Transportation Research Part C 98 (2019) 338–357

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Transportation Research Part C

journal homepage: www.elsevier.com/locate/trc

Integrated optimization of terminal maneuvering area and airport

T
at the macroscopic level
Ji Maa, , Daniel Delahayea, Mohammed Sbihia, Paolo Scalab,
⁎

Miguel Antonio Mujica Motab

a
ENAC, University de Toulouse, 7 Avenue Edouard Belin, Toulouse 31055, France
b
Aviation Academy, Amsterdam University of Applied Sciences, Amsterdam, the Netherlands

ARTICLE INFO ABSTRACT

Keywords: Airports and surrounding airspaces are limited in terms of capacity and represent the major
Integrated optimization bottlenecks of the air traffic management system. This paper addresses the problems of terminal
Terminal maneuvering area airspace management and airport congestion management at the macroscopic level through the
Airport integrated control of arrivals and departures. Conflict detection and resolution methods are
Simulated annealing
applied to a predefined terminal route structure. Different airside components are modeled using
network abstraction. Speed, arrival and departure times, and runway assignment are managed by
using an optimization method. An adapted simulated annealing heuristic combined with a time
decomposition approach is proposed to solve the corresponding problem. Computational ex-
periments performed on case studies of Paris Charles De-Gaulle airport show some potential
improvements: First, when the airport capacity is decreased, until a certain threshold, the
overload can be mitigated properly by adjusting the aircraft entry time in the Terminal
Maneuvering Area and the pushback time. Second, landing and take-off runway assignments in
peak hours with imbalanced runway throughputs can significantly reduce flight delays. A de-
crease of 37% arrival delays and 36% departure delays was reached compared to baseline case.

1. Introduction

With the steady growth of air traffic demand, the current air network is facing capacity problems, leading to delays and con-
gestions. One of the most critical parts is the airport and its surrounding airspaces. Increasing use of saturated airfield capacity will
adversely impact predictability and punctuality. European SESAR (Single European Sky ATM Research) program (Eurocontrol, 2015)
and FAA’s NextGen (Next Generation Air Transportation System) plan (Federal Aviation Administration, 2016) aim to increase the
network traffic throughput in order to accommodate the forecast demand with a sufficient margin. To achieve this goal, new
technologies integrating existing optimization support systems in order to act as holistic decision-support tools for all airport partners
are proposed, such as the Total Airport Management Concept (TAM) (Günther et al., 2006). Efficient planning and optimization
approaches of airport operations are critical to alleviate traffic congestion.
In previous work, segregated problems on runway sequencing and scheduling, and airport ground optimization have been studied
extensively. Bennell et al. (2011) gave a brief review of the techniques and tools for scheduling aircraft landings and take-offs. Atkin
et al. (2010) provided an overview of the research for ground movement and the integration of various airport operations.

Corresponding author.
⁎

E-mail addresses: ji.ma@recherche.enac.fr (J. Ma), daniel@recherche.enac.fr (D. Delahaye), mohammed.sbihi@enac.fr (M. Sbihi),
p.m.scala@hva.nl (P. Scala), m.mujica.mota@hva.nl (M.A. Mujica Mota).

https://doi.org/10.1016/j.trc.2018.12.006
Received 2 March 2018; Received in revised form 27 November 2018; Accepted 12 December 2018
0968-090X/ © 2018 Elsevier Ltd. All rights reserved.
J. Ma et al. Transportation Research Part C 98 (2019) 338–357

