Physica A 441 (2016) 151–157 Contents lists available at ScienceDirect Physica A journal homepage: www.elsevier.com/locate/physa Human activity under high pressure: A case study on fluctuation scaling of air traffic controller’s communication behaviors Yanjun Wang a,b,∗ , Qiqian Zhang a,b , Chenping Zhu c , Minghua Hu a,b , Vu Duong d a College of Civil Aviation, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, PR China b National Key Laboratory of Air Traffic Flow Management, Nanjing 210016, PR China c College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, PR China d John von Neumann Institute - Vietnam National University, Ho Chi Minh City, Viet Nam highlights • • • • • We perform fluctuation scaling analysis of air traffic controllers’ communications One real operational dataset and one real-time training dataset were investigated We found controller’s communications behavior follows Taylor’s power law The scaling exponent found in operational data is larger than that in training data Human dynamics under pressure is more likely dominated by the exogenous force article info Article history: Received 25 August 2014 Received in revised form 26 May 2015 Available online September 2015 Keywords: Fluctuation scaling Air traffic control Taylor’s law Human dynamics ∗ abstract Recent human dynamics research has unmasked astonishing statistical characteristics such as scaling behaviors in human daily activities However, less is known about the general mechanism that governs the task-specific activities In particular, whether scaling law exists in human activities under high pressure remains an open question In air traffic management system, safety is the most important factor to be concerned by air traffic controllers who always work under high pressure, which provides a unique platform to study human activity Here we extend fluctuation scaling method to study air traffic controller’s communication activity by investigating two empirical communication datasets Taken the number of controlled flights as the size-like parameter, we show that the relationships between the average communication activity and its standard deviation in both datasets can be well described by Taylor’s power law, with scaling exponent α ≈ 0.77 ± 0.01 for the real operational data and α ≈ 0.54 ± 0.01 for the real-time training data The difference between the exponents suggests that human dynamics under pressure is more likely dominated by the exogenous force Our findings may lead to further understanding of human behavior © 2015 Elsevier B.V All rights reserved Corresponding author at: College of Civil Aviation, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, PR China E-mail addresses: ywang@nuaa.edu.cn (Y Wang), zhangqq@nuaa.edu.cn (Q Zhang), oldpigman1234@126.com (C Zhu), minghuahu@nuaa.edu.cn (M Hu), vu.duong@jvn.edu.vn (V Duong) http://dx.doi.org/10.1016/j.physa.2015.08.040 0378-4371/© 2015 Elsevier B.V All rights reserved 152 Y Wang et al / Physica A 441 (2016) 151–157 Introduction Scaling behavior is thought to be one of the hallmarks of a complex system, indicating that no characteristic scale dominates the dynamics of underlying process In the past few decades, considerable work has been contributed to the study of scaling behaviors emerged from various fields, ranging from biology, through economic systems to human social activities [1–5] Human as the most complex one exhibits this astonishing phenomena at different scales as well, deep down from cell activities and DNA behavior, up to social activities Given the importance of human activities, research from biology, cognitive science, and brain science has long sought to explain the underlying mechanisms from different perspectives [6] Recently, there is a surge of reports on human dynamics which have uncovered regular patterns of human communications and other interactive activities, patterns that are characterized with heavy-tailed, power-law distributions instead of ever-belief Poisson-like random distributions [7–15] Several kinds of mechanisms have been suggested to explain the mechanisms which govern human activities, including priority based queuing processes when human execute tasks [7], interests driven human behavior [16], cascading non-homogeneous Poisson process with circadian cycle [10], and the combination of Poisson processes and decision-based queuing processes [13] Quantitative assessments from the circulations of bank notes and investigations on mobile phone datasets have found that the human trajectories in daily activities show a high degree of temporal and spatial regularity Models based on Lévy flights and Random Walk have been developed to explain the mechanisms which can lead to the scaling law of human trajectories [17–21] It should be noted that all the above examined data are got from deliberate human activities Unfortunately, there are few evidences from a task-specific activity, for instance, the logistics operation [22], to support the universal mechanisms governing the instinct nature of human activities Particularly, human operators in the safety-crucial complex systems, such as air traffic controllers, usually work under heavy pressure, and they are requested to give correct responses promptly to any change of system states In contrast to the routinized behaviors, they are clearly aware of the purposes of their actions since any error or failure may result in the loss of life or property Data limitations used to hinder the efforts to systematically analyze their activities across a wide range of fields In air traffic management system, however, we