# Uncertainty Management at the Airport Transit View

^{1}

^{2}

^{3}

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## Abstract

**:**

## 1. Introduction and Motivation

## 2. Background and Contribution

## 3. Materials and Methods

#### 3.1. Model for Airspace/Airside Integrated Operations

- The final approach and inbound ground section of the inbound flight.
- The turnaround process section in which the inbound and the outbound flights are linked.
- The outbound ground section and the initial climb segment of the outbound flight.

- Arrival delay: ALDT-SLDT.
- Taxi-in delay: Actual taxi-in duration (AIBT-ALDT) versus scheduled taxi-in duration (SIBT-SLDT)
- Turnaround delay: Actual turnaround time (AIBT-AOBT) versus scheduled turnaround time (SIBT-SOBT)
- Taxi-out delay: Actual taxi-out duration (AOBT-ATOT) versus scheduled taxi-out duration (SOBT-STOT)
- Departure delay: The sum of arrival upstream delay (reactionary) and the aggregated delay at the on-ground stage: system delay (primary delay), which is composed of taxi-in, turnaround and taxi-out delays. Hence, four mutually exclusive and complementary stages were evaluated to characterise the system’s schedule adherence: arrival, taxi-in, turnaround and taxi-out.

- Determine significant events to track the progress of a flight (arrival, landing, taxi-in, turnaround, taxi-out and departure) and the distribution of these key events as milestones.
- Ensure linkage between arriving and departing flights.
- Assess time efficiency performance, which is measured for each milestone or between two milestones.
- Enable early decision-making when there are disruptions to an event.
- Appraise the operational relationships and interdependences between processes that will shape the structure of the causal model for uncertainty management (identify variables).

#### 3.2. Case Study for Uncertainty Characterisation and Management at the ATV

#### 3.2.1. Statistical Characterisation of Processes and Uncertainty Drivers at the ATV

^{2}goodness-of-fit test were used to ensure the “power” of curve fitting [83]. Fricke and Schultz [32] and Wu [6] previously found this procedure to be efficient when analysing on-ground processes. When a parametric distribution could not properly describe the data, we used a Kernel density estimation approach to obtain a nonparametric representation of the probability density function of the variable [84]. See Figure 7 and Figure 8 for some examples.

#### 3.2.2. Causal Model for Uncertainty Management at the ATV

_{1}│π

_{1}), … p(x

_{n}│π

_{n})} is a set of n conditional probability densities (CPD), one for each variable. π

_{i}is the set of parents of node x

_{i}in G. Set P defines the associated joint probability density of all nodes with the following equation (the chain rule for BNs) [52,85]:

_{2}and X

_{3}are parent nodes of X

_{4}(child node for X

_{2}and X

_{3}). The probability distribution of X

_{4}depends exclusively on the value of its parent variables (X

_{2}and X

_{3}), i.e., X

_{4}is conditionally independent of X

_{1}given knowledge of X

_{2}and X

_{3}.

- Nodes 1–5 represent meteorological conditions.
- Nodes 6–13 include data regarding the arrival airspace: timestamps and congestion metrics (throughput, queues and holdings).
- Nodes 14–15, 26 and 38–39 illustrate infrastructure information.
- Nodes 16, 22–25 and 40 refer to operator, aircraft, route and flight data.
- Nodes 17–21, 27–37 and 41–42 include data regarding airside operational times and regulations.
- Nodes 43–49 represent delay causes according to the IATA coding system [74].

- Scenario 1 (forward/inter-causal scenario). The model predicts departure delay (output-child node) by setting the probability of having a certain configuration, i.e., by setting one or more parent-input nodes.
- Scenario 2 (backward inference). The model delivers a particular configuration in the parent nodes by setting the delay node to a target value. It provides understanding about the main contributors to delay (if delay is settled to a high positive value) or what configuration optimises operations (if delay is settled to a negative value).