The runway sequencing and scheduling problem aims to find the optimal schedule for aircraft in order to reduce delay and to
maximize runway throughput, taking into account safety and operational constraints. Arrivals and departures are often considered as
separate problems. Past efforts have also been made for mixed operations (simultaneous arrival and departure scheduling on a single
runway). Beasley et al. (2000) presented a mixed-integer, zero-one program to schedule aircraft landings. Atkin et al. (2007) pro-
posed a hybrid metaheuristic system to improve runway scheduling at the London Heathrow airport. Balakrishnan and Chandran
(2010) presented dynamic programming algorithms for the problem of mixed operations under constrained position shifting. An
interesting rolling horizon approach to the aircraft sequencing problem for arrivals and departures was proposed by Furini et al.
(2015).
Runway sequencing is intimately linked to other airport ground operations. The problem becomes more complicated for finding
the best schedules and routes with respect to taxiing separation, route choices, runway wake turbulence separation etc. Gotteland
et al. (2001, 2009) presented a hybrid algorithm combining a genetic algorithm, and branch and bound to solve the ground
movement and runway sequencing problem. Lee and Balakrishnan (2012) introduced a mixed-integer linear programming model to
optimize both taxiway and runway schedules. Jung et al. (2010) presented two decoupled optimization algorithms to provide se-
quence and timing advisories for pushback and take-off. Ma et al. (2017) proposed a global optimization approach to solve the
surface operations problem and compared different control strategies (controlled pushback time, taxi reroutes and controlled holding
time).
Recently, more research focuses on the integrated optimization of TMA (Terminal Maneuvering Area) and airport. Integrating
terminal airspace management with existing route network is a more complicated, but more realistic problem than considering only
the runway scheduling and sequencing problem in TMA. Khadilkar and Balakrishnan (2016) modeled departure operations using a
network abstraction, and combined with published arrival routes, used dynamic programming to solve the integrated control pro-
blem in order to get the optimal times of departures. Xue and Zelinski (2013) modeled terminal airspace by spatially and temporally
segregating arrival and departure routes. Bosson et al. (2015) extended previous research with surface operations to integrate
taxiway and runway operations. Frankovich (2012) proposed unified approaches on both strategic and tactical levels to optimize the
traffic flowing through an airport.
Preliminary research on merging flows in TMA using a time decomposition approach (Ma et al., 2016a) and reducing airport
capacity overload (Ma et al., 2016b) has been presented. This paper studies the integrated problem of terminal airspace management
for arrivals and departures, and airport capacity management through the abstraction model of terminal, taxi network, and runway. A
fast metaheuristic algorithm combined with a time decomposition approach is proposed. The case studies based on Paris CDG airport
show some potential benefits: First, assuming a decrease of airport capacity based on the current level, until a certain threshold, the
overload can be mitigated properly by adjusting the flight time decisions. Second, the benefits of landing and take-off runway
assignments in peak hours are studied.
The remaining parts of this paper are organized as follows. Section 2 presents the mathematical model of the integrated terminal
airspace management and airport congestion management problem. A metaheuristic method combined with a time decomposition
approach aiming at minimizing the airspace conflicts, airport overload, and total flight delays is presented in Section 3. Computa-
tional experiments conducted with the proposed methodology are presented in Section 4. Conclusions and perspectives are discussed
in Section 5.

2. Problem description and model

In the terminal airspace, aircraft from different entry points must be merged and sequenced into an orderly stream, follow the
Standard Terminal Arrival Routes (STAR), then prepare to land on the runway. After slowing down the speed and exiting the runway,
aircraft taxi towards the assigned gate. Then, after a certain turnaround duration for disembark, embark and other ground-holding
operations, aircraft push back, taxi out, depart, and follow the designated Standard Instrument Departure (SID) routes.
Based on different levels of fidelity, the airport models are broadly described as microscopic or macroscopic. In microscopic
levels, individual aircraft trajectories with detailed information about taxiway routing, gate occupancy are explicitly considered.
However, the simulations can be computationally intensive. In macroscopic models, the airport components (terminals, taxi network)
can be globally modeled as resources with specific capacities (as opposed to individual aircraft or taxiway links). This level of
abstraction can help better understand the airport congestion situations and integrate into decision support tools.
Our first step is to consider the terminal and airport integration problem at the macroscopic level, in order to be sufficiently
flexible to resolve airspace conflicts (which implicitly represents potential workload for air traffic controllers), to mitigate airport
congestion, and to reduce delays. We focus on the pre-tactical off-line planning phase, i.e., we assume the planning time to be several
hours, or at least 30 min, prior to actual arrival/departure time. The integrated problem is considered in a moving time frame to
reduce computational burden and to account for the frozen flights, which were already optimized in the previous time window and
are traveling in the current time window. In future work, the model will be improved to on-line planning taking into account
uncertainties. The uncertainty of aircraft arrival time will increase as time passes by, thus a more robust occupancy curve is built and
evaluated.