are able to record air traffic controller’s communication activities Statistical physics has been applied to air traffic control field to understand the underlying dynamics of the system [23–25] Previous study has shown that air traffic controller’s communication activities exhibit heavy-tailed feature, with inter-communication times characterized by inverse Gaussian distributions [26] Due to the heterogeneous working environments, the universal mechanism of air traffic controller remains unknown To further investigate controller’s behavior, we turn to the method of fluctuation scaling Human, like many dynamical systems, is subject to stochastic perturbations, therefore exhibits fluctuations It is believed that fluctuations reflect functional states of the system, providing important clues to the underlying dynamics Complex fluctuation scaling phenomena have been observed in many systems, ranging from ecology [27–31], river flow [32], through human gait [33,34], electroencephalogram [35], and musical rhythms [36,37] to financial markets [38–42], urban transportation systems [43–45], and social activities [4,46] Taylor’s power law has been applied successfully to various complex systems to characterize the relationship between the fluctuations in the activity of an element and the average of the activity [27] The relationship can be described as fluctuation ≈ ⟨average activities⟩α The origin of fluctuation scaling is becoming increasingly of interest to the statistical physicists [47–49] Our primary interest here is to investigate the adaptive behavior of controllers through the study of the fluctuations of their communications In this paper, we performed the standard ensemble fluctuation scaling analysis on two empirical datasets by defining the number of controlled aircraft as the size-like parameter Analytical results show that air traffic controllers’ communication activity exhibit fluctuation scaling phenomena We found that the scaling exponent in the real operational dataset is larger than that in the simulation dataset, which suggests that human activity under pressure is more likely to be dominated by the exogenous factors Our findings may lead to further understanding of human behavior Background on air traffic control and fluctuation scaling 2.1 Air traffic control and controller’s communication activities Air traffic control is the service provided by the air traffic controllers who are responsible for expediting and maintaining a safe and orderly flow of aircraft traffic To keep the traffic manageable, the controlled airspace/airport is subdivided into sectors with one or two controllers managing the flights inside Cognitive analyses have demonstrated that controllers are required to complete many tasks in response to the rapidly changing of air traffic, many of which must be time-shared and communication related with high pressure [50] Controllers direct aircraft moving on the ground and in the air by delivering the instructions and clearances to the pilots through a unique frequency between them Communication between pilots and controllers must be in a clear and unambiguous way in order to ensure the safety and efficiency of air traffic To maximally utilize the capacity of communication channel while to reduce the risk of misunderstanding, controllers and pilots use standardized phraseology during air–ground communication [51] In general, the grammar structure of transmission is determinate, and the vocabulary is limited The speech rate should be adjusted to allow clearances etc., to be written down if necessary Y Wang et al / Physica A 441 (2016) 151–157 153 Fig Succession of a controller’s communications during his work The horizontal axis denotes time (in s) and the height of vertical line corresponds to the length of a communication The overall intervals between communications can be characterized by inverse Gaussian distribution [26] The communication here is defined as the event that a controller presses the Push-To-Talk button (PTT) and holds it in order to send a transmission to a pilot, disregarding the content of the transmission Fig gives an example of the communications of a controller in about one-hour’s work As can be seen from the figure, most of the communications are less than s The controller usually gives quick response after pilot spoke 2.2 Fluctuation scaling Here we briefly depict the summary of fluctuation scaling (FS) A more detailed discussion and the example of using FS to study the effect of social influence can be found in Refs [46,47] Given a complex system with large number of nodes i, for any time window [t , t + t ] the quantity fi that measures the activities of node i can be decomposed as the sum of all the constituents which contribute to fi during the time interval, that is Ni t (t ) fi t ( t ) = Vi,nt (t ), n=1 where Ni (t ) is the number of constituents, and Vi,nt (t ) ≥ is the value of nth constituent in the time window Then the time average activities fi during observed interval [0, T ] can be obtained as t t ⟨fi ⟩ = Q −1 Q q =0 Q −1 N (q t ) i t fi (q t ) = t Q q=0 Vi,nt (q t ), n =1 where Q = T / t The fluctuation can be calculated as σi2 ( t ) = ⟨[fi t ]2 ⟩ − ⟨fi t ⟩2 Since ⟨fi t ⟩ ≡ t ⟨fi ⟩, when one varies the node i while keeping and the mean of f can follow a power-law t fixed, the relationship between the standard deviation σi ( t ) ∝ ⟨fi ⟩αT Normally the exponent αT is in range [1/2, 1] This power-law relationship is known as fluctuation scaling, or Taylor’s law Because the above calculations were based on temporal average, it is referred as Temporal