Prototype models and small academic examples...Consortium coordinator: Univerzitet u Beogradu...

Prototype models and small academic examples

D5.1

COCTA Grant: 699326 Call: H2020-SESAR-2015-1 Topic: Sesar-05-2015 Consortium coordinator: Univerzitet u Beogradu – Saobracajni fakultet Edition date: 10 July 2017 Edition: 01.00.00

EXPLORATORY RESEARCH

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The opinions expressed herein reflect the author’s view only. Under no circumstances shall the SESAR Joint Undertaking be responsible for any use that may be made of the information contained herein.

Authoring & Approval

Authors of the document

Name/Beneficiary Position/Title Date

Arne Strauss/UW Principal researcher (OR) 10/07/17

Stefano Starita/UW Post-doc researcher (OR) 10/07/17

Radosav Jovanović/UB-FTTE Principal Researcher (ATM) 10/07/17

Nikola Ivanov/UB-FTTE Researcher (ATM) 10/07/17

Goran Pavlović/UB-FTTE Researcher (ATM) 10/07/17

Frank Fichert (FF)/HW Principal Researcher (Economics) 10/07/17

Reviewers internal to the project


Obrad Babić Senior Expert (ATM) 11/07/17

Approved for submission to the SJU By — Representatives of beneficiaries involved in the project


Radosav Jovanovic/UB-FTTE Principal Researcher (ATM) 11/07/17

Arne Strauss/UW Principal Researcher (OR) 11/07/17

Frank Fichert/HW Principal Researcher (Economics) 11/07/17

Rejected By - Representatives of beneficiaries involved in the project


Document History

Edition Date Status Author Justification

00.00.01 05/05/17 Initial Draft AS, SS, RJ, NI, GP, FF Initial draft

00.00.02 10/05/17 Draft AS, SS, RJ, NI, GP, FF Draft (some elements to be discussed at the AB meeting)

00.00.03 30/05/17 Final Draft AS, SS, RJ, NI, GP, FF Final draft including some of the AB comments and suggestions

00.01.00 01/06/17 Final AS, SS, RJ, NI, GP, FF Approved

00.02.00 10/07/17 Final AS, SS, RJ, NI, GP, FF Approved (responding to the SJU comments)

01.00.00 10/07/17 Final version AS, SS, RJ, NI, GP, FF Approved and version updated to 01.00.00

DELIVERABLE 5.1 - PROTOTYPE MODELS AND SMALL ACADEMIC EXAMPLES

© – 2017 – COCTA consortium. All rights reserved. Licensed to the SESAR Joint Undertaking under conditions.

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COCTA COORDINATED CAPACITY ORDERING AND TRAJECTORY PRICING FOR BETTER-PERFORMING ATM

This deliverable is part of a project that has received funding from the SESAR Joint Undertaking under grant agreement No 699326 under European Union’s Horizon 2020 research and innovation programme.

Abstract

This deliverable proposes an initial mathematical formulation to be used at different stages of the COCTA mechanism. An optimization model is built upon the ideas introduced in the deliverables D3.1 and D4.1. The aim is to minimize the overall cost of capacity provision by managing airspace sectorisation over time. A small academic example is introduced to assess the model’s complexity as well as to provide a numerical analysis. Different demand distribution and capacity budget scenarios are considered and a sequential algorithm is designed as a benchmark. The example shows that centralizing the capacity management, in combination with demand management, has a potential for significant savings within the proposed optimization model. Results of this deliverable will be fed to the following deliverables, developing more complex and realistic mathematical tools to support the final COCTA mechanism.

Acknowledgment

We would like to express our gratitude to members of COCTA Advisory Board (in alphabetical order): Marc Baumgartner, Gerard Boydell, Xavier Fron and Branka Subotić, for their continuous support and valuable feedback upon the general project concept and, in particular, upon the initial mechanism design, received during the meeting in Brussels on 11th May 2017. We also thankfully acknowledge valuable comments and suggestions contributed by Guglielmo Guastalla, EUROCONTROL PRU. We have incorporated many of their suggestions into this document. However, all opinions expressed in this document are exclusively those of the authors.

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Table of Contents

1 Introduction ............................................................................................................... 5

2 Background ............................................................................................................... 6

3 Optimization model ................................................................................................... 8

4 Case study description .............................................................................................. 14

5 Numerical analysis ................................................................................................... 19

6 Next steps ................................................................................................................ 39

7 References ............................................................................................................... 40

Appendix A ..................................................................................................................... 41



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1 Introduction

In this deliverable, we introduce an optimisation model which can be used as the core of the mechanism introduced in WP3 and WP4 deliverables. The model represents the first step in the development of a Decision Support System (DSS) for COCTA and therefore is based on a set of simplistic assumptions. These assumptions will be gradually relaxed in the upcoming deliverables, and more modules (e.g. AO’s route choice forthcoming in D5.2) will be added to the model.

The model builds on top of the main COCTA ideas to co-ordinately decide on capacity and demand management. The NM decides how much capacity units, sector-hours in this case, to order from each Air Navigation Service Provider, to provide the most cost-efficient service to Aircraft Operators. The model is formulated for a busy part of a single day and its objective is to minimize the overall cost imposed on airlines: costs of capacity provision and costs of delays or re-routings. By analysing these different cost components, we are also able to identify significant trade-offs and to determine the effects on other Key Performance Indicators.

An academic example of comprehensible size is used a) to test the optimisation model and demonstrate how the COCTA mechanism works under different circumstances and b) to compare the optimisation model results against results obtained by a sequential assignment algorithm. The model is tested under different capacity scenarios to evaluate the impact of the available capacity ordered by the NM on airspace sectorisation in different ANSPs, and on overall costs. Furthermore, in this deliverable, we assess how traffic distribution influences capacity ordering decisions by testing the model with two traffic profiles: one evenly distributed traffic pattern and one with traffic peaks.

Business Aviation (BA) is not explicitly incorporated into the model because we assume that these flights would appear at the tactical level, while the COCTA process time horizon is, for the time being, strategic and pre-tactical. However, to explore the potential impact of BA on the COCTA process, i.e. to decide what role BA should play in the model, an additional simulation analysis is provided to estimate the influence of BA on costs and decisions.

To sum up, this document introduces an optimization approach which is set to be the starting point for the development of systematic DSS tools that will provide the backbone of the COCTA mechanism.

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2 Background

2.1 Modelling framework

COCTA is the first research project to consider coordinated ATC capacity and air traffic demand management actions to optimize a vector of network performance indicators. We briefly summarize the research efforts carried out so far which set the basis for the COCTA modelling.

The COCTA team first reviewed the state of the art in ATM, Economics and Regulation and Operations Research (D2.1). Redesigning the ATM value-chain (D3.1) and defining the COCTA capacity and demand management process was the second step. COCTA capacity and demand management mechanism, as well as products and transactions between stakeholders (the NM, ANSPs and AOs) were defined in D4.1, based on D3.1. Finally, the data management report (D2.2) summarizes data requirements for modelling, as well as data availability.

The deliverable D5.1 formalizes the COCTA mechanism by introducing the second version in the series of COCTA mathematical models1. The model presented in Section 3 comprises basic elements elaborated in D3.1 and D4.1. For the sake of readability of this document, the reader is referred to previous deliverables for more details. We briefly outline the framework in which the model works.

In the COCTA model, the capacity ordering process of the Network Manager extends over a longer period, based on traffic forecasts which are adjusted regularly against the background of the actual traffic development. For the model in this deliverable it is sufficient to distinguish between two different phases: the medium and the short-term phase.

In a first step (medium term phase) the network manager and the ANSPs agree on a maximum capacity provision for a future period, e.g. one year/six months in advance. Based on this agreement, the ANSP can take decisions which affect maximum capacity provision, e.g. on ATCO training, scheduling of leave days, maintenance work, etc. In the model, we distinguish between three scenarios (high, medium, and low capacity). The decision on these maximum capacities (together with long term decisions not considered in this model) basically determines the fixed costs of the ANSPs. In the model, we assume a simplified cost function for maximum capacity provision with higher maximum capacity leading to higher costs. However, since this model only deals with capacity ordering in the short-term phase (i.e. the decision whether the ANSPs provide a high, medium, or low maximum capacity has been taken before the beginning of the modelling period), these costs are considered to be fixed costs and

1 The initial COCTA model was presented at SESAR Innovation Days 2016 in Delft (Deliverable D6.1).



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therefore will not influence the optimum in this modelling environment. In future models, this can be varied (see Appendix A).

In a second step, rather shortly before the actual day of operation (e.g. seven days before), the Network Manager decides to which degree it wants to make use of the capacity within the given framework, i.e. which sector configuration (sectors and opening/closing times) should actually be chosen. This decision influences the variable costs of capacity provision. In the model we assume constant costs for each additional unit of capacity; this also can be varied in future models. In the model we call these costs, which depend on actual sector hour provision within the respective capacity scenario, variable costs.

In this deliverable D5.1 we analyse trade-offs between capacity and demand management actions to improve overall cost-efficiency:

• Capacity management: Ordering (more) capacity, and thereby increasing the cost of capacity provision, to reduce costs of delaying or re-routing flights (uniformly termed “displacement costs” throughout the document) vs

• Demand management: Delaying or re-routing flights to reduce cost of capacity provision.

While cost-efficiency is the primary model objective in this deliverable, we also measure and monitor trade-offs between different key performance indicators (Section 5). Further optimisation model modifications toward more complex (and therefore closer to reality) models are discussed in Section 6.

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3 Optimization model

3.1 Assumptions

3.1.1 Network, flights and trajectories

The problem deals with a set of flights 𝐹 flying over an airspace network. Each flight 𝑓 connects an origin (𝑜) to a destination (𝑑) airport. Trajectories for each 𝑜-𝑑 couple are chosen from set 𝑅𝑜𝑑 which contains the shortest route and some alternatives. Capacity limitations may lead to situations where the shortest, or some alternative routes, are not available. The displacement cost is defined as the additional cost incurred by an AO when it flies a route which is not its favourite (i.e. any route other than shortest route without delay is associated with non-zero displacement cost). The displacement

cost of trajectory 𝑟 for flight 𝑓 is 𝑑𝑟𝑓

. In this deliverable, we assume that AOs prefer flying shortest routes which are also the cheapest in the COCTA context (see 3.1.2). Finally, let us also use 𝐵 to denote the route-sector-time incidence matrix (𝑏𝑟𝑠𝑡 = 1 if route 𝑟 uses sector 𝑠 at time 𝑡, 0 otherwise).

3.1.2 Cost recovery

Within the COCTA mechanism the trajectory pricing will be used to move demand from specific to flexible products (as described in D4.1). In this deliverable, only specific trajectory products are considered and therefore there is effectively no possibility of influencing AOs’ purchase behaviour by means of pricing. Nonetheless, to be coherent with the COCTA mechanism and to provide a formulation which can be easily extended, the model explicitly includes pricing decision variables. One important contribution of the COCTA framework is the abandoning of airspace’s charges in favour of airports pairs’ charges. The rationale is that with such charging scheme AOs are encouraged to fly the shortest route, leading to a considerable improvement of the environmental KPI (no incentives to choose longer route through airspace with lower charges).

We consider the NM to be revenue neutral, i.e. the NM is not seeking to make profits. Charges are chosen from a discrete set and the total revenue collected must cover the fixed and variable costs of capacity provision, within a known tolerance set by parameter 𝛾 ∈ [0,1].

3.1.3 Sectorisation

We consider a network of airspaces 𝑎 ∈ 𝐴, with each airspace 𝑎 composed by a set of elementary sectors 𝑠 ∈ 𝑆𝑎. An airspace 𝑎 has a known number of sector configurations at which it can operate. Let 𝐶𝑎 be the set of these configurations, indexed by 𝑐. A configuration 𝑐 is identified by a partition 𝑃𝑐. Elements of a partition are indexed by 𝑝, to represent how the airspace is split among air traffic controllers. In other words, an element 𝑝 is a portion of the airspace, identified by a subset of elementary sectors 𝑠 ∈ 𝑆𝑝 ⊆ 𝑆𝑎. In this deliverable, the case study considers only horizontal division



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of airspace, i.e. the airspace cannot be split in a vertical sense. However, the formulation of the model introduced is equally suitable to cope with vertical sectorisation as well.

To better comprehend the notation, let us consider the following example:

Figure 3.1 represents an airspace. The airspace is composed of four elementary sectors. Different colours are used to identify collapsed sectors. Elementary sectors are denoted with an id (ESX):

Figure 3-1 An airspace with four elementary sectors - illustration

Now, let us assume that the airspace has three possible configurations, as displayed in Figure3.2:

For example, the first configuration has three sectors that cover the entire airspace (one collapsed and two elementary) whereas the last one has all the elementary sectors collapsed together. Formally, the first configuration is represented as follows:

𝑃1 = {(1,4); (2); (3))}

Meaning that the airspace is split into three areas identified by elementary sectors (1, 4), (2) and (3) respectively. Similarly, the two other configurations are formalized as follows:

𝑃2 = {(1); (2, 3, 4)}𝑃3 = {(1, 2, 3, 4)}

Every element p in a partition has a capacity 𝑘𝑝 denoting the maximum number of flights allowed to

enter the airspace portion identified by 𝑝, per time period (commonly referred to as “entry counts”).

Figure 3-2 Different sector configurations within an airspace - illustration

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A configuration is also defined by the number of sector-hours ℎ̅𝑎𝑐which it consumes in every time period.

3.1.4 Time scales

Two time scales are considered: a fine-scale used to describe trajectories and a coarse-scale used to model the dynamics of airspace configurations. Parameters �̅�and �̅� are the size of the fine-scale and coarse-scale time period, respectively. More specifically, �̅� represents the minimum unit used to define trajectories (e.g., 5-10min) and �̅� represents how often a sector configuration can change (e.g., 30-60min). For simplicity, we assume that a coarse-scale time period can be divided into an integer number of fine-scale time periods (i.e., �̅�%�̅� = 0).

3.2 Model notation and formulation

Under the assumptions summarized in the previous section, we can now formulate the optimization model. The notation used is summarized in the following table:

Sets:

𝑂 Set of origin-destination pairs

𝐹, 𝐹𝑜𝑑 Respectively, the set of all flights and the set of flights connecting 𝑜𝑑

𝑅𝑜𝑑 The set of routes connecting 𝑜𝑑

𝑇 Fine-scale time horizon

𝑈 Coarse-scale time horizon

𝐴 Set of airspaces

𝐶𝑎, 𝑆𝑎 Set of configurations and elementary sectors for airspace 𝑎

𝑃𝑐 Partition of elementary sectors corresponding to a configuration

𝑆𝑝 Subset of elementary sectors forming the aggregated sector within a configuration

𝑋𝑜𝑑 Set of charges 𝑔 for pair 𝑜𝑑

Indices:

𝑓 Flights

𝑜𝑑 Origin and destination airports

𝑡 Fine-scale time index



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𝑢 Coarse-scale time index

𝑟 Route

𝑎 Airspace

𝑐, 𝑐′ Airspace’s configuration

𝑝 Airspace portion

𝑠 Elementary sector

Parameters:

𝑣𝑓 Charge weight dependent on the type of aircraft used by 𝑓

𝜌𝑎 Variable cost of providing one sector-time unit for airspace 𝑎

𝛿𝑎 Cost of purchasing one additional sector-time unit for airspace 𝑎

𝑘𝑝 Maximum capacity of airspace portion 𝑝

𝑞𝑎 Fixed cost of airspace 𝑎

𝛾 Percentage of cost recovery

ℎ̅𝑎𝑐 Number of sector hours consumed by airspace 𝑎 working in configuration 𝑐

�̅� Length (min) of a fine-scale time unit

�̅� Length (min) of a coarse-scale time unit

𝐵 Route-sector-time incidence matrix, with 𝑏𝑟𝑠𝑡 = 1 if route 𝑟 crosses 𝑠 at time 𝑡

𝑑𝑟𝑓

Displacement cost of route 𝑟 for flight 𝑓

𝑔𝑑𝑟 Ground delay for route 𝑟

𝑡𝑜𝑓 Flight 𝑓 scheduled take off time

𝑏𝑟𝑠𝑢(𝑡𝑜𝑓) Is equal to 1 if route 𝑟 uses sector 𝑠 at time 𝑢, assuming take off 𝑡𝑜𝑓, 0

otherwise

𝑙𝑟 Length of route 𝑟 expressed as number of time periods 𝑡

Variables:

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𝑥𝑜𝑑𝑔

= {1, if charges𝑔 are implemented between 𝑜and 𝑑0, otherwise

𝑧𝑎𝑐𝑢 = {1, if airspace𝑎 uses configuration 𝑐 at time 𝑢0, otherwise

𝑦𝑟𝑓

= {1, if flight𝑓 chooses route 𝑟 when booking early0, otherwise

𝑤𝑎 Is the sector-hour capacity increment for airspace 𝑎

The problem of identifying optimal Airspaces Configurations and Route Charges (ACRC) is formulated below as a linear program:

[ACRC] min

𝒛,𝒙𝒉,𝒚

∑ ∑ 𝑣𝑓𝑔𝑥𝑜𝑑𝑓

𝑔

𝑔∈𝑋𝑜𝑑𝑓𝑓∈𝐹

+ ∑ ∑ 𝑑𝑟𝑓

𝑦𝑟𝑓

𝑟∈𝑅𝑜𝑑𝑓𝑓∈𝐹

(1)

s. t. ∑ 𝑦𝑟

𝑓

𝑟∈𝑅𝑜𝑑𝑓

= 1 ∀𝑓 ∈ 𝐹 (2)

∑ 𝑥𝑜𝑑𝑔

𝑔∈𝑋𝑜𝑑

= 1 ∀𝑜𝑑 ∈ 𝑂 (3)

∑ 𝑧𝑎𝑐𝑢 = 1

𝑐∈𝐶𝑎

∀𝑎 ∈ 𝐴,

𝑢 ∈ 𝑈 (4)

∑ ∑ ∑ 𝑏𝑟𝑠𝑢(𝑡𝑜𝑓 + 𝑔𝑑𝑟) 𝑦𝑟

𝑓

𝑠∈𝑆𝑝

≤ 𝐾𝑝𝑧𝑎𝑐𝑢 + |𝐹| ∑ 𝑧𝑎𝑐′𝑢

𝑐′≠𝑐𝑟∈𝑅𝑜𝑑𝑓𝑓∈𝐹

∀𝑎 ∈ 𝐴,

𝑐 ∈ 𝐶𝑎 ,

𝑝 ∈ 𝑃𝑐,

𝑢 ∈ 𝑈

(5)

∑ ∑ 𝑣𝑓𝑔𝑥𝑜𝑑𝑓

𝑔

𝑔∈𝑋𝑜𝑑𝑓𝑓∈𝐹

≥ 𝛾 ∑(𝑞𝑎

𝑎∈𝐴

+ 𝜌𝑎

∑ ∑ ℎ̅𝑎𝑐𝑧𝑎𝑐𝑢

𝑐∈𝐶𝑎𝑢∈𝑈

+ 𝛿𝑎 𝑤𝑎) (6)



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∑ ∑ ℎ̅𝑎𝑐𝑧𝑎𝑐𝑢

𝑐∈𝐶𝑢∈𝑈

≤ ℎ𝑎 + 𝑤𝑎 ∀𝑎 ∈ 𝐴 (7)

𝑧𝑎𝑐𝑢 ∈ {0, 1}

∀𝑎 ∈ 𝐴,

𝑐 ∈ 𝐶𝑎 ,

𝑢 ∈ 𝑈

(8)

𝑦𝑟𝑓

∈ {0, 1} ∀𝑓 ∈ 𝐹

𝑟 ∈ 𝑅𝑜𝑑𝑓

(9)

𝑥𝑜𝑑𝑔

∈ {0, 1} ∀𝑜𝑑 ∈ 𝑂

𝑔 ∈ 𝑋𝑜𝑑 (10)

𝑤𝑎 ∈ {0, 1, 2, … , �̅�} ∀𝑎 ∈ 𝐴 (11)

The objective (1) is to minimize the total costs imposed on airlines, i.e. o-d charges plus displacement costs. The NM decides on the working sector configuration of each airspace, capacity budget increments and charges for each airport pair and on the flight-to-route assignments. In this deliverable, we only analyse the decision on sector configurations and route assignments. Constraints (2) ensure that each flight must be assigned to one and only one route. Equations (3) guarantee that exactly one charge is selected for each (𝑜, 𝑑). Constraints (4) state that an operating sector configuration must be defined at any time, for each airspace. Inequalities (5) set the capacity limitations across the network. More specifically, if partition 𝑝 belongs to configuration 𝑐 and 𝑐 is chosen as configuration at time 𝑢 (i.e., 𝑧𝑎𝑐𝑢 = 1), then no more than 𝐾𝑝 aircraft can use the aggregated sector identified by 𝑝, at time

𝑢. To compute the number of flights using a sector at time u, we need to consider the actual take off

time given by𝑡𝑜𝑓 plus the ground delay 𝑔𝑑𝑟 generated by trajectory 𝑟. Finally, the sum of all flights

using collapsed sector 𝑝 at time 𝑢 (“entry count”), must be less or equal than 𝐾𝑝. On the other hand,

if configuration 𝑐 is not chosen, the constraint becomes inactive. Constraint (6) enforces that the revenue collected must entirely cover the costs of capacity provision. Inequalities (7) are the sector-hours budget constraints for each airspace which accounts for the fixed budget. Finally, (8)-(11) define

the limitations for the decision variables.

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4 Case study description

We test the model using an academic example, Figure 4-1.

Figure 4-1 Airspace structure for the case study

There are five ANSPs represented with different colours in Figure 4-1. Four bordering ANSPs have two elementary sectors, while the central ANSP has three. Capacity of elementary and collapsed sectors, are given in Table 4-1, and any combination of the elementary/collapsed sectors is an option for airspace configuration/sectorisation. The costs of capacity provision are discussed in Appendix A.



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Table 4-1 Sector types and capacities

ANSP Sector names

Type 30 minute capacities

T T Collapsed 19

T T1 Elementary 17

T T2 Elementary 17

R R1 Elementary 18

R R2 Elementary 18

R R Collapsed 18

Q Q Collapsed 18

Q Q1 Elementary 16

Q Q2 Elementary 16

Q Q3 Elementary 17

Q Q12 Collapsed 17

Q Q23 Collapsed 18

Q Q31 Collapsed 18

U U Collapsed 18

U U1 Elementary 18

U U2 Elementary 18

S S Collapsed 19

S S1 Elementary 17

S S2 Elementary 17

The total of 150 flights is assumed to enter the network during the considered time period. There are two main traffic flows: F1 (East and West) and F2 (South and North). There are several sub-flows with indicated shortest routes in figure 4-1.

• Flow from West to East (F11E, F12E) and from East to West (F11W, F12W) ;

• From North to South (F21S, F22S) and from South to North (F21N, F22N).

We assume that the F1 is a more dominant flow, with approximately two times more flights than the flow F2. Also, eastern flows are more dominant than western, as well as southern compared to northern flows. Figure 4-2 shows the traffic profile over two hours. The blue line represents the aggregated traffic and shows two major peaks after 30 and 80 minutes.

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We consider three aircraft sizes small (E145), medium (A320) and large (B752). Share of these three aircraft sizes in the flows are presented in Table 4-2. In total, the demand comprises 44 flights operated with small aircraft, 90 medium sized ones, and 16 large aircraft.

Table 4-2 Percentage shares of aircraft types per traffic flow.

Aircraft type

Flow Small Medium Large

F11E 30 60 10

F11W 30 60 10

F12E 25 65 10

F12W 25 65 10

F21S 40 50 10

F21N 40 50 10

F22S 25 65 10

F22N 25 65 10

0

2

4

6

8

10

12

14

5 1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5 5 0 5 5 6 0 6 5 7 0 7 5 8 0 8 5 9 0 9 5 1 0 0 1 0 5 1 1 0 1 1 5 1 2 0

NU

MB

ER O

F FL

IGH

TS

MIN

DEMAND WITH TRAFFIC PEAKS

F11E F12E F21S F22S F11W

F12W F21N F22N TOTAL

Figure 4-2 Demand with traffic peaks (“Peaked demand”)



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Preferred routes are shortest and we consider several alternative routes, as shown in Table 4-3. For simplicity, both east and westbound and south and northbound flows have the same alternative, just vertically separated. Therefore, in Table 4-3 flows F11E and F11W are reported as F11; the same stands for all the other flows. There is a set of alternative routes for each flow. Rows represent shortest and alternative routes, the first column presents traffic flow and the second column shows the route type (shortest or alternative route):

• Shortest route, which is the preferable route (shortest).

• Shortest route with delay up to 30 minutes (S-delay_min). For instance, S-10min denotes shortest route delayed for 10 minutes.

• Several re-routing options for each flow (F_flow_number-alternative_route-ID). For example, F11-1 denotes a first re-routing option for flows F11, which is up to 40 NM longer than the shortest route.

Route description shows the sequence of elementary sectors and how many elementary time periods (5 min) a flight spends in each of them. A flight from the flow F11 spends 2 elementary periods (10 minutes) in sector R1 when flying on shortest route (R1, 2), then spends 10 minutes in Q1, Q2 and U1 respectively. Displacement costs are calculated for each of the alternative routes for each aircraft type; it is zero for the shortest route and non-zero for other routes (costs are in EUR). For displacement cost calculation and functions see Appendix A.

Table 4-3 Available routes

Route description Displacement cost (EUR)

Flow Route type Route (elementary sector, time_in_sector) Small Medium Large

F11 Shortest (R1, 2) (Q1, 2) (Q2, 2) (U1, 2) 0 0 0

F11 F11-1 (R1, 2) (S2, 4) (U1, 2) 152 280 355

F11 F11-2 (R1, 2) (S2, 2) (Q2, 2) (U1, 2) 69 127 162

F11 F11-3 (R1, 2) (Q1, 2) (S2, 2) (U1, 2) 69 127 162

F11 S-5min (R1, 2) (Q1, 2) (Q2, 2) (U1, 2) 47 90 100

F11 S-10min (R1, 2) (Q1, 2) (Q2, 2) (U1, 2) 120 236 313

F11 S-15min (R1, 2) (Q1, 2) (Q2, 2) (U1, 2) 204 450 560

F11 S-20min (R1, 2) (Q1, 2) (Q2, 2) (U1, 2) 321 693 888

F11 S-25min (R1, 2) (Q1, 2) (Q2, 2) (U1, 2) 453 1004 1275

F11 S-30min (R1, 2) (Q1, 2) (Q2, 2) (U1, 2) 611 1390 1740

F12 Shortest (R2, 2) (Q3, 4) (U1, 2) 0 0 0

F12 F12-1 (R2, 2) (T1, 4) (U2, 2) 152 280 355

EDITION [01.00.00]

18


Flow Route type Route (elementary sector, time_in_sector) Small Medium Large

F12 S-5min (R2, 2) (Q3, 4) (U1, 2) 47 90 100

F12 S-10min (R2, 2) (Q3, 4) (U1, 2) 120 236 313

F12 S-15min (R2, 2) (Q3, 4) (U1, 2) 204 450 560

F12 S-20min (R2, 2) (Q3, 4) (U1, 2) 321 693 888

F12 S-25min (R2, 2) (Q3, 4) (U1, 2) 453 1004 1275

F12 S-30min (R2, 2) (Q3, 4) (U1, 2) 611 1390 1740

F21 Shortest (S1, 1) (S2, 1) (Q1, 2) (Q3, 2) (T1 ,1) (T2, 1) 0 0 0

F21 F21-1 (S1, 1) (S2, 1) (R1, 2) (R2, 2) (T1 ,1) (T2, 1) 152 280 355

F21 F21-2 (S1, 1) (S2, 1) (Q1, 2) (R2, 2) (T1 ,1) (T2, 1) 69 127 162

F21 S-5min (S1, 1) (S2, 1) (Q1, 2) (Q3, 2) (T1 ,1) (T2, 1) 47 90 100

F21 S-10min (S1, 1) (S2, 1) (Q1, 2) (Q3, 2) (T1 ,1) (T2, 1) 120 236 313

F21 S-15min (S1, 1) (S2, 1) (Q1, 2) (Q3, 2) (T1 ,1) (T2, 1) 204 450 560

F21 S-20min (S1, 1) (S2, 1) (Q1, 2) (Q3, 2) (T1 ,1) (T2, 1) 321 693 888

F21 S-25min (S1, 1) (S2, 1) (Q1, 2) (Q3, 2) (T1 ,1) (T2, 1) 453 1004 1275

F21 S-30min (S1, 1) (S2, 1) (Q1, 2) (Q3, 2) (T1 ,1) (T2, 1) 611 1390 1740

F22 Shortest (S1, 1) (S2, 1) (Q2, 2) (Q3, 2) (T1, 1) (T2, 1) 0 0 0

F22 F22-1 (S1, 1) (S2, 1) (U1, 2) (U2, 2) (T1, 1) (T2, 1) 152 280 355

F22 F22-2 (S1, 1) (S2, 1) (Q2, 2) (U2, 2) (T1, 1) (T2, 1) 69 127 162

F22 S-5min (S1, 1) (S2, 1) (Q2, 2) (Q3, 2) (T1, 1) (T2, 1) 47 90 100

F22 S-10min (S1, 1) (S2, 1) (Q2, 2) (Q3, 2) (T1, 1) (T2, 1) 120 236 313

F22 S-15min (S1, 1) (S2, 1) (Q2, 2) (Q3, 2) (T1, 1) (T2, 1) 204 450 560

F22 S-20min (S1, 1) (S2, 1) (Q2, 2) (Q3, 2) (T1, 1) (T2, 1) 321 693 888

F22 S-25min (S1, 1) (S2, 1) (Q2, 2) (Q3, 2) (T1, 1) (T2, 1) 453 1004 1275

F22 S-30min (S1, 1) (S2, 1) (Q2, 2) (Q3, 2) (T1, 1) (T2, 1) 611 1390 1740



19

5 Numerical analysis

In this section, we perform a numerical analysis to show the potential advantages of implementing smart capacity management with the optimisation model introduced in Section 3. Results are compared against a benchmark (labelled “sequential analysis”) which has been developed to mimic the current system. We use a peaked demand profile to study how the network performs in a highly congested scenario. Furthermore, the impact of the demand peaks is assessed by comparison to a flat demand profile. Three capacity budgets are considered to evaluate scenarios in which the NM has high, medium and low sector-hours availability. Finally, investigate the impact of business aviation (BA) - which appears randomly on the day of operation - on the system’s costs via a simulation study. Since COCTA focusses on the pre-tactical stage, the simulation study is intended to deliver insights into whether we need to incorporate BA effects into modelling and decision-making in the pre-tactical stage.

5.1 Optimization approach vs sequential assignments

To provide a benchmark for the optimization model, in this section we introduce a sequential assignment algorithm. The basic idea is to randomly build a sequence of show up of all flights 𝑓 ∈ 𝐹. These flights are assigned to the best available route in the order of this sequence. Given the randomness of the algorithm, the assignments are repeated for 200 iterations and the output of the simulation are the averaged results.

1 Initialize sector capacities to their highest possible level

2 for iter = 0 : NumIter

3 Randomly generate a sequence of users (flights) show up of all flights in 𝐹

4 while there are flights left in the sequence

5 assign next flight in the sequence to the best available route

6 update sectors’ capacities

7 end

7 end

8 return averaged results

The airspace network is initially assumed to function at its highest operational level (i.e., every elementary sector open). After collecting the data from the simulation, capacity configurations are further refined by collapsing portions of airspaces whose overall percentage usage is less than 100%.

EDITION [01.00.00]

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For example, if during the first 30 minutes R1 and R2 have percentages of usage equal to 51% and 35%, they are collapsed to a single sector with usage level of 86%. This ex-post analysis is necessary because the algorithm does not implement any coordinated capacity management and therefore solutions always return inefficient airspace configurations. Figure 5-1 illustrates the outcome of the sequential algorithm – sector opening scheme.

Figure 5-1. Sector opening scheme – sequential algorithm

Working configurations are colour-coded: collapsed sectors are identified by the elementary sectors with the same colour. For instance, airspace R for the first 30 min works with R1 and R2 aggregated, subsequently, both elementary sectors are open until the end of the time horizon.

Table 5-1. Capacity consumption and variable cost – sequential algorithm

ANSP Active sector-half-

hourly periods Variable capacity

cost (Euro)

R 7 5,250

S 7 3,220

U 4 2,600

T 7 3,990

Q 11 10,120

Total 36 25,180

Table 5-1 shows the number of sector half hourly periods used by each ANSP and the resulting variable costs. For instance, airspace T uses 7 sector periods, leading to a 3,990€ expenditure. The total variable capacity cost is 25,180€. This cost should be added to the fixed cost of 26,200€ to obtain the total capacity provision cost. The underlying assumptions for deriving the costs of capacity provision are explained in appendix A. For example, the variable costs for operation ½ sector hour by ANSP R are assumed to be 750 EUR, leading to total variable cost of 5,250 EUR (=7 * 750 EUR).



21

In Table 5-2 we analyse the assignment for each aircraft category. Columns 2 and 3 show the average number and percentage of flights assigned to the shortest (optimal) route, respectively. Percentages of best route assignments do not change dramatically among aircraft categories. This is expected given that no priority rules in favour of large aircraft are set in the algorithm. Columns 4 and 5 list the average total delay and average delay per delayed flight. Last two columns report the total average displacement and average displacement per displaced (i.e. delayed or rerouted) flight. Importantly, on average about 6 flights per iteration remain unassigned, i.e. have no trajectory available at the moment of their show-up. To facilitate the comparison of sequential algorithm with optimisation outcomes we associated the cost of 60 minute at-gate delay with each such flight. Given the strongly increasing delay cost with time (see Appendix), this assumption results in dramatic increase of displacement costs in the sequential algorithm.

Table 5-2 Summary statistics – sequential algorithm

(1) (2) (3) (4) (5) (6) (7)

Aircraft type

Shortest-route

assignments (# flights)

Shortest-route

assignments (%)

Total delay (min)

Average delay per delayed

flight (min)

Total displacement

cost (EUR)

Average displacement

cost per displaced

flight (EUR)

Small 26.4 60.0% 218.7 12.6 5,242.0 297.5

Medium 57.7 64.1% 329.5 10.5 16,101.3 497.7

Large 9.1 57.0% 99.2 15.0 7,419.9 1,076.9

Total 93.2 62.1 647.4 11.7 28,763.2 505.5

Table 5-3 provides a more detailed insight on how flights that cannot be allocated to their shortest route are displaced. Unsurprisingly, given the inherent individual (selfish) flight perspective, as long as there is sufficient capacity flights go for cheaper option available – i.e. first for at-gate delays and only very seldom choose re-routings (less than two flights per iteration on average).

Table 5-3 Distribution of displaced flights – sequential algorithm

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

Aircraft type

re-route up to 20NM

re-route up to 40NM

Delay

5min

Delay

10min

Delay

15min

Delay

20min

Delay

25min

Delay

30min

Non-accommodated

flights

Small 0.3% 0.4% 32.4% 0.7% 0.4% 0.4% 0.0% 0.5% 5.0%

Medium 0.4% 0.6% 30.2% 0.5% 0.1% 0.3% 0.5% 0.5% 2.9%

Large 1.4% 0.4% 32.8% 0.0% 0.1% 0.6% 0.3% 0.3% 7.1%

EDITION [01.00.00]

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Columns 2 and 3 show the average percentage of flights which are assigned routes that are up to 20 NM or up to 40 NM longer than the shortest route. Columns 4 to 9 report the average percentages of flights which have been assigned 5, between 5 and 10 minutes of ground delay and so on. Finally, column 10 shows the average percentage of flights which could not have been accommodated, i.e. for which there was no available route at the moment of their show up, since the associated capacities were already consumed by previous users. The table indicates that short ground delay is expectedly an option preferred to re-routing, when the shortest route is unavailable. However, an important outcome of a sequence of selfish (non-coordinated) individual trajectory choices is also a non-negligible share of flights that cannot be accommodated within available airspace capacities.

Re-routing flights on longer routes has an obvious environmental impact due to the increase in CO2 emissions. Table 5-4 shows the total CO2 emission (Kg) increments for each aircraft category, compared to shortest routes. The overall effect of re-routings is estimated at 3,195 Kg, corresponding to about 1,014 Kg of additional fuel burn.

Table 5-4 Additional CO2 emission – sequential algorithm

Aircraft type

Additional CO2 (Kg) due to 20NM

re-routings


re-routings

Total additional CO2 (Kg)

Small 180 46 226

Medium 2,242 363 2,605

Large 235 129 364

Total 2,657 538 3,195

Finally, Figure 5-2 shows the average percentage utilisation of each sector (elementary or collapsed), based upon 200 algorithm runs. It shows that for 39% of sector-periods the capacity utilisation is between 85% and 100%. On the other end of the spectrum, only 11% of sector-periods have capacity utilisation of up to 50%. Exactly one half of all sector-periods have utilisation of 50-84%.

Figure 5-2 Sector utilisation – sequential algorithm



23

5.2 Optimisation scenarios

In the following sections, results from the sequential algorithm are compared with results obtained by the optimization model ACRC, tested under different capacity and demand scenarios.

5.2.1 High capacity scenario (“Opt-High”)

In this section, we test the optimisation model with a high capacity budget. More specifically, we assume that the number of sector-hours available is sufficient to keep every elementary sector open for two hours. Parameters of this scenario are summarised in Table 5-5.

Table 5-5 Available capacities – Opt-High

ANSP Sector-hour budget, 𝒉𝒂

R 4

S 4

U 4

T 4

Q 6

Figure 5-3 shows the optimal airspace configuration profiles returned by the model. Despite having a large capacity budget, the solution of the model shows a rather parsimonious usage of sector hours. Airspace S, for instance, operates at its lowest capacity level (S1 and S2 aggregated) for the entire horizon. The reason is that, as specified by the model objective function, opening more sectors has a direct impact on the variable costs of the system. Consequently, the model deals with the trade-off of reducing both displacement and variable capacity costs.

Figure 5-3 Sector opening scheme – Opt-High

EDITION [01.00.00]

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Table 5-6 shows that using the optimization model reduces variable capacity costs by almost one third compared to the sequential assignment algorithm (18,880€ vs. 25,180€).

Table 5-6 Capacity consumption and variable cost – Opt-High

Active sector-half-hourly periods

Variable capacity cost (Euro)

R 6 4,500

S 4 1,840

U 5 3,250

T 5 2,850

Q 7 6,440

Overall 27 18,880

On the other hand, Table 5-7 highlights that a slightly lower number of flights are assigned to the shortest route compared to the sequential algorithm. However, since in Opt-High there are no unassigned flights, unlike with the sequential algorithm, the total displacement cost strongly decreases from the 28,763€ of the sequential algorithm to 9,492€. Taking into account the savings on the capacity provision costs too, the net effect is the cost reduction of 31.9% (i.e. total cost reduces from 80,143 EUR to 54,573 EUR).

Table 5-7 Summary statistics – Opt-High

(1) (2) (3) (4) (5) (6) (7)

Aircraft type

Shortest-route


Shortest-route

assignments (%)

Total delay (min)

Average delay per delayed flight (min)

Total displacement

cost (EUR)


cost per displaced

flight (EUR)

Small 14 31.8% 115 7.2 3,035.0 101.2

Medium 55 61.1% 160 6.7 6,095.5 174.1

Large 13 81.3% 10 5.0 362.1 120.7

Total 82 54.7% 285 6.8 9,492.6 139.6

Table 5-8 provides a more detailed insight on how the ACRC model manages flights that cannot be assigned to the shortest route for capacity reasons. It shows that the most common model outcome is to assign a short delay (up to 10 minutes). Nonetheless, considerable share of flights are re-routed, especially those using small aircraft.



25

Table 5-8 Distribution of displaced flights – Opt-High

(1) (2) (3) (4) (5) (6) (7) (8) (9)

Aircraft type

re-route up to 20NM

re-route up to 40NM

Delay

5min

Delay

10min

Delay

15min

Delay

20min

Delay

25min

Delay

30min

Small 11.4% 20.5% 25.0% 9.1% 0.0% 2.3% 0.0% 0.0%

Medium 2.2% 10.0% 17.8% 8.9% 0.0% 0.0% 0.0% 0.0%

Large 6.3% 0.0% 12.5% 0.0% 0.0% 0.0% 0.0% 0.0%

The CO2 emission increments are listed in Table 5-9. The big share of emission increment is primarily due to 18 flights being assigned re-routings on 40NM longer routes, and the associated fuel burn increment. Table 5-9 shows that while ACRC strongly reduces total costs compared to the sequential algorithm, the CO2 emissions in the ACRC assignment are notably higher. This results from the fact that a great deal of capacity cost savings compared to sequential algorithm is apparently enabled by a more frequent application of re-routing measures in the ACRC (with 26 flights assigned longer routes in total). It is worth remarking that ACRC does not explicitly aim to minimize the emissions. Therefore, this number could possibly be further reduced by enforcing it in the objective function.

Table 5-9 Additional CO2 emission – Opt-High

Aircraft type


re-routings


re-routings


Small 795 2,862 3,657

Medium 660 5,940 6,600

Large 444 0 444

Total 1,899 8,802 10,701

Finally, Figure 5-4 highlights an arguably more efficient capacity resource usage compared to the sequential algorithm, now with no sector-period having utilisation lower than 50%. However, 55% of sector-periods end up with fully used capacities, which is not necessarily the most desired feature (re. robustness of the solution), as shall be reflected upon in more detail during the discussion on business aviation inclusion effects (Chapter 6).

EDITION [01.00.00]

26


Figure 5-4 Sector utilisation – Opt-High scenario

5.2.2 Medium capacity scenario (“Opt-Med”)

In this section, we consider a medium capacity scenario represented by table 5-10.

Table 5-10 Available capacity – Opt-Med

ANSP Sector-hour budget, ℎ𝑎

R 3

S 2

U 2

T 3

Q 3

Under these capacity assumptions, there is no longer enough capacity to keep all the elementary sectors open during the entire time horizon. Furthermore, the budget is not enough to replicate the solution obtained in the previous scenario. The optimal airspaces configuration profile returned by the model is shown in Figure 5-5.



27

Figure 5-5 Sector opening scheme – Opt-Med

The first obvious consequence of a smaller budget is the reduction in the variable costs from 18,880€ to 16,740€, Table 5-11. The impact of a smaller budget is particularly evident in the profile of airspaces U and T which have no other choice than operating at the lowest capacity configuration for the entire horizon.

Table 5-11 Capacity consumption and variable cost – Opt-Med


hourly periods

Variable capacity cost

(Euro)

R 6 4,500

S 4 1,840

U 4 2,600

T 4 2,280

Q 6 5,520

Total 24 16,740

Table 5-12 shows that the number of assignments to shortest routes compared to Opt-High scenario shows no change for large aircraft and an increment (+3) for small aircraft. Conversely, the same number decreases from 55 to 44 for medium-sized aircraft. Table 5-12 also shows that despite having the same number of displaced large aircraft the corresponding displacement cost more than doubles: from 362€ to 760€. The reason is that with less capacity, displacement measures start to be more “aggressive” (i.e. longer re-routings and delays) on large aircraft as well. In fact, Table 5-13 shows that

EDITION [01.00.00]

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for the first time one large aircraft (correspondent to 6.4% of the demand) is assigned a longer than 5 minutes ground delay.

The total variable cost (variable capacity cost + displacement cost) in this scenario is 35,840.7 EUR which is below the benchmark without optimization but above the total variable cost in the high capacity scenario. Although the fixed costs of maximum capacity provision are lower in the medium capacity scenario than in the high capacity scenario, the overall costs are still lower in the high capacity scenario.

Table 5-12 Summary statistics – Opt-Med

(1) (2) (3) (4) (5) (6) (7)

Aircraft type

Shortest-route


Shortest-route

assignments (%)

Total delay (min)


Total displacement

cost (EUR)


cost per displaced

flight (EUR)

Small 17 38.6% 280 13.3 5,046.7 186.9

Medium 44 48.9% 450 10.5 13,294.0 289.0

Large 13 81.3% 25 8.3 760.0 253.3

Total 74 49.3 755 11.3 19,100.7 251.3

Table 5-13 Distribution of displaced flights – Opt-Med

(1) (2) (3) (4) (5) (6) (7) (8) (9)

Aircraft type

re-route up to 20NM

re-route up to 40NM

Delay

5min

Delay

10min

Delay

15min

Delay

20min

Delay

25min

Delay

30min

Small 6.8% 6.8% 15.9% 13.6% 4.5% 4.5% 2.3% 6.8%

Medium 3.3% 0.0% 22.2% 12.2% 3.3% 6.7% 3.3% 0.0%

Large 0.0% 0.0% 12.5% 0.0% 6.3% 0.0% 0.0% 0.0%

Under the medium capacity scenario ground delay assignment is the by far more often applied displacement measure than re-routing (67 flights delayed at-gate vs. 9 assigned longer routes). This is very clearly reflected in the estimation of CO2 emissions (Table 5-14). Only 2,421 Kg of additional CO2 emissions are caused by re-routings. This is significantly less than what was observed within the high capacity scenario (10,701 Kg) and slightly lower than the outcome of the sequential assignment algorithm (3,195 Kg).

The usage of the activated airspace capacities is shown in Figure 5-6. Most notable differences compared to the High capacity scenario concern the drops in the usage of airspace T at the beginning of the model period. This is likely due the increment in the ground delay assignments which has the effect of spreading the demand across the horizon.



29

Table 5-14 Additional CO2 emission – Opt-Med

Aircraft type

Additional CO2

(Kg) due to 20NM re-routings


re-routings


Small 477 954 1,431

Medium 990 0 990

Large 0 0 0

Total 1,467 954 2,421

Overall, 50% of active sector-periods end up with full declared capacity used, while several sector-periods exhibit utilisation of about 50% or less.

Figure 5-6 Sector utilisation – Opt-Med

5.2.3 Low capacity scenario (“Opt-Low”)

In this section, we consider a low capacity scenario described in table 5-15.

The capacity levels considered are the minimum possible. A further decrement in the budget would lead to unfeasible solutions as long as capacity re-ordering is not considered.

EDITION [01.00.00]

30


Table 5-15 Available capacities – Opt-Low

ANSP Sector-hour budget, ℎ𝑎

R 3

S 2

U 2

T 2

Q 2

The optimal airspaces configuration profile shows that, with a small budget, airspaces S, U, T and Q must operate with their elementary sectors collapsed for the entire time horizon (Figure 5-7). Airspace R’s configuration is the same as in previous scenarios.

Figure 5-7 Sector opening scheme – Opt-Low

Table 5-16 shows that the minimum variable cost to allow a feasible solution of the problem is 14,900€. Unsurprisingly, however, savings on variable costs are counteracted by significant increments in displacement costs, as highlighted by Table 5-17. For instance, two out of three medium sized aircraft and one out of four large aircraft are either rerouted or delayed. The total displacement cost is 148% and 23% higher than in the high and medium capacity scenarios, respectively.

Table 5-18 suggests a significant increment in the assignments of longer ground delays (10, 15 min). Both small and medium sized aircraft are strongly affected by the tight capacity budget. Furthermore, the incidence of long re-routing increases, with 12 flights assigned a 40NM longer route, compared to only three such flights in the Medium capacity scenario.



31

Table 5-16 Capacity consumption and variable cost – Opt-Low


hourly periods

Variable capacity cost

(Euro)

R 6 4,500

S 4 1,840

U 4 2,600

T 4 2,280

Q 4 3,680

Total 22 14,900

Table 5-17 Summary statistics – Opt-Low

(1) (2) (3) (4) (5) (6) (7)

Aircraft type

Shortest-route


Shortest-route

assignments (%)

Total delay (min)


Total displacement

cost(EUR)


cost per displaced

flight (EUR)

Small 16 36.4% 285 13.6 5,237.2 187.0

Medium 30 33.3% 505 10.7 1,7261.1 287.7

Large 12 75.0% 25 8.3 922.1 230.5

Total 58 38.7% 815 11.5 23,420.4 254.6

Table 5-18 Distribution of displaced flights – Opt-Low

(1) (2) (3) (4) (5) (6) (7) (8) (9)

Aircraft type

re-route up to 20NM

re-route up to 40NM

Delay

5min

Delay

10min

Delay

15min

Delay

20min

Delay

25min

Delay

30min

Small 6.8% 9.1% 13.6% 13.6% 9.1% 2.3% 2.3% 6.8%

Medium 5.6% 8.9% 20.0% 18.9% 2.2% 7.8% 3.3% 0.0%

Large 6.3% 0.0% 12.5% 0.0% 6.3% 0.0% 0.0% 0.0%

EDITION [01.00.00]

32


The total variable cost (variable capacity cost + displacement cost) in this scenario is 38,320.4 EUR which is below the benchmark without optimization but well above the total variable cost in the high and well as in the medium capacity scenario. Although the fixed costs of maximum capacity provision are lower than in the other two scenarios, the total costs within this scenario are the highest in all three optimization models.

Owing to greater incidence of re-routings, the quantity of CO2 emissions increases dramatically (Table 5-19) compared to medium capacity scenario, reaching an amount (9,123 Kg) similar to the one obtained within the high capacity scenario.

Table 5-19 Additional CO2 emission – Opt-Low

Aircraft type


re-routings


re-routings


Small 477 1,272 1,749

Medium 1,650 5,280 6,930

Large 444 0 444

Total 2,571 6,552 9,123

The capacity usage levels are pretty much in line with what was observed in the Medium capacity scenario (Figure 5-8), which is not surprising given the quite similar capacity budgets and the challenging traffic profile.

Figure 5-8 Sector utilisation – Opt-Low



33

5.2.4 Flat demand and high capacity scenario (“Opt-High-Flat”)

A major factor which impacts capacity decisions and displacement cost is the profile of the demand over time. In the previous sections, demand was intentionally challenging for the airspace network, with a peak of flights appearing in the middle of the time horizon. In this section, we experiment with a flatter distribution of the demand. More specifically, we consider the same set of flights, while equally spreading the take-off times across the time horizon.

With such a ‘flat’ demand, as described in Figure 5-9, we perform an analysis using the available capacity (budget) as in the high scenario (Table 5-5).

Figure 5-9 Demand with flat (uniform) traffic profile

The airspace configuration profile (Figure 5-10) shows some small differences in activity of airspaces R, U and T compared to the peaked demand profile (Figure 5-3). However, the total number of active sector-periods remains unchanged. Nevertheless, a marginal increase in variable cost (80 EUR)

0

1

2

3

4

5

6

7

8

5 1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5 5 0 5 5 6 0 6 5 7 0 7 5 8 0 8 5 9 0 9 5 1 0 0 1 0 5 1 1 0 1 1 5 1 2 0

NU

MB

ER O

F FL

IGH

TS

MIN

"FLAT" DEMAND

F11E F12E F21S F22S F11W

F12W F21N F22N AGGR

EDITION [01.00.00]

34


between the flat and the peaked demand scenario is at place, due to the fact that the former necessitates one more sector-period in airspace U and one fewer in airspace T.

Figure 5-10 Sector opening scheme – Opt-High-Flat

More noticeable is the impact of the flat demand on the optimal assignments and displacement costs (Table 5-20). Compared to the peaked demand scenario, the percentages of small and medium sized aircraft flights assigned to shortest routes increases from 31.8% to 45.5% and 61.1% to 65.6%, respectively. Ultimately, this results in a reduction of the total displacement cost from 9,492€ to 8,583€ (~10%).

Table 5-20 Summary statistics – Opt-High-Flat

(1) (2) (3) (4) (5) (6) (7)

Aircraft type

Shortest-route


Shortest-route

assignments (%)

Total delay (min)

Average delay per delayed

flight (min)

Total displacement

cost (EUR)


cost per displaced

flight (EUR)

Small 20 45.5% 40 8.0 2,772.1 115.5

Medium 59 65.6% 180 6.9 5,042.7 162.7

Large 13 81.3% 15 7.5 768.0 256.0

Total 92 61.3% 235 7.1 8,582.8 148.0

Savings in the displacement costs compared to the peaked demand scenario are mainly due to less frequent delay assignments (mostly relating to 5-min delays though), as suggested by Table 5-21. A flatter demand has expected beneficial impacts on environmental performance, as shown in Table 5-22. Specifically, the impact of re-routings on CO2 emissions drops from 10,701Kg to 8,787Kg (almost 18% reduction).



35

Table 5-21 Distribution of displaced flights – Opt-High-Flat

(1) (2) (3) (4) (5) (6) (7) (8) (9)

Aircraft type

re-route up to 20NM

re-route up to 40NM

Delay

5min

Delay

10min

Delay

15min

Delay

20min

Delay

25min

Delay

30min

Small 15.9% 27.3% 6.8% 2.3% 2.3% 0.0% 0.0% 0.0%

Medium 1.1% 4.4% 17.8% 11.1% 0.0% 0.0% 0.0% 0.0%

Large 0.0% 6.3% 6.3% 6.3% 0.0% 0.0% 0.0% 0.0%

Table 5-22 Additional C02 emission – Opt-High-Flat

Aircraft type


re-routings


re-routings


Small 1,113 3,816 4,929

Medium 330 2,640 2,970

Large 0 888 888

Total 1,443 7,344 8,787

A less peaked demand expectedly yields somewhat different sector usage pattern. Figure 5-11 shows that, except for Q, all airspaces tend to have lower usage levels as compared to the peaked demand scenario (“Opt-High”). About 15% of sector-periods have capacity utilisation of up to 50%.

Figure 5-11 Sector utilisation – Opt-High-Flat

EDITION [01.00.00]

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5.3 Impact of Business Aviation

In this section, we perform a simulation to assess the impact of business aviation (BA) on the system’s performance. We assume BA flights to be additional 6% on top of previously considered demand (i.e. nine BA flights in addition to 150 flights already being dealt with) and that all BA flights are on small aircraft. The pseudo-code of the simulation is summarised below:

1 solve ACRC with normal demand and store the optimal assignments

2 for iter = 0 : NumIter

3 generate BA demand share by randomly selecting o-d and take-off times

4 set all BA flights to use small aircraft

5 solve ACRC model with augmented demand while fixing non-BA flights assignments as in 1

6 store results (route assignments, displacement and variable costs)

7 end

8 return average results

The first step of the simulation requires solving the ACRC model with initial demand (150 flights). Subsequently, for each step of the simulation, a new BA demand is generated by randomly selecting origin-destination and take off time for each flight. The ACRC is then solved again with assignments of non-BA flights fixed to the optimal obtained in step 1 and then by assigning BA flights by the ACRC. A total of 200 iterations were run. Results of iterations are stored in global variables. The simulation returns the results averaged by the number of iterations.

The simulation is run for the three capacity scenarios and two demand profiles (peaked and flat) and results are summarized in Table 5-23. Columns 2 and 3 show the average percentages of shortest-route assignments of BA flights. Columns 4 and 5 report the displacement costs faced by BA flights. Finally, columns 6 and 7 indicate how many times problem ACRC was feasible within the simulation. Infeasibility of ACRC means that at least one BA flight cannot be accommodated within available airspace capacities. When this happens, to estimate the associated displacement cost we assume that such non-accommodated flight has been delayed by 60 minutes.

Table 5-23 BA simulation output (results averaged based on 200 simulation runs)

(1) (2) (3) (4) (5) (6) (7)

Capacity scenario

BA shortest-route

assignments with PEAKED demand (%)

BA shortest-route

assignments with FLAT

demand (%)

BA total displacement

cost with PEAKED

demand (Euro)

BA total displacement cost with FLAT demand (Euro)

Feasibility rate with PEAKED demand

Feasibility rate with

FLAT demand

High 2.0% 3.9% 16,252.3 13,657.2 8% 27%

Medium 0.6% 1.4% 17,107.5 16,455.9 3% 8%

Low 0.0% 0.4% 17,532.0 17,143.6 0% 3%



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Coherently with previously discussed results, the peaked demand proves to be very challenging. Only 8% of times ACRC is feasible (i.e. all BA flights accommodated within already active airspace capacities) and percentages of shortest-route assignments of BA traffic are very low. Results with flat demand show significant improvements. For instance, with high capacity in 27% of cases BA share was successfully allocated in the remaining capacity. This clearly results into a significant lower displacement cost for BA traffic (13,657 vs. 16,252 EUR). The difference between the feasibility rates of two demand profiles shrinks as the capacity budget decreases. To put these results into perspective it should however be stressed that the capacity assumptions in the case study were purposely developed to be challenging already with the initial 150 flights demand. Therefore, it is not surprising that including some further demand often results into unfeasible problems and significant cost increments.

5.4 Overview: summary results

In this section, to enable an easier insight into comparative performance of the network, we present an overview of the case study results in already discussed different capacity and demand scenarios.

Table 5-24 sublimates a number of performance indicators for different capacity assumptions and different modelling approaches, under the peaked demand profile. It clearly points to trade-offs involved between capacity provision costs, displacement costs and environmental performance.

Table 5-24 Summary results per scenario – peaked demand

Scenario

Performance indicator Seq-High Opt-High Opt-Med Opt-Low

Fixed capacity cost (EUR) = [F] 26,200 26,200 25,000 24,750

Variable capacity cost (EUR) = [V] 25,180 18,880 16,740 14,900

Displacement cost (EUR) = [D] 28,763 9,493 19,101 23,420

Total cost (EUR) = [F] + [V] + [D] 80,143 54,573 60,841 63,070

Shortest-route assignments (% of all flights) 62.1% 54.7% 49.3% 38.7%

Delayed ≥15 min (% of all flights) 5.3% 0.7% 14.0% 14.7%

Re-routed (% of all flights) 1.0% 17.3% 6.0% 14.0%

Sector-periods with capacity utilisation ≥85% (% of all sector-periods)

38.9% 66.7% 54.2% 59.1%

CO2 emissions due to re-routings (Kg) 3,195 10,701 2,421 9,123

Successful accommodation of entire BA traffic (% simulation runs)

n/a 8% 3% 0%

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The comparative performance of optimisation model vs. sequential algorithm was already discussed in section 5.2.1. Concerning the comparison of optimisations with different capacity budgets, the Opt-High scenario yields by far lowest total cost, but at the same time has poorest environmental performance due to more frequent assignment of re-routings compared to other scenarios. Opt-High also, expectedly, performs better than the other two scenarios when it comes to capabilities to absorb additional BA traffic, with however only 8% of instances when complete BA traffic can be accommodated within already active capacities. Such low rate is, as already mentioned, primarily due to extremely challenging demand/capacity profile, designed as such already for the initial traffic (150 flights).

The Opt-Med scenario saves 3,340 EUR on capacity costs, but this is unsurprisingly outweighed by dramatically higher displacement costs (nearly 10,000 EUR increase vs. Opt-High). Medium capacity scenario is also expectedly associated with lower remaining capacities to absorb the subsequently appearing BA traffic. Interestingly, Opt-Med is a best-performing scenario when it comes to environmental effects, owing to very few re-routings applied (and very frequent at-gate delays).

The Opt-Low scenario is, as already mentioned, barely an indication as to lowest capacity budget which can still accommodate the entire initial demand (150 flights). As such, it unsurprisingly performs poorly on all indicators other than capacity provision cost.

Finally, we briefly reflect on the impact of traffic profile on network performance in the high capacity scenario, Table 5-25. The most notable differences between the peaked and the flat demand profile arise when it comes to environmental performance (due to more shortest-route assignments possible with flat demand), and, in particular, with the capabilities to accommodate the BA traffic with already active airspace capacities.

Table 5-25 High capacity scenario – peaked vs. flat demand

Demand profile

Performance indicator Peaked Flat

Variable capacity cost (EUR) 18,880 18,960

Displacement cost (EUR) 9,493 8,583

Variable capacity cost + displacement cost (EUR) 28,373 27,543

Shortest-route assignments (% of all flights) 54.7% 61.3%

Delayed ≥15 min (% of all flights) 0.7% 0.7%

Re-routed (% of all flights) 17.3% 16.7%

Sector-periods with capacity utilisation ≥85% (% of all sector-periods)

66.7% 55.6%

CO2 emissions due to re-routings (Kg) 10,701 7,344

Successful accommodation of entire BA traffic (% simulation runs)

8% 27%



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6 Next steps

In this deliverable, we have proposed an algorithmic framework that mainly serves to illustrate the impact of trading off costs of capacity provision versus cost of displacement in the context of a small case study.

As envisaged in COCTA D3.1, and following feedback from the Advisory Board, we have introduced an OD pair charge structure which will be exploited in the following deliverables. This has some major consequences on the pricing approach that we originally anticipated. Charges cannot be set different for different trajectories between a given OD pair, and therefore cannot be used to influence AOs so that they may self-select trajectories that lead to a more efficient distribution of traffic. In the current model, charges do not play a role given that all flights are deterministically known (except business aviation on the day of operation), and therefore prices cannot be used to influence demand. Controlling OD-pair prices over the time of the booking horizon in a way such that trajectory requests are more likely to come in earlier in the time horizon does not provide us with any additional benefits since all demand is known anyway, regardless of when the request show. In future deliverables, we intend on allowing for such temporal price differentiation by introducing uncertainty in some portion of the flights (so that there is value in revealing flight trajectory requests early).

We gained some insights into the role of business aviation and to what extent its inclusion or exclusion from the optimisation would likely impact on the cost effectiveness of our approach.

A large proportion of time spent on this deliverable has been dedicated to obtaining realistic parameters, especially related to costs. We intend to refine these parameters even further, for example, by considering piecewise-linear cost increments of capacity.

We are well aware of the fact that our current solution approach does not scale to large applications. Its purpose was only to get insights to the problem on a case study that is sufficiently small to interpret the findings. Going forward, we need to develop an effective heuristic, scalable approach. Prof Juergen Branke, UW, will be consulted on this since he is a specialist on heuristics. One challenge is the exponentially growing number of possible airspace configurations.

Finally, we have been operating in a single-objective framework so far, while only monitoring the impact on key performance indicators other than total cost. In forthcoming work we intend to test incorporation other objectives as well, and this will further complicate the optimisation problem. A simulation-based optimisation approach may be suitable to tackle the multi-objective problem; again, Prof Branke (UW) will be consulted on this since he also specialises on multi-objective optimisation methods.

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7 References

[1] Cook, A., Tanner, G., 2015. European airline delay cost reference values, v4.1. Final Report. University of Westminster for EUROCONTROL Performance Review Unit.

[2] COCTA consortium, 2016. Deliverable D2.1 – State of the art report. Ver. 01.00.00. Final.

[3] COCTA consortium, 2017. Deliverable D3.1 – ATM value-chain redesign. Ver. 00.01.00.

[4] COCTA consortium, 2017. Deliverable D4.1 – Initial mechanism design. Ver. 00.01.00.

[5] COCTA consortium, 2017. Deliverable D2.2 – Data management report. Ver. 00.01.00.

[6] Performance Review Commission, 2016. Performance Review Report. Brussels.



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Appendix A

Cost of capacity provision

In economics, the distinction between fixed and variable costs refers to their dependence on output variations. Within the COCTA framework the Network Manager orders sector hours from the ANSPs, therefore we define the distinction between fixed and variable costs based on the number of sector hours provided rather than on an output measure, e.g. composite flight hours. Moreover it has to be taken into account that the distinction between fixed and variable costs also depends on the time horizon. In the short term, the largest part of total costs is usually fixed (i.e. cannot be influenced) whereas in the longer term more costs are variable.

Information on ANSPs’ costs of capacity provision is only available on an annual basis, making it difficult to identify costs of additional capacity provision. The Performance Review Report [6] contains ANSP data for total sector hours and for en-route costs with the following differentiation: staff costs (including ATCOs and other staff), non-staff operating costs, depreciation, capital costs, and exceptional costs.

For 2014, average costs per sector hour (without exceptional costs) for selected ANSPs were (own calculations based on [6]):

• Germany: 1,713 EUR

• Switzerland: 2,758 EUR

• Austria: 3,728 EUR

• Belgium 3,838 EUR

• Netherlands: 4,015 EUR

The share of staff costs is between 72% and 77% for the ANSPs listed above.

Within the COCTA framework, the contractual relations between the NM and the ANSPs refer to three different time horizons (short, medium, and long term):

• In the long term (e.g. five years in advance) they agree on the maximum structural capacity of the ANSP, i.e. the maximum number of sectors which can be opened at the same time. For the model in D5.1 this maximum structural capacity is considered to be given. This agreement determines investment (esp. technical equipment), leading to fixed costs in the short and medium term.

• In the medium term (e.g. one year or even six months in advance) they agree on a maximum number of sector hours which can be provided in a specific period, e.g. during one week and/or one day. In the model this period is set at two hours to simplify the calculations, and we distinguish three scenarios (high, medium, low capacity). Based on this agreement the ANSP can take decisions regarding strategic staff planning (e.g. leave days, training courses). We assume a slight increase in (staff and other operating) costs with an increasing number of

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maximum sector hours during a given period (e.g. because more ATCOs will have to be on standby). These costs are fixed costs in the short term.

• In the short term (e.g. one week in advance) the NM purchases the actual number of sector hours. We assume the costs per sector hour to be constant (i.e. linear cost function). This assumption will be further specified in forthcoming deliverables.

Consequently, we have three types of costs (using the example of ANSP 'Q' in our case study):

• Structural capacity costs: 5,000 EUR per 2 hours (fixed in the medium and short term)

• Maximum capacity provision costs: 1,200 EUR/900 EUR/800 EUR per 2 hours (high/medium/low capacity), fixed in the short term

• Actual capacity provision costs: 920 EUR/30 minutes sector operation (variable)

In the case study, we use the example of five hypothetical ANSPs (Q, T, R, U, S). Table 7-1 shows the structure of capacity provision costs assumed for the case study calculations.

Table 7-1 Cost of capacity provision breakdown per scenario

Q T R U S

Maximum sectors simultaneously open 3 2 2 2 2

Minimum capacity (sector-hours per 2 hours) 2 2 2 2 2

Structural capacity cost (EUR per 2 hours) 5,000 4,000 4,000 4,000 4,000

Actual capacity provision cost (EUR per active ½ sector hour)

920 570 750 650 460

High capacity scenario

Max. capacity (sector-hours per 2 hours)

Maximum capacity provision cost (EUR per 2 hours)

6

1,200

4

1,000

4

1,000

4

1,000

4

1,000

Medium capacity scenario



3

900

3

850

3

850

2

700

2

700

Low capacity scenario



2

800

2

700

3

850

2

700

2

700



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Displacement cost considerations

The two demand management measures considered for this deliverable are the administrative measures which are current used in practice: a flight could be either delayed or re-routed (a combination of the two is not considered, to keep the example simple in this deliverable). These measures impose costs on the flights subject to those measures. To calculate such cost, we rely on European airline delay cost reference values, prepared by the University of Westminster for the Performance Review Unit in 20112 [1].

Reference cost values in [1] are calculated for three different “types” of delay. “Strategic delay” is accounted in advance and is delay which occurs in strategic phase - when an airline decides on schedule buffers (or padding). Tactical delays are delays which occur on the day of operation. These delays are also called “primary” (original/first) delays. “Reactionary” (secondary) delays are ‘knock on’ delays caused by primary delays; for instance, a subsequent flight is delayed, because the previous flight in the aircraft rotation is late. Note that these delay groups are commonly used in aviation community and are reported as such (e.g. EUROCONTROL CODA). Figure 6-1 summarizes which costs are accounted for in for each delay group.

Figure 7-1 Costs considered per delay type, Source [1]

Finally, delay cost values in [1] are calculated and tabulated for three different scenarios (low, base, high) and for different flight phases (at gate, taxi and en-route) for several different aircraft types.

For the modelling purpose in D5.1, we use tactical delays and do not consider strategic delays (which are inbuilt in airline schedules as schedule buffers). Tactical delays are generally higher than strategic for the same aircraft types and the intention is to stay on the conservative side when calculating delay

2 We rely on the updated document version 4-1 from 2015 [1].

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costs for airlines. Since we delay flights on the ground, we use AT GATE costs for base scenario defined in [1]. We use cost of delay values for three different aircraft types to represent small (E145), medium (A320) and large (B752) aircraft in the case study. In figure 6-2, we present estimated delay cost functions based on tabulated cost values for delays of 5, 15, 30 and 60 minutes of tactical at-gate delay.

The total rerouting costs3 were calculated according to the “re-route example” methodology presented in [1] and they include crew costs, hard and soft passenger costs, as well as fuel and maintenance costs incurred because of the additional flight time. The cost functions for different aircraft (E145 – small, A320 – medium, B752 – large) were obtained by the polynomial regression fit over the values calculated for 10, 20, 30, 40 and 50NM of route extension (Figure 6-2).

Figure 7-2 Tactical primary cost of delay, Source: [1]

3 Also account for additional flying time, therefore total.

y = 0.4101x2 + 7.8621x

y = 1.0343x2 + 14.504x

y = 1.3157x2 + 18.103x

0

1000

2000

3000

4000

5000

6000

0 10 20 30 40 50 60 70

Co

st o

f ta

ctic

al p

rim

ary

del

ay (

EUR

)

Delay (min)

Tactical primary cost of delay (base scenario)

Small

Medium

Large

Poly. (Small)

Poly. (Medium)

Poly. (Large)



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Figure 7-3Total rerouting costs, Source: [1]

y = 0.0184x2 + 3.065x

y = 0.0317x2 + 5.7123x

y = 0.0381x2 + 7.3518x

0

50

100

150

200

250

300

350

400

450

500

0 10 20 30 40 50 60

Tota

l rer

ou

tin

g co

sts

(€)

∆D (NM)

Total rerouting costs (base scenario)

Small

Medium

Large

Poly. (Small)

Poly. (Medium)

Poly. (Large)

*fuel price: 0.8€/kg

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Prototype models and small academic examples...Consortium coordinator: Univerzitet u Beogradu...

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