrate the procedure of the calculation of thecommunication activities, we first define the followingterms.
F : Set of the flights that have entered the sector.

Lf : List of the flight call-signs decoded from thecommunication events. The call-signs are arranged inexactly the same order as the communication events. It
should be mentioned that empty flight call-sign has also
been included.
C : Set of the cumulative number of the communication
events. It has the same size as F . C (i ) is the number ofcommunication events when there have been i flights
entered the sector.

180

q : The cumulative number of the communication events;

160
Number of the communication events

m : The number of the flights in F .
We then present in Fig. 1the skeleton of the algorithm forthe computation of the number of the communication
events associated with the number of the flights haveentered the sector in each exercise.
Step 1. Set the start point s and the end point e .

m = 0, q = 0. F = ∅14012010080604020

Step 2. Calculate m and C based on the time sequence ofthe flight call-sign.

005

10152025
Number of the flights

30354045Fig. 2. Results on the number of the communication activities associatedwith the number of the flights have entered the sector (50 exercises). Eachmarker stands for the cumulative number of the communication activities
correspond to the number of the flights. Errorbar shows the average of thenumber of the communication activities and the standard deviation of thedata.

FOR i=s : eIF Lf (i) ≠ ∅ & &Lf (i) ∉ F

m = m + 1;
q = q + 1;
F = F ∪ {Lf (i )};We then plot the standard deviation according to theaverage of the communication activities in the Fig. 3 (a).
Solid line is the linear fit of the empirical data. The residual
shown below indicates the linear fitting is applausive.
Hence, the standard deviation of the activities and theaverage activities has a clear Taylor’s power low
relationship with α = 1 .

IF m > 1 ,C (m − 1) = q;
END;
ELSE

q = q + 1;
END;
i = i + 1;
END

C (m) = q
Step 3. Output the result.
Fig. 1. The scheme for the computation of the number of thecommunication events and the number of the flights entered the sector.

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Y. Wang, M. Hu, and V. Duong
Hence, following the last paper [16] we study thedistribution of the number of communication events of eachflight. The percentages of the flights as the function of thenumbers of communication events in each exercise areplotted in the Fig. 4.

a25

STD

20y = 0.14*x + 0.7

151050020

40

60

80

10012014080

100120140

While we were expecting that the curves of each line could
be collapsed into a single one, however, the unknown
airspace configuration and the traffic distribution make it
impossible to scale the obtained results. The shapes of thecurves differ from each other (see “All the 50 Exercises”).
According to the horizontal position of the climax of thecurve, we classify all the 50 exercises into three groups:
Group 1, Group 2, and Group 3. After categorization, thecurves in the same group vary similarly. The difference
between the shapes of the curves in three groups may result
from the different types of the sectors simulated: en routesectors, approach sectors, and the approach sectors withflying over route. More information is needed to formulate
the distribution function of the communication events andto explain its association with the EFS found in this paper.

Meanb21.5
10.5
0-0.5-1-1.5-2020

4060

Fig. 3. Empirical results of the fluctuation scaling in the communication
activities.

3.2 EFS and communication activities distribution
If we know the statistical characteristic of thecommunication activities on each flight, then it will beeasier to formulate the reasonable explanation of the originsof the EFS in the communication activities.

All the 50 Exercises

Group 1 (29 Exercises)

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

02

4

68

10

1202

14 15

4

Group 2 (17 Exercises)

68

10

12

14 15

Group 3 (4 Exercises)

0.5

0.4

0.4

0.3

0.3
0.2
0.2
0.1

0.1
02

3

4

5

6

78

902

103

4

5

6

78

Fig. 4. The percentages of the flights as the functions of the numbers of messages received by the flight (complete flights). Vertical axis is the percentage ofthe number of the flights, while the horizontal axis is the number of the communication events involved by the flight. Different colored maker stands for thedifferent exercise.

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ENRI Int. Workshop on ATM/CNS. Tokyo, Japan. (EIWAC 2010)

4. CONCLUSION
The analysis from ATCOSIM data shows that with theincreasing number of flights entering sector, both the mean
and the variance of the controller communication activities
grow, with a power law ( α = 1 ) relationship between thetwo quantities. Validation will be made by the use of othersimulation or operation data before the claim of theTaylor’s power law in the controller communication
activities.
In a recent paper, the authors propose the universal
mechanism underlying the Taylor’s law observed indifferent scientific disciplines. They show that the law
results from the density of state function characterizing theconsidered system [14]. If the validation of the EFS in thecontroller communication activities from the othersimulation or operation data is acceptable, then it will be ofgreat value to investigate the mechanism behind thephenomenon.

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U. Harder, and M. Paczuski, “Correlated dynamics in humanprinting behavior,” Physica A: Statistical Mechanics and itsApplications, vol. 361, no. 1, pp. 329-336, 2006.

[9]

T. Zhou, H. Kiet, J. B. Kim et al., “Role of activity in humandynamics,” EPL, vol. 82, no. 28002, 2008.

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M. C. Gonzalez, C. A. Hidalgo, and A.-L. Barabasi, “Understandingindividual human mobility patterns,” Nature, vol. 453, no. 7196, pp.
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[11] A.-L. Barabasi, “The origin of bursts and heavy tails in humandynamics,” Nature, vol. 435, no. 7039, pp. 207-211, 2005.
[12] L. R. Taylor, “Aggregation, Variance and Mean,” Nature, vol. 189,no. 476, pp. 4, 1961.
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5. ACKNOWLEDGMENTS
The authors would like to acknowledge Mr. Horst Hering
for the providing of the ATCOSIM corpus database.

[15] H. Hering, Technical analysis of ATC controller to pilot voicecommunication with regard to automatic speech recognition system,
EEC Note N. 01/2001, EUROCONTROL Experimental Centre,Paris, France, 2001.

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7. COPYRIGHTThe authors confirm that they, and/or their company orinstitution, hold copyright of all original material includedin their paper. They also confirm they have obtainedpermission, from the copyright holder of any third party
material included in their paper, to publish it as part of theirpaper. The authors grant full permission for the publicationand distribution of their paper as part of the EIWAC2010
proceedings or as individual off-prints from theproceedings.

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