=Paper=
{{Paper
|id=Vol-3732/paper08
|storemode=property
|title=Delays analysis in air transportation with ADS-B large dataset
|pdfUrl=https://ceur-ws.org/Vol-3732/paper08.pdf
|volume=Vol-3732
|authors=Ivan Ostroumov,Nataliia Kuzmenko,Byambajargal Sukhbaatar
|dblpUrl=https://dblp.org/rec/conf/cmse/OstroumovKS24
}}
==Delays analysis in air transportation with ADS-B large dataset==
<pdf width="1500px">https://ceur-ws.org/Vol-3732/paper08.pdf</pdf>
<pre>
                                Delays analysis in air transportation with ADS-B large
                                dataset
                                Ivan Ostroumov1,*,†, Nataliia Kuzmenko1,† and Byambajargal Sukhbaatar1,2,†

                                1 National Aviation University, Liubomyra Huzara Ave., 1, Kyiv, 03058, Ukraine

                                2 MIAT Mongolian Airlines, Ulaanbaatar, 17120, Mongolia



                                                Abstract
                                                Civil aviation is an important part of global transportation system. Numerous advantages of civil
                                                aviation stimulate a continuous growth in the amount of services provided by air transport
                                                except Covid-19 global lockdown. Civil aviation uses a wide network of flight routes to provide
                                                main transportation services. Nominal transportation network operation grounds on well-
                                                planned air traffic. However multiple factors may affect the system, which significantly degrade
                                                network performance and could reduce the safety of air transportation. Low precision of air
                                                traffic or action of rare factors results in delays of provided services. In this paper, we provide a
                                                statistical analysis of air traffic delays based on probabilities. We use a kernel probability density
                                                function to fit punctuality data and estimate risks to be delayed at a particular time. As input data
                                                for delay analysis, we use a database of historical flight trajectories archived by Automatic
                                                Dependent Surveillance-Broadcast (ADS-B) technology. Air traffic punctuality depends on many
                                                factors, however, in trajectory data, we have only the result of their action with no data about
                                                reasons. We propose a specially developed software for automatic delay analysis based on ADS-
                                                B large datasets. Considered examples of delay analysis for particular flights.

                                                Keywords
                                                big data, ADS-B, airplane trajectory, transportation system, air navigation 1



                                1. Introduction
                                Aviation uses one of the most complicated transportation networks to provide passenger
                                and cargo transfer over the globe [1, 2]. Airplanes use a flight route network to organize air
                                traffic on the basis of flight safety and efficiency [3, 4]. Each participant of air traffic needs
                                to follow certain rules and directions to minimize mid-air collision and risk of collision with
                                a terrain [5]. Air traffic management is provided by numerous automatic systems and air
                                traffic control teams to make sure the airplanes stay safe and don't bump into each other by
                                guiding them over the whole flight.




                                CMSE’2024: International Workshop on Computational Methods in Systems Engineering, June 17, 2024, Kyiv,
                                Ukraine
                                ∗ Corresponding author.
                                † These authors contributed equally.

                                    ostroumov@ukr.net (I. Ostroumov); nataliiakuzmenko@ukr.net (N. Kuzmenko);
                                byambajargal831@gmail.com (J. Sukhbaatar)
                                     0000-0003-2510-9312 (I. Ostroumov); 0000-0002-1482-601X (N. Kuzmenko); 0009-0004-0032-2920
                                (J. Sukhbaatar)
                                           © 2024 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).




CEUR
                  ceur-ws.org
Workshop      ISSN 1613-0073
Proceedings
   Over recent years, the growth of air traffic has been remarkable, reflecting the increasing
demand for air travel worldwide. This expansion can be attributed to various factors,
including globalization, economic development, and advances in aviation technology [6]. As
more people and goods seek efficient transportation options, the aviation industry has
experienced a surge in both passenger and cargo traffic. Aviation has shown a clear
tendency to grow up to 2020. That has been approved by global number of flights
represented in Figure 1. However, alongside the opportunities brought by this growth, there
are also challenges, such as congestion at airports and in airspace, which necessitate
ongoing innovation and collaboration to ensure safe and efficient air travel for all.