## 4. Results and Discussion

#### 4.1. Operational Characterisation for the Case Study

^{2}= 0.733) between the arrival delay and turnaround delay, which was statistically significant at the p = 0.02 level. The turnaround step is elastic enough to somehow adapt itself to arrival delay—when the arrival delay increased by 1 min, turnaround delay decreased by approximately by 0.8 min. The system responds to arrival delay through time buffers or by reducing operational times (improving efficiency), and hence, on ground turnaround partially absorbs the arrival delay. The elasticity of turnaround delay with respect to arrival delay depends on the type of operation (hour, airline, aircraft and route). Low cost carriers (LCCs) at midday hours and network carriers (NCs) with high scheduled turnaround times present the highest potential for recovery. Negative values in arrival delay usually result in positive turnaround delay values due to slot adherence (LEMD is a coordinated airport). Data do not demonstrate a clear positive relationship between delay (at the different stages) and the number of operations. Nevertheless, the correlation becomes stronger and statistically significant during congested hours (when the airport operates near its declared capacity). The elasticity of the “pure” turnaround delay with respect to arrival delay changes depends on the number of operations. Its threshold of less than 20 operations/h shows the higher potential for arrival delay recovery. Table 5 includes relevant information with respect to traffic mix and infrastructure utilization in order to better understand the discussion about the test cases results.

_{1}− k(Q

_{3}− Q

_{1}), Q

_{3}+ k(Q

_{3}− Q

_{1})], with k = 1.5 [101], where Q

_{1}and Q

_{3}are the lower and upper quartiles respectively. The first quartile, denoted by Q

_{1}, is the median of the lower half of the dataset. This means that about 25% of the observations in the dataset lie below Q

_{1}and about 75% lie above Q

_{1}. The third quartile, denoted by Q

_{3}, is the median of the upper half of the dataset. This means that about 75% of the observations in the dataset lie below Q

_{3}and about 25% lie above Q

_{3}. During the analysis, these outliers (that could be due to faulty data or potential non-representative operations) might be excluded from the main sample, because of the possibility of biased results [they have an impact on the mean value (μ) and on the range (spread of data increases)]. Nevertheless, for items which are highly cantered at zero with wide variation (Figure 22), these outliers are important for the analysis, as they provide significant operational information.

#### 4.2. Cross-Influences at the ATV Stage

- Main delay triggers and their quantitative influences, e.g., a high amount of arrivals at early hours of the day, congestion at ASMA and E-TMA, bad weather conditions, tight scheduled duration of processes, LCCs operating domestic flights, changes in runway configuration, departure rates approaching runway capacity, and the existence of external delay causes (traffic flow restrictions, aircraft technical problems, crew schedule adherence requisites).
- Ability of processes to compress themselves and achieve punctuality (potential for recovery), e.g., the overall turnaround delay decreases at a higher rate when the airport throughput is below the threshold of 20 operations/h, taxiing processes reduce their delay at certain runway configurations, longer scheduled turnarounds at midday and late evening act as time-efficiency “protectors” for the system, the unconstrained duration of airspace processes reaches a limit when the airport is operating near its declared capacity, and certain airlines are especially active in recovering arrival delay on the ground (reducing duration of processes).

## 5. Summary and Conclusions

- Achieve a comprehensive understanding of operations at the ATV stage (airspace/airside integration).
- Appraise the influence of changes in tactical decisions and policies on delay management (“what-if” scenarios).
- Ensure some target levels of efficiency are met, improve predictability and manage uncertainty regarding operations through the causal model.
- Estimate the final departure delay (settlement of buffer time and optimal rotation times) using “forward” analysis.
- Identify the main contributors (causes) to a final delay (locate inefficiencies) using “backward” analysis.

## Author Contributions

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**Extension of the ATV concept. Adapted from [9].

**Figure 4.**Unified Modelling Language (UML) for the Business Process Model (BPM) of the aircraft flow (airport/airspace integrated operations).

**Figure 5.**Combination of the BMP for the airport–airspace integrated operations and the A-CDM concept.

**Figure 6.**Functional structure of Madrid airport (LEMD). Adapted from [81].

**Figure 7.**Histogram and distribution fitting for (

**a**) additional time at ASMA 60 NM (s); (

**b**) arrival delay (min).

**Figure 8.**Histogram and distribution fitting for (

**a**) actual taxi-out time (min) and (

**b**) wind intensity (kts).

**Figure 9.**Histogram and distribution fitting for turnaround: (

**a**) actual duration (min); (

**b**) starting time delay (AIBT–SIBT) (min); and (

**c**) finishing time delay (AOBT–SOBT) (min).

**Figure 10.**“Pure” turnaround delay (without considering the ATFCM delay): (

**a**) histogram/curve fitting and (

**b**) average hourly delay (min/operation) throughout the day (the error bars denote intervals of one standard deviation).

**Figure 14.**BN model to understand the interdependencies between factors that influence delay performance and system saturation. Colours represent different BN layers.

**Figure 15.**Receiver operating characteristic curves (ROC) curves for predicting (

**a**) departure delays between 3 and 15 min and (

**b**) departure delays over 15 min.

**Figure 17.**(

**a**) Traffic demand profile (22 July 2016) and (

**b**) arrival/departure accumulated hourly delay profile (22 July 2016).

**Figure 18.**Evolution of average hourly (

**a**) arrival delay (min/operation); and (

**b**) departure delay (min/operation) throughout the day (the error bars denote one standard deviation intervals).

**Figure 19.**Relationship between arrival delay and (

**a**) taxi-in delay; (

**b**) turnaround delay; and (

**c**) taxi-out delay (min).

**Figure 20.**(

**a**) Contribution of each stage to departure hourly average delay (min/operation), and (

**b**) evolution of average taxiing hourly delay (min/operation) throughout the day.

**Figure 21.**Relationship between “pure” turnaround delay (without considering the ATFCM delay) and arrival delay, (

**a**) for the complete dataset (only short delays) and (

**b**) for the baseline day scenario (22 July 2016).

**Figure 22.**Boxplot for (

**a**) arrival delay, in-block adherence, turnaround delay and departure delay; and (

**b**) taxi-in delay and taxi-out delay.

**Figure 23.**(

**a**) Average landing rate as a function of the number of queuing aircraft; and (

**b**) average take-off rate as a function of the number of departing aircraft on the ground.

Organisation | Stakeholder |
---|---|

AENA—Spanish Airport Authority and Airport Manager | Airport operator |

IBERIA—Member of the International Airlines Group (IAG) | Airline |

ENAIRE—Spanish Air Navigation Service Provider | Air Navigation Service Provider (ANSP) |

IBERIA Airport Services | Ground Handling Agent |

DGAC—Spanish General Directorate of Civil Aviation (a public body answerable to the Ministry of Public Works) | Policy maker—Regulator |

**Table 2.**Selected milestones along the flight process (A-CDM concept). Adapted from [68].

Milestone Number | Milestone Meaning |
---|---|

M1 | EOBT (estimated off-block time)—3 h |

M2 | EOBT (estimated off-block time)—2 h |

M3 | Take-off from outstation |

M4 | Local radar update |

M5 | Final approach |

M6 | ALDT (actual landing time) |

M7 | AIBT (actual in-block time) |

M8 | Actual ground handling starts |

M9 | TOBT (target off-block time) |

M10 | TSAT (target start-up approval time) |

M11 | Boarding start |

M12 | ARDT (aircraft ready time) |

M13 | ASRT (actual start-up request time) |

M14 | ASAT (actual start-up approval time) |

M15 | AOBT (actual off-block time) |

M16 | ATOT (actual take-off time) |

Type of Data | Information |
---|---|

Airport infrastructure | Runway and stand use (terminal area). Runway declared capacity (arrivals, departures and total). |

Airline | Operator, type (low cost carrier/network/cargo/general aviation) and associated handling agent. |

Aircraft | Model, wake turbulence category (super heavy/heavy/medium/light), size (narrow/wide body) and registration number. |

Flight | Flight number, type (commercial or private) and Air Traffic Control (ATC) call sign. |

route | Origin and destination, category (Domestic/European/Long Haul). |

Operational times & regulations | Date, aircraft milestones (from the E-TMA entrance to its exit: approach, on-ground turnaround and climb), timestamps (schedule adherence), duration of processes, holding patterns, aircraft separation, number of aircraft queuing for the inbound traffic flow and ATFCM regulations. |

Arrival congestion | Arrival Sequencing and Metering Area (ASMA) additional time (average arrival runway queuing time on the inbound traffic flow, during congestion periods). |

Throughput (airspace and airside) | E-TMA throughput (movements per hour), runway throughput (movements per hour). |

Meteorology | Wind (direction and intensity), visibility, RVR (runway visual range), clouds (type and amount), temperature, atmospheric pressure and presence of fog. |

Delay causes | Delay causes according to the codes developed by IATA [74] |

Node Number | Meaning | Node Number | Meaning |
---|---|---|---|

1 | Amount of clouds | 26 | Terminal area (T1/T2/T3/T4/T4S/cargo area/general aviation area)—associated to stand location (ramp) |

2 | Type of clouds | 27 | Scheduled turnaround time (SOBT–SIBT) |

3 | Visibility | 28 | Actual turnaround time (AOBT–AIBT) |

4 | Wind direction | 29 | Actual “pure” turnaround time (without considering ATFCM delay) |

5 | Wind intensity | 30 | Turnaround delay for the operation |

6 | Aircraft queuing at ASMA 60 NM | 31 | “Pure” turnaround delay for the operation |

7 | Throughput (aircraft landed) in the previous hour, when aircraft reaches ASMA 60 NM | 32 | System delay for the operation |

8 | Additional ASMA time (60 NM) | 33 | Existence of ATFCM regulation for this flight |

9 | Aircraft queuing at ASMA 40 NM | 34 | ATFCM delay for the operation |

10 | Throughput (aircraft landed) in the previous hour, when aircraft reaches ASMA 40 NM | 35 | Scheduled taxi-out time |

11 | Additional ASMA time (40 NM) | 36 | Actual taxi-out time (ATOT–AOBT) |

12 | Amount of holding patterns | 37 | Taxi-out delay for the operation |

13 | E-TMA arrival transit time | 38 | Departure configuration (north/south) |

14 | Arrival configuration (north/south) | 39 | Departure runway |

15 | Arrival runway | 40 | Route destination (domestic/European/long-haul) |

16 | Route origin (domestic/European/long-haul) | 41 | Departure time–associated with ATOT (morning/afternoon/evening/night) |

17 | Arrival time–associated with ALDT (morning/afternoon/evening/night) | 42 | Departure delay for the operation |

18 | Arrival delay for the operation | 43 | Existence of delay according to the IATA coding system [74] |

19 | Scheduled taxi-in time | 44 | Air Traffic Management related codes [74] |

20 | Actual taxi-in time (AIBT–ALDT) | 45 | Aircraft related delay codes [74] |

21 | Taxi-in delay for the operation | 46 | Airline related delay codes [74] |

22 | Type of airline operator (low cost/network/cargo/general aviation) | 47 | Airport related delay codes [74] |

23 | Aircraft size (narrow body/wide body) | 48 | Meteorology related delay codes [74] |

24 | Wake-turbulence category (H/M/L) | 49 | Other delay codes [74] |

25 | Handling agent |

Arrival Configuration | Arrival Runway | Terminal Area | Most Used Parking Stands | Fleet Mix (Wake Turbulence Category) [99] | Traffic Share | Origin | Departure Configuration | Departure Runway | Destination |
---|---|---|---|---|---|---|---|---|---|

North (76%) | 32L (34%) 32R (66%) | T4-T4S (55%) T123 (45%) | Ramps 10–11–12 (41%) | Super heavy (0.2%) Heavy (15.9%) Medium (83.5%) Light (0.4%) | NCs (69%) LCCs (29%) Cargo (1%) General aviation (1%) | Domestic (34%) European (48%) Long haul (18%) | North (90%) South (10%) | 36L (44%) 36R (46%) 14L (5%) 14R (5%) | Domestic (33%) European (48%) Long haul (19%) |

South (24%) | 18L (64%) 18R (36%) | T4-T4S (54%) T123 (46%) | Ramps 10-11–12 (44%) | Super heavy (0.1%) Heavy (9.7%) Medium (90.1%) Light (0.1%) | NCs (67%) LCCs (31%) Cargo (1%) General aviation (1%) | Domestic (34%) European (55%) Long haul (11%) | North (28%) South (72%) | 36L (14%) 36R (14%) 14L (40%) 14R (32%) | Domestic (35%) European (53%) Long haul (12%) |

**Table 6.**Statistical characterisation of the aircraft flow through the airspace/airside integrated operations.

Metric | Mean Value (μ) and Standard Deviation (σ) |
---|---|

E-TMA transit time | μ = 29.6 min, σ = 10.0 min |

Additional ASMA 40 NM. Excess in approach queuing time | μ = 1.3 min, σ = 2.2 min |