Fluctuation Scaling (TFS) Empirical results on TFS are reported in complex networks [52], stock markets [53], human dynamics [47] etc If there is a well defined size-like parameter S for all the nodes, for instance, the linear extension (L), area (A), or a fixed constituents (N), and the i-dependence of ⟨f ⟩ and σ is only manifested via S, then we can obtain the Ensemble Fluctuation Scaling (EFS) by the following steps In this case, both t and t are fixed First, the ensemble average of f within S can be calculated as fS = MS ∀i:S =S i fi , where MS is the number of the nodes which have a size Si = S Then the standard deviation is given by σS2 = [fS ]2 − fS 154 Y Wang et al / Physica A 441 (2016) 151–157 Fluctuation scaling can also arise as α σS ∝ fS E The classic study of EFS is reported by Taylor [27], who measured the means and the variances of the natural populations in the different sizes of area A With the increase of the sizes of area both the mean and the variance of the population grow, with a power law relationship between the two quantities Data To investigate controller’s communication behavior, we collected temporal data of their communications and associated traffic data from EUROCONTROL Experimental Center and Shanghai Area Control Center (Shanghai ACC), forming two datasets that were analyzed in this work 3.1 Paris TMA simulation dataset This dataset was obtained from Paris Terminal Maneuvering Area (TMA) simulation database, which was recorded during a two-week real-time training at EUROCONTROL Experimental Center in June 2010 Around 100 participants and thirty sectors were involved in the simulations Fourteen exercises were identified as good exercises that can be analyzed Apart from traffic initialization and the end of simulation, each exercise is about 90 long There are 79,847 communication events made by controllers A more detailed description on this dataset can be found in Ref [26] From the recorded data, we picked up controller’s communication data and Flight Transfer Data of 10 en route sectors that are for our investigation 3.2 Shanghai ACC operational dataset The second dataset was constructed from operational database of Shanghai ACC As one of the three busiest area control centers in China, Shanghai ACC is responsible for providing air traffic control service to the flights that fly above flight level 6000 m in the whole region of East China, covering airspace of more than 900,000 km2 The controlled airspace is subdivided into 20 en route sectors Two or more adjacent sectors will be combined as one according to operation needs The automation systems in the ACC center record flights trajectory data and air–ground communication data Flights trajectory data details the positions of every aircraft in terms of longitude, latitude, and altitude every minute Specific data filtering algorithms have to be implemented to the trajectory data due to the noise The temporal communication data is completely anonymous, without any message content, and records only the start moments and the end moments of the radio transmissions made by controllers or pilots Sector boundaries data is also required to determine the moment at which a flight entering or leaving a sector Here, we examined the records of en route sectors operating between 08:00 and 20:00 (UTC + 8) from 05 March, 2013 to 20 March, 2013 The data consists of over 200,000 controllers’ communications and more than 60,000 flights An overview of hourly traffic activities and controllers’ communication activities in two datasets is presented in Table ⟨Nf ⟩ and ⟨Nc ⟩ are the average of hourly traffic (i.e number of flights) and controller’s communications (number of communication events), while σf and σc are the associated standard deviation It can be seen from the table that there are large variations in traffic and communications Depending on the sector, the average number of messages a flight received normally varies between and Results We first examined whether there exists temporal fluctuation scaling in controller’s communications The number of communications during the observation time window ( t ) and the associated standard deviations were calculated Although there is a positive correlation between the two quantities in the log–log plane, we could not give a conclusive remark due to the limited number of sectors Another question arising is that whether there is fluctuation scaling in the traffic arrival rates as road transportation systems exhibit [54] Unexpectedly but not surprisingly, we did not find such behavior from our datasets One main reason could be the limited number of sectors and low traffic volume Comparing with five years’ traffic data in the Minnesota transportation network, it is not surprising that the fluctuation scaling did not emerge in these two traffic datasets To minimize the effects of traffic factors on controllers’ communications, we performed the ensemble fluctuation analysis following the steps depicted in previous section Similarly to Taylor’s work, we calculated the average of controller’s communication activities fs and the standard deviation σ s according to the number of the flights (s) has been controlled by the controller When a flight flies into a sector, the controller will give several control instructions and clearances to avoid conflict until handing it out into next sector Thus, the communication activities can be obtained by fs = s Vi , i=1 where Vi is the number of transmissions sent to flight i The cumulative number fs expresses the number of messages a controller has sent to these s aircraft The