Figure 1: Statistics of number of total flights for the last decade.

   The total number of flights experienced consistent growth from 2013 to 2020 (pre-
COVID). However, with the onset of the COVID-19 pandemic, there was a notable decline,
amounting to a reduction of 23.9 million flights. In 2021, the total number of flights
rebounded to 22.2 million [7, 8].
   Delay is one of the main parameters of transportation system's effective operation. Delay
indicates time actual air traffic is late from planned activities [9, 10]. Thus, delays indicate
precision of planning tools and air traffic system resistance to action degradation factors
[11]. Airspace volume is limited by existence of flight routes network and system used to
meet minimums of safety levels [12, 13]. Thus, further support of continuous growth in air
traffic requires significant changes in air space structure and increasing the level of
automation in all systems used for air traffic control [14, 15]. A free-route airspace is one of
the possible solutions to increase airspace capacity [16, 17]. Development and global
implementation of automatic air traffic control systems are other important reasons that
limit wide integration of Unmanned aerial vehicles in controlled airspace.
   In the paper, we use delay analysis to estimate the probability of an airplane being
delayed at a particular time which is an important input data for automatic air traffic control
system based on risks. Delays analysis based on probabilities will help to tune
transportation system precisely and help improve air traffic prediction.
   The organization of the paper is the follows: In the second section, we study reasons for
delays and classify factors that have a significant impact on delay forming. In the third
section, we describe delay analysis based on probabilities. In the fourth section, a numerical
demonstration of developed software for delay analysis is validated with a Large ADS-B
dataset of real air traffic data.

2. Delays in air traffic
In recent years, the aviation industry has faced a notable increase in delays due to several
factors. The expanding volume of air traffic has led to congestion along flight routes, posing
challenges in efficient route planning. Furthermore, limited airspace capacity has strained
existing infrastructure, contributing to delays in departure and arrival schedules. The
heightened workload on air traffic controllers has necessitated meticulous coordination to
ensure the safe and timely flow of flights. Additionally, aging airport infrastructure has
struggled to keep pace with the demands of modern aviation, exacerbating delays. If we
want to decrease the amount of delays and want to expand the aviation industry,
collaboration among aviation stakeholders to enhance airspace capacity through strategic
infrastructure upgrades and modernization initiatives is crucial.
   In the 2022 edition of the CODA Digest [18], which analyzes all-causes delays and
cancellations in European air transport, it was found that the average delay per flight
reached a 5-year peak of 17.3 minutes per flight. This represents a notable increase
compared to 2021, where the average delay per flight stood at 9.2 minutes (Figure 2). The
surge in delays coincided with a significant rise in the number of flights, which increased by
48% compared to the previous year.