2.1. Network model of TMA and airport surface

We model the TMA arrival and departure routes by a graph, ( , ) , in which the aircraft are allowed to fly in the airspace,
where is the node set and is the link set. Each route is defined by a sequence of nodes and links; the first link starts from an

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Fig. 1. Terminal route network of arrivals and departures in CDG in west configuration.

entering point (a so-called Initial Approach Fix (IAF) for arrivals and runway threshold for departures) and the last link ends at the
exit point (runway threshold for arrivals and last SID waypoint for departures).
Fig. 1 displays an example model of a route network for the Paris Charles De-Gaulle (CDG) airport. CDG is one of the busiest
passenger airports in Europe, it is composed of four parallel runways (two for landings and two for take-offs) and three terminals. The
West configuration with runways 26L/26R and 27L/27R is illustrated in Fig. 1, arrival and departure procedures are respectively
represented by black and gray colors. In the arrival procedure, four-corner routes fuse into one to each runway. Each of the starting
nodes of these four routes is an IAF. The set of entering points here is e = {MOPAR, LORNI, OKIPA, BANOX}. For the departure
procedure, one route starts at the runway threshold and ends with one of the SID waypoints in the set x = {OPALE, NURMO,
NEPAR, BEKOS, DOPAP, RBT, LESGA}. The set of routes is denoted as = {re e e x } . Each aircraft follows exactly one of these
routes corresponding to its entering point and landing runway for arrivals, and exit point and take-off runway for departures.
According to real radar data and published routes, departure and arrival trajectories are separated in altitude. The arrival flows
from the North-West (South-West) maintain their flight level at about 12,000 ft (13,000 ft) on the route section overlapping with
departure flows between MOPAR and PG560 (DOMUS and PG515), and the departure flows to the North (South) pass below them. In
the Eastern part, IF27R keeps a flight level of 5000 ft, IF26L keeps 4000 ft, so that the departures are able to fly above the arrivals.
Different airport components are considered using a network abstraction. Runways and terminals are modeled as resources with a
specific capacity. We only take into account the overall capacity of a terminal without considering its individual gates. Taxiway is
seen as a network with a threshold of total allowed number of taxi-in and taxi-out aircraft. The network model of TMA and airport
surface is illustrated in Fig. 2.
In the next section, we describe an integrated global optimization model of TMA and airport. We first give the flight input data.
Then, decision variables are defined. Lastly, we clarify constraints and introduce the objective function.

Fig. 2. Network model of TMA and airport surface. Each component is considered as resource with a specific capacity.

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2.2. Input data

Assume that we are given a set of flights (or aircraft), = , where is a set of arrivals, flights that land at the
airport and stay until the end of the day; is a set of arrival-departures, flights that arrive at the airport and depart from it after a
turnaround duration; is a set of departures, flights that are parked at the airport at the beginning of the day and depart later.
For each flight f , the following data is given: wake turbulence category for f , assigned terminal for f , entering
waypoint at TMA for f , exit waypoint at TMA for f , taxi-in duration for f , taxi-out duration for
f , initial landing runway number for f , initial departure runway number for f , initial off-block
time for f , turnaround duration for f and initial exit time at the exit SID waypoint for f . Moreover, we know:

• T : initial RTA (Required Time of Arrival) at the entering waypoint of TMA ( f

0
);
•
f
V : initial
0
speed at the entering waypoint of TMA ( f );
• P : initial off-block time ( f
f
0
f ), it is the earliest time that an aircraft is ready to depart from its parking position.

Here are the assumptions and simplifications we make for our model:

• Flights are assumed to be able to park at any gates in their assigned terminal;
• We use an average taxi-in and taxi-out duration with regard to terminal and runway for each flight, due to the fact that we do not
have information about the gate for the macroscopic model of the airport. Detailed study of airport taxi routings can be found in
Ma et al. (2017);
• Each aircraft has a constant deceleration or acceleration in the TMA. However, our model can tackle other types of trajectory (real
radar data, BADA data) by discretizing the airspace into a space-time grid and detecting conflicts, as done in the work of
Chaimatanan et al. (2014)

2.3. Decision variables

The optimization model we are using has five types of decision variables. For arrivals, we have to attribute the entering time in the
TMA, the entering speed in the TMA, and the landing runway:

1. Entering time in the TMA for f : First, we assume that we are given a maximum delay and a maximum advance,
denoted respectively Tmax and Tmin , which define the range of possible entering times in the TMA. We therefore define, for each
flight f , a time-slot decision variable t f f , where

f = {T f0 + j T Tmin / T j Tmax / T , j },

where T is a discretized time increment, whose value is to be set by the user. In order to shift an aircraft entering time in the
TMA, we can either decrease or increase its speed in the en-route phase. In practice, the latter strategy burns more fuel, and may
be far less attractive for the airlines. As a consequence, our time slot interval can be asymmetric, with Tmax Tmin . In the
following sections, the notation delay is used to indicate the time deviation of a flight.
2. Entering speed in the TMA for f : vf f , where

f = {V fmin + j v
f j , j (V fmax V fmin )/ v
f },

with vf is a (user-defined) speed increment, V fmin and V fmax are given as input data corresponding to the minimum and maximum
allowable speeds for aircraft f.
3. Landing runway for f : r fl is the landing runway decision for arrivals. Runway assignment is used to balance the
capacity when one runway gets overloaded while another is still able to accommodate more aircraft. Fig. 3 gives an example of
how flight delay can be reduced by assigning the landing runways. In Case 1, with a First-Come-First-Served strategy, a total of
470 s is required for all five aircraft to land when all the traffic arrives on southern runway 26L. In Case 2, after optimizing the
landing sequence for the same runway, a total of 258 s is required. In Case 3, the total landing time is reduced to 120 s with the
possibility of runway assignment. Runway aircraft assignment enables to increase overall throughput with less delay comparing
with the case where aircraft have no options to change their landing runway.
For departures, we have to decide the departure runway and the pushback time:
4. Departure runway for f : r fd is the take-off runway decision variable for departures. Similarly, it’s possible to yield
flights to another take-off runway when the current assigned one is busy.
5. Pushback time for f : pf f , where

f = {P f0 + j T 0 j p
Tmax / T, j },

where p
is the maximum pushback delay. In contrast to the entering time decision in the TMA for arrival flights, we can only
Tmax
delay a departure with regard to its earliest initial off-block time.

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Case 1: First−Come−First−Served
Heavy Medium
27R

26L 157 s 60 s 96 s 157 s

Case 2: Optimize landing sequence

27R

26L 60 s 60 s 96 s 96 s

Case 3: Optimize landing sequence + landing runway

27R 96 s

26L 60 s 60 s

Fig. 3. Three landing sequences comparison. In Case 1, First-Come-First-Served strategy is applied; In Case 2, the landing sequence is optimized with
regard to wake turbulence separation requirements; In Case 3, by assigning a landing runway and optimize landing sequence, less delay is achieved.

To summarize, our decision vector is x = (t, v, l, d, p) , where t is the vector for which the f th component is the decision variable
t f , v is the vector for which the f th component is the decision variable vf , l is the vector for which the f th component is the decision
variable r fl , d is the vector for which the f th component is the decision variable r fd ,and p is the vector for which the f th component is
the decision variable pf .

2.4. Constraints

We have two main constraints: wake turbulence separation, and single-runway separation for arrivals and departures. Before
taking into account these separations, we first calculate the passage times at which the aircraft passes each resource (node, link,
runway, taxi network, terminal) based on the decision vector x . Let us denote respectively the passage time at the resource m, the
entering time to the resource m, and the exit time from the resource m by T fm (x), TInf , m (x) , and TOut
f ,m
(x) .

2.4.1. Conflicts detection in the TMA

In this paper, we make the assumption that the arrival and departure routes are separated in altitude, which corresponds to real-
world TMA operations. Therefore, we detect conflicts separately for arrivals and for departures. Considering the above-described
TMA route network structure, the TMA separation violation may happen either in the link or in the node:

• Link conflict: As shown in Fig. 4(a), for two consecutive flights f , g that are flying through a link l = (u, v ) , the minimum
separation between these two aircraft, sfg , is obtained based on their respective wake turbulence category as shown in Table 1.
Then, the actual separation distance of these aircraft at the entry time, dufg (x) , and at the exit time of link l, d fgv (x) , are computed
and compared with sfg to detect an eventual link conflict.
Let us define, the link conflict indicator, Lfgl (x) , for aircraft f and g at link l:

Fig. 4. Airspace conflict detection illustration.