ASMA 40 NM transit time | μ = 13.6 min, σ = 3.7 min |

Arrival delay. | μ = 8.3 min, σ = 30.5 min |

Taxi-in delay | μ = 0.3 min, σ = 2.2 min |

Actual taxi-in time | μ = 8.9 min, σ = 3.6 min |

In-block adherence (AIBT-SIBT) | μ = 8.6 min, σ = 30.6 min |

Turnaround delay | μ = 4.8 min, σ = 28.2 min |

Actual turnaround time | μ = 165.6 min, σ = 179.7 min |

Push delay | μ = 3.2 min, σ = 8.9 min |

Start-up delay | μ = −1.2 min, σ = 16.5 min |

Off-block adherence (AOBT–SOBT) | μ = 13.4 min, σ = 25.7 min |

Taxi-out delay | μ = 0.9 min, σ = 4.4 min |

Actual taxi-out time | μ = 16.6 min, σ = 5.3 min |

System delay (primary delay) | μ = 5.8 min, σ = 28.6 min |

Departure delay (total delay) | μ = 14.1 min, σ = 26.5 min |

BN Layer | Most Influential Factor | Threshold for Reaching a Probability of Having Departure Delay >15 min above 60% |
---|---|---|

Meteorology | East wind (coming from the east and blowing toward the west) | An intensity over 15 kts |

Airspace | ASMA 60 NM Additional time and holding patterns | Above 10 min for ASMA 60 NM additional time and more than 2 holding patterns |

Infrastructure | South runway configuration | Combination of south runway configuration, terminal area T123 and 14L departing runway |

Operator, aircraft type and route | LCCs operating a domestic or intra-European flight, with NB aircraft | |

Airside | Tight scheduled duration of processes | Turnaround and taxi allocated times below the average for each operation type |

IATA delay codes | Reactionary | Probability of an inherited reactionary delay above 50% |

**Table 8.**Most probable states (and its associated probabilities) for different influence factors, when setting targets of operational time efficiency.

Departure Delay (min) | Departure Configuration & Departure Runway | Terminal Area | Aircraft Type (NB-WB) | Departure Time Frame (ALDT) | Route Destination & Operator Type |
---|---|---|---|---|---|

d < −15 | North (75%), 36R (38%) | T4 (40%) | NB (84%) | Evening (13–20 UTC) (42%) | European (70%), NCs (70%) |

−15 ≤ d < −3 | North (75%), 36R (38%) | T4 (41%) | NB (83%) | Evening (13–20 UTC) (39%) | European (70%), NCs (68%) |

−3 ≤ d < 3 | North (70%), 36R (35%) | T4 (41%) | NB (80%) | Evening (13–20 UTC) (41%) | Domestic (39%), NCs (69%) |

3 ≤ d < 15 | North (69%), 36R (37%) | T123 (43%) | NB (85%) | Morning (6–11 UTC) (39%) | European (49%), NCs (69%) |

15 ≤ d | North (65%), 36R (39%) | T123 (42%) | NB (80%) | Morning (6–11 UTC) (38%) | European (51%), NCs (70%) |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Rodríguez-Sanz, Á.; Gómez Comendador, F.; Arnaldo Valdés, R.; Cordero García, J.M.; Bagamanova, M. Uncertainty Management at the Airport Transit View. *Aerospace* **2018**, *5*, 59.
https://doi.org/10.3390/aerospace5020059

**AMA Style**

Rodríguez-Sanz Á, Gómez Comendador F, Arnaldo Valdés R, Cordero García JM, Bagamanova M. Uncertainty Management at the Airport Transit View. *Aerospace*. 2018; 5(2):59.
https://doi.org/10.3390/aerospace5020059

**Chicago/Turabian Style**

Rodríguez-Sanz, Álvaro, Fernando Gómez Comendador, Rosa Arnaldo Valdés, Jose Manuel Cordero García, and Margarita Bagamanova. 2018. "Uncertainty Management at the Airport Transit View" *Aerospace* 5, no. 2: 59.
https://doi.org/10.3390/aerospace5020059