calculation can be done repeatedly for various sizes of s through all the sectors Y Wang et al / Physica A 441 (2016) 151–157 155 Table The basic statistics of two empirical datasets Dataset Sector name ⟨Nf ⟩ σf ⟨Nc ⟩ Paris TMA AOUS AP AR OGRT OYOT TE THLN TML TP UJ 76.8 38.7 51.8 41.2 45.2 45.9 46.3 70.9 44.3 64.6 13.2 4.5 6.4 5.5 7.4 5.4 9.1 7.9 7.0 10.2 323.0 102.4 229.1 198.9 234.7 233.4 169.3 244.4 208.9 258.2 σc 55.8 47.6 41.5 25.6 33.3 56.6 44.2 45.6 47.7 51.3 Shanghai ACC AR04 AR05 AR14 AR15 AR21 AR26 AR28 AR32 37.1 25.3 29.9 50.7 55.9 34.2 42.6 23.3 6.3 9.0 7.5 6.8 8.2 5.9 6.3 6.1 96.4 89.0 105.0 140.9 221.0 70.4 85.8 141.7 33.2 17.9 52.2 62.7 105.4 26.9 34.0 84.4 Fig Fluctuation scaling of communication activity in Paris TMA dataset The horizontal axis denotes the average of communication activities, while the vertical axis represents the standard deviations Each point corresponds to different sizes of s Solid line is the power-law fitting function with exponent α = 0.54 ± 0.01 (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) We plotted the standard deviation according to the average numbers of the communicationsin Figs and The early findings on Paris TMA dataset was presented at an internal workshop in Ref [55] In spite of the heterogeneities of traffic patterns and airspace configurations, we can clearly observe a linear fit of the empirical data in the log–log plot (solid red lines), which indicates that controller’s communication activity exhibit a Taylor’s power-law relationship with α ≈ 0.54 ± 0.01 for Paris TMA dataset and α ≈ 0.77 ± 0.01 for Shanghai ACC dataset There are strong fluctuations at the beginning with few data points, which may be due to the initialization of traffic for first few flights It is possible that air route structure and the count of flights s may have particular influence on the controller’s communications The exceptional quality of Shanghai ACC dataset allows us to test the hypothesis by investing the fluctuation scaling in individual activity To so, we repeated the scaling plot for each sector in Shanghai ACC dataset, and found that the power laws and the obtained exponents are quite similar to each other, with most of them varying between 0.6 and 0.9 As would be expected, the approximate agreement between the exponents obtained for every sector can be considered as a generalization of Taylor’s law, suggesting that the mechanisms underlying the growth of communications of controller may originate in their cognitive activities The exponent α in other complex systems is usually reported between 1/2 and α = 1/2 indicates that system fluctuation is dominated by random internal dynamics, whereas α = implies that the fluctuation is the result of external force The exponents found here suggest that controller’s dynamics is not dominated by any single factor, instead by the combination of the two, with air traffic as external force and controller’s strategies as internal force Larger α observed in Shanghai ACC dataset may be due to the strong external force by the safety consideration Given the pressure they face in real operation, they have less freedom to manage the traffic In contrast, controllers during simulation are more likely to 156 Y Wang et al / Physica A 441 (2016) 151–157 Fig Fluctuation scaling of communication activity in Shanghai ACC dataset The horizontal axis (f ) denotes the average of communication activities, while the vertical axis (σ ) represents the standard deviations Each point corresponds to different sizes of s Solid line is the power-law fitting function with exponent α = 0.77 ± 0.01 (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) implement their own strategies regardless of occurrences of unsafety events Controllers under pressure are more cautious in real operation, and they tend to communicate with pilots alternatively Conclusion We have shown that air traffic controller’s communication activity can be characterized by Taylor’s power-law Our finding implies that high pressure may result in large scaling exponent due to the force from exogenous factors The contribution of our work is twofold From the operation point of view, the detection of fluctuation scaling is particularly noteworthy On one hand, it captures the interesting adaptive phenomena of controllers’ activities with respect to increasing traffic On the other hand, it may reveal the inherent nature of the air traffic management system with controllers being important elements With the evolution of the system, such complex phenomena are critical to our understanding of its dynamical aspects From the view point of statistical physics, the finding of fluctuation scaling in controllers’ communications provides evidence that human activity under pressure is more likely to be dominated by the exogenous factors, adding new insights into human dynamics studies Acknowledgments We thank Dr Vlad Popescu from Georgia Institute of Technology, Dr Andrea 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Shanghai ACC operational dataset The second dataset was constructed from operational database of Shanghai ACC As one of the three busiest area control centers in China, Shanghai ACC is responsible... datasets that were analyzed in this work 3.1 Paris TMA simulation dataset This dataset was obtained from Paris Terminal Maneuvering Area (TMA) simulation database, which was recorded during a. .. Fig Fluctuation scaling of communication activity in Paris TMA dataset The horizontal axis denotes the average of communication activities, while the vertical axis represents the standard deviations