Figure 2: Statistic of airline-reported delays in Europe.
    Among the causes attributed to airlines, ground handling and staff shortage-related
delays ranked second, accounting for an average delay of 4.9 minutes per flight.
    Delays are usually associated with the capacity problems, staff shortage, runway closure,
obstruction, night curfew etc.
    En-route Air Traffic Flow Management (ATFM) delays showed a sharp escalation,
reaching 1.8 minutes per flight. The network experienced a substantial increase in ATFM
capacity issues throughout 2022. Additionally, the Ukrainian crisis played a significant role
in generating ATFM delays, starting from February 22, 2022, as traffic flows shifted due to
the closure of the Ukrainian Flight Information Region [19]. Airport delays are related to
labour shortages, parking stands, gate limitations and ramp congestion. Governmental
delays are mostly associated to COVID-19 documentation checks, immigration and security.
    Understanding the reasons behind flight delays and their various categories is essential
for efficient aviation management. Without standardized reporting systems, different
systems used by airlines worldwide would lead to confusion and complications.
Fortunately, airlines under the International Air Transport Association (IATA) have
adopted standardized procedures for reporting flight delays and movement messages
electronically, streamlining operations for airline workers, ground handling agents, and
airports [20]. The IATA Delay code system comprises nine category sets, described using
either a two-digit numeric code or a two-letter alpha code, with numeric formats being
more common.
    For instance, the delay code 11, associated with late check-in, and code 15, linked to
boarding discrepancies and missing passengers at the gate, are the most frequently
encountered delays caused by passengers and baggage. This type of delay typically occurs
due to various reasons such as passengers arriving late at the airport, long queues at the
check-in counters, issues with documentation or baggage handling. For aircraft and ramp
handling issues, code 36 relating to fueling or refueling, code 32 relating to loading and
unloading, and staff shortages, are commonly observed. Fueling delays, for instance, stem
from operational problems like equipment malfunctions or staffing shortages.
    Technical issues delays is used for non-scheduled maintenance, entail unplanned aircraft
maintenance outside regular schedules, prompted by pre-flight checks or crew reports [21,
22]. These may lead to flight delays or cancellations until maintenance is completed for the
safe conduction of flight.
    Weather-related delays could be connected with departure or destination station
weather, occur due to adverse weather conditions such as thunderstorms, snow, or fog,
impacting flight safety and visibility. Air traffic control (ATC) delays are often used for
delays related to airport and air traffic control, such as ATC holds and immigration
processes. An ATC hold occurs when air traffic control restricts aircraft departure or arrival
in specific airspace or at an airport for various reasons. These delays often occur at busy
international airports with high air traffic volume, resulting in increased workload, runway
demand, and gate capacity constraints. Reactionary delays are used for “Late inbound
aircraft," occurs when the aircraft that will be used for the flight arrives late from a previous
flight. This can cause a delay in the departure of the subsequent flight, also known as
“Aircraft Rotation”.
Regardless of the delay type, the consequences remain consistent, including missed
departure slots, extended ground times, potential cascading delays, passenger discomfort,
and increased operational costs due to aircraft and crew idle time. Overall, flight delays
significantly impact airlines and passengers alike, affecting operational efficiency, customer
satisfaction, and financial performance.

3. Delay analysis based on probabilities
Delays and airplane punctuality could be estimated based on trajectory data available via
Automatic Dependent Surveillance-Broadcast technology (ADS-B). Each participant in air
traffic has to be equipped with a specific transponder of Mode 1090ES to inform all other
users and air traffic control authority about airplane identification and exact position. Air
traffic management uses ADS-B trajectory data and user's position measured by conventual
surveillance equipment like surveillance radars and multilateration systems to provide air
traffic control. Also, networks of Software-Defined Radios are used to receive position
reports that are transferred over a 1090 MHz data channel. Position of each airspace user
is decoded and stored in a global surveillance database. These databases may include
trajectories of each airspace user from the day of airplane has been in use.
    Big data of ADS-B airplane trajectories could be used for delay analysis in fully automatic
mode. Based on rules of surveillance equipment use, on-board ADS-B transponder should
be initiated at the moment of starting moving from the gate.
    Time of departure (TD) or time of gate left could be obtained by detection of airplane
moving initiation. It could be done by calculating the lengths between airplane positions. In
case of airplane path is out of two standard deviation errors of primary on-board
positioning system the time of gate left could be detected.
    Time of take-off (TTO) could be obtained by simple airplane altitude tracking. Point at
which airplane starts climbing from runway altitude indicates the time of take-off.
    Time of landing (TL) also could be estimated by altitude dataset at the point when
altitude became constant to a destination airport runway.
    Time of arrival (TA) or time of gate reached is a time when an airplane stops moving at
the final leg before ADS-B transponder is shot down.
    For general safety reasons publicly available services of ADS-B data sharing limit data
set in a time when airplanes are on the ground. Mostly simple filter data by 600 ft altitude
is applied to grant permission to the data only when airplanes are in the air.
    Air navigation databases provide access to scheduled air traffic data. Scheduled data
could be compared to actual and delays could be calculated. Calculation of delays for each
scheduled time for historical flights is important and makes it possible to analyze influence
of different factors on flight. Result of this analysis identifies the most valuable impact in
delay forming and recommendations to airline or air navigation service providers could be
issued to minimize delay forming at a particular leg of the flight phase.
    Another important step is a statistical analysis of times TD, TTO, TL, and TA. Results of
its fluctuations indicate importance to passengers and other users of air transport services.
Results of statistical analysis indicate about probability of being delayed in a particular
flight connection. These probabilities are important components of risk management in
supply chains for cargo delivery.
    Risks could be estimated based on a probability density function (PDF). The probability
of an airplane being delayed could be estimated as the area below PDF within a particular
time frame (Figure 3) [23, 24]. Scheduled time is used as a reference point to get a time
frame for a delayed period. Probability of fixing a particular time within defined perils could
be estimated as follows:
                                                   𝑡
                              P[𝑡𝑎 < 𝑡 < 𝑡𝑏 ] = ∫𝑡 𝑏 𝜌(𝑥)𝑑𝑥.                               (1)
                                                         𝑎