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Table 1
Distance-based separation on approach and departure according to aircraft categories (in NM). For example, the minimum distance separation
between an heavy aircraft followed by a medium aircraft is 5 NM.
Category Trailing aircraft

Heavy Medium Light

Leading aircraft Heavy 4 5 6

Medium 3 3 5
Light 3 3 3

if T fu (x) < Tgu (x) and (dfgu (x) < sfg or dfgv (x) < sfg
1,
Lfgl (x) = or Tfv (x) > Tgv (x))
0, otherwise

where T fu (x) is the passage time of flight f at the entry node u of link l, T fv (x) is the passage time of flight f at the exit node v of link
l.
• Node conflict: If no link conflict is detected, wake-turbulence separation can be guaranteed. However, at the intersection of two
successive links, violation of the horizontal separation requirement between any two consecutive aircraft (3 NM in TMA) may still
occur. Therefore, we check that when an aircraft flies over a node, the horizontal separation with other aircraft is maintained.
Considering a node n and two aircraft f , g that fly over node n, we consider a disk centered at node n with radius Rn , defined as a
detection zone. Rn can be simply defined as 3 NM for all the nodes, we have refined this value with regard to intersection angles of
two links at the common node, more details can be found in Ma et al. (2016a). We must ensure that at every moment only one
aircraft passes this detection zone. Suppose that aircraft f enters the zone of node n before aircraft g. We denote the entering time
to and exit time from this zone for aircraft f (g, respectively) as TInf , n (x) (TIng, n (x) ) and TOut
f ,n
(x) (TOut
g, n
(x) ). A conflict is detected when
TIn (x) < TOut (x) , which means that aircraft g enters the detection zone before aircraft f exits.
g, n f ,n

We define the node conflict indicator for aircraft f (leading) and g (following) as follows:

1, if TInf , n (x) TIng , n (x) < TOut

f ,n
(x)
N fgn (x) =
0, otherwise

2.4.2. Runway conflict evaluation

The landing/take-off time difference of any two consecutive aircraft must respect the time separation. The runway separation
rules are calculated by incorporating the different flight speeds and their impact on the final approach segment. Here, the separation
requirements are shown in Table 2, where A refers to Arrival, D refers to Departure, and C refers to Crossing. Due to the runway
configuration in CDG, arrivals have to cross departure runways to get to the terminal. We consider that the crossing time of an arrival
is 40 s.
One runway can be modeled as a specific resource with capacity 1. During high traffic demand periods, the upcoming flights may
violate the separation rules and cause runway congestions. Therefore, we note the number of times that the separation is violated and
the duration of separation violation for all pairs of aircraft as an indicator for our runway evaluation.
We define the runway conflict indicator between two successive aircraft f and g as:

1, if 0 Tgr (x) T fr (x) < t fg

Pfg (x) =
0, otherwise

Table 2
Single-runway separation requirements according to aircraft categories and to operations (in seconds). A refers to Arrival, D refers to Departure, and
C refers to Crossing. H refers to Heavy, M refers to Medium, and L refers to Light. For example, the minimum runway separation between an “A-H”
(Arrival-Heavy) and a “D-M” (Departure-Medium) is 60 s.
Operation-category Trailing aircraft

A-H A-M A-L D-H D-M D-L C

Leading aircraft A-H 96 157 207 60 60 60 –

A-M 60 69 123 60 60 60 –
A-L 60 69 82 60 60 60 –
D-H 60 60 60 96 120 120 60
D-M 60 60 60 60 60 60 60
D-L 60 60 60 60 60 60 60
C – – – 40 40 40 10

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Fig. 5. Loss of separation in case “Departure-Heavy (D-H) – Crossing (C)– Departure-Medium (D-M)”. The minimum separation between “D-H” and
“C” (“C” and “D-M”) is 60 (40) seconds respectively. However, the minimum separation between “D-H” and “D-M” is 120 s, thus it induces 20 s loss
of separation if only the required separations between successive aircraft are checked.

where T fr (x) denotes the time at which aircraft f arrives at the runway threshold, and t fg is the minimum runway separation between
flights f and g as shown in Table 2.
One particular case must be considered for the departure runway with a sequence of “Heavy Departure-Crossing-Small/Medium
Departure”. As shown in Fig. 5, each pair of successive flights satisfies to the separation requirement, however, loss of separation
occurs between the aircraft “D-H” and the aircraft “D-M”. Therefore, besides detecting the minimum separation between any two
successive flights, the loss of triangle inequality as shown in Fig. 5 must be detected too.
The total number of conflicts with regard to decision vector x is defined as follows:

A (x) = N fgn (x) + Lfgl (x) + Pfg (x)

f, g n r f rg l r f rg
f g

The TMA separation and the runway separation are ensured by

A (x) = 0

2.5. Objective

Our objective function is a weighted sum of the overloads for terminal and for taxi network and flight delays.