where 𝑡𝑎 , 𝑡𝑏 are time frame perils for confidence band; 𝜌(𝑥) is PDF.
  The probability of airplane arrival in time could be estimated as a cumulative function:
                                                 𝑠𝑡
                                      P[𝑡𝑠 ] = ∫− 𝜌(𝑥)𝑑𝑥.                                   (2)
where 𝑡𝑠 is a scheduled time.
  The risk of an airplane being delayed at a particular time could be estimated as follows:
                                                  +
                                      R[𝑑] = ∫𝑡 +𝑑 𝜌(𝑥)𝑑𝑥.                                   (3)
                                                  𝑠

where 𝑑 is the time of airplane being delayed.

          ρ(t)


                     Scheduled
                       Time
                                            P(ta<t<tb)              PDF
                                                  )

                                 ts    ta                tb                        Time


Figure 3: Probability of airplane being delayed.

    Simple PDF (Gaussian or Generalized Error) doesn’t provide adequate statistical data
due to the action of multiple factors which is not Normal. A kernel PDF (KPDF) could provide
better fitting in case of a mix of different PDFs [25, 26]. We use a common KPDF with the
following model:
                                              1               𝑡−𝑇
                                  𝜌(𝑡) = 𝑛𝐵𝑑 ∑𝑛𝑖=1 𝐶 ( ℎ 𝑖),                                 (4)
                                                 𝑒𝑥𝑝(−𝑥 2 ⁄2)
                                      𝐶(𝑥) =                    ,                            (5)
                                               ∫ 𝑒𝑥𝑝(−𝑥 2 ⁄2)𝑑𝑥

where 𝑇 is a matrix of statistical times, for each flight; 𝑖 is a flight index; 𝑛 is the number of
flights processed; 𝐶(𝑥) is the Gaussian kernel function; 𝐵 is bandwidth.
    Fitting with KPDF required to use effective bandwidth 𝐵 which could be calculated by
minimum of Mean Square Error:
                                                       1
                                          4𝜇         𝑑+4
                                𝐵 = (𝑛𝜎4 𝐿2 𝑝(𝑥)2 𝑑𝑥) ,                                (6)
                                        ∫

where 𝜇 is a mean value; 𝜎 is a standard deviation; 𝐿 is a Laplace function.
  A special software for delay analysis has been developed for use in MATLAB
environment. A structure scheme of software is given in Figure 4.


                                   ADS-B DataBase              DataBase of
                                     of airplane              scheduled air
                                     trajectories                traffic
                                             API                     API

              Flight               Select trajectory
            Number                       data


                                     Calculation              Initial delays
                                   TD, TTO, TL, TA              analysis


                                     KPDF fitting            Histograms plot


                              Probabilities estimation

                                                              Visualization
                       Sofware for delay analisis

Figure 4: Structure scheme of software for delay analysis.

   As input software requires only a particular flight number to be studied. Based on flight
number, software requests available trajectory data from ADS-B large-scale database with
API. Airplane trajectories are replied in JSON data format which is easily integrated into
internal variables of software. Then for each airplane trajectory values of TD, TTO, TL, and
TA are calculated. Calculated differences between actual and scheduled times gives delays.
Delay values are accumulated in arrays by each flight number and processed. Results of
delays frequency distribution estimation are visualized with a histogram plot. A KPDF is
applied for each set of times TD, TTO, TL, and TA. Probabilities of airspace users being
delayed are estimated by cumulated PDF (2). As a result, software prepares a set of
histograms with a result of KPDFs fitting which could be saved in a separate folder titled
with flight number.

4. Numerical demonstration
In numerical demonstration, we use developed software to provide delay analysis of flight
OM137 (MGL137). Flight OM137 connects international airports of Sergelen Sum (ZMCK,
Mongolia) and Frankfurt am Main (EDDF, Germany) operated by airline “Mongol Air”.
Airplanes B 787 and B 763 have been used to serve this flight. We use ADS-B trajectory
dataset obtained by publicly available API [27]. In the study, we use only recent data for
period January-May 2024. This period gives 53 flight realizations. Flight OM137 is a
scheduled flight that is repeated on a timetable basis. Therefore, scheduled times of TD,
TTO, TL, and TA are still mostly constant exсapt summer-winter timetable changes.
Duration of ground operations from gate departure to take-off for ZMCK is 10 min. Also,
taxing in EDDF from landing to the gate is planned to be 10 min. The scheduled time of ZMCK
gate left is 2:30 (2:00 summer time) UTC and scheduled time for EDDF gate arrival is 12:10
(11:00 summer time) UTC. We use calculated delays as the difference between scheduled
and actual times for TD, TTO, TL, and TA. Results of statistical analysis in delays for TD, TTO,
TL, and TA are presented in Figure 5– 8.




Figure 5: Delay for time of departure.




Figure 6: Delay for time of take-off.
Figure 7: Delay for time of Landing.




Figure 8: Delay for time of arrival.

Results of delay analysis for OM137 flight are given in Table 1. We calculate parameters of
mean and standard deviation of delay for each considered time TD, TTO, TL, and TA. Also,
we estimate probabilities of airplanes being early or at least in scheduled time based on (2)
for both models NPDF (𝑃𝑁𝑃𝐷𝐹 ) and KPDF (𝑃𝐾𝑃𝐷𝐹 ).

Table 1
Results of delay analysis for OM 137 flight
                Time                   Mean   Standard deviation    𝑃𝑁𝑃𝐷𝐹     𝑃𝐾𝑃𝐷𝐹
       Time of departure (TD)     00:22:54 00:21:58                14.86%    4.57%
       Time of take-off (TTO)     00:28:39 00:22:06                9.75%     2.10%
        Time of Landing (TL)      -0:02:30 00:26:49                53.73%    59.30%
        Time of arrival (TA)      00:00:03 00:26:00                49.91%    57.62%
Results in Table 1 show the difference in models. Probability 𝑃𝑁𝑃𝐷𝐹 is very different from
𝑃𝐾𝑃𝐷𝐹 . Thus, the simplified model with NPDF gives values with less precision.
    Results of cumulated PDF (CPDF) estimation by (2) for KPDF model are shown in Figure
9. CPDF gives a probability of an airplane being delayed at a particular duration.




Figure 9: CDF for considered times.

   Obtained results indicate that for particular flight connection probability of airplane
being delayed in the departure airport (TD and TTO) is high enough (the probability of
being delayed in 30 min is more than 70%). However, during the flight airplane corrects its
total delayed time to guarantee arrival at the destination airport in scheduled time with a
probability of no less than 60%.

5. Conclusions
Delay analysis is an important task performed by each airline to increase performance of
provided services. Delay analysis identifies the main reasons for delays and helps to
concentrate airline activity to minimize degradation factors action. Usually, delays are
associated with direct additional costs for airlines spent on the operation of a particular
flight. Thus, delay minimization is one of the primary tasks of airlines. Public available
airplane trajectories archive via ADS-B database opens a new possibility for delays analysis.
Long-term archives of particular flight connections help to identify the main times for delay
analysis: time of gate left, take-off, landing times, and time of arrival at the gate of
destination airport.
    A KPDF is useful for simply fitting the statistical data for delay analysis. Normal PDF does
not fit well due to multiple degradation factors action with different natures. Fitted KPDF
makes it easy to estimate probabilities of airplanes being delayed, which are important
components in supply chain optimization based on risk models.

Acknowledgements
This project has received funding through the EURIZON project, which is funded by the
European Union under grant agreement No. 871072 (Project EU #3035 EURIZON “Research
and development of Ukrainian ground network of navigational aids for increasing the safety
of civil aviation”).

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