• Terminal and taxiway congestion evaluation:

We have two metrics to measure the terminal congestion. First, the maximum overload number is the maximum value over the
period of the difference between the number of aircraft in the terminal and the given terminal capacity. This metric gives us an
idea of the time at which severe congestion occurs. However, the maximal overload does not provide sufficient information on the
level of congestion. Therefore, another important metric to consider is the average congestion.
Suppose that we have a discretized time window = {1, 2, …, } , let us define the occupancy indicator for i :

Om (i) = Card{f TInf , m (x) i f ,m

TOut (x)}

where TInf , m (x) and TOut

f ,m
(x) correspond to the entering time and the exit time of resource m (i.e., terminal or taxi network). It counts
the number of aircraft at time i. The overload of resource m at time i is then defined as:
Gm (i ) = max{Om (i) Om, 0}

where Om is the imposed maximum capacity of the resource m.

G m (i )
The average overload is then defined as i .
To conclude, the airside capacity overload is expressed as

i
Gt (i) i
Gn (i)
S (x) = + max Gt (i ) + + max Gn (i )
i i

where Gt (i ) and Gn (i ) are respectively the terminal overload and the taxi network overload at time i.
Let us consider a simple example to show how we propose to measure the terminal congestion level. As illustrated in Fig. 6,
suppose that we have one terminal with three gates (i.e., the capacity Ot = 3), and 5 flights turnaround in this terminal during a
period of two hours, = {10: 00, 10: 01, …, 12: 00} . The upward (respectively, downward) arrow represents the in-block (off-
block) time of one aircraft, linked by a dotted line. We count the cumulated number of aircraft in the terminal as time goes by.
Here, the maximum terminal occupancy is 5, therefore the maximum overload max Gt (i) is 2. We calculate the total overload
i
Gt (i) as well, which is 55 here (the red surface shown in Fig. 6). The congestion criterion is 2 + 55/120 2.458.
•
i
Flight delays: The flight delays D (x) are defined as the total time deviation between the optimized and initial values of RTA and

pushback time, D (x) = f

pf P f0 + f
tf T f0 .

The conflict-avoidance constraint is relaxed into the objective function. Thus, our objective function, to be minimized is therefore

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Fig. 6. Example of terminal congestion evaluation. Five aircraft turnaround in a terminal with a maximum capacity Ot of 3. The congestion time
period is shown in red area.

a weighted sum of these functions:

a A (x) + s S (x) + d D (x)

where a, s , and d are respectively weighting coefficients for the total number of conflicts in airspace, A (x) , the airside capacity
overload, S (x) , and the flight delays D (x).

3. Solution approaches

The complexity of the integrated problem would grow compared to the segregated problem, when in practice the computational
time is critical. It is known that the sub-problem of this integrated optimization, aircraft landing scheduling, is NP-hard (Beasley
et al., 2000). Heuristics and hybrid methods may have more potential than exact approaches for tackling this problem (Atkin et al.,
2010). In this paper, we propose a time decomposition approach combined with a simulated annealing algorithm to address the
integrated terminal airspace management and airport congestion management. In the following of this section, the time decom-
position approach and simulated annealing algorithm are introduced and detailed.

3.1. Time sliding-window decomposition approach

The time sliding-window decomposition approach addresses the original problem by decomposition into several sub-problems
using a sliding window in order to reduce the problem size and consequently the computational burden. This specific approach is
generic and can be extended and applied to other real-time operation problems.
Suppose that we are given a total time interval, [tINIT, tFINAL], over which we want to optimize. Let us introduce some notations:

• W: the time length of the sliding window;

• S: the time shift of the sliding window at each iteration;
• TT ((kk)):: the starting time of the k sliding window, T (k ) = t
th + kS ;
•
s s INIT
e the ending time of the k sliding window, T (k ) = t
th
e INIT + kS + W .

Fig. 7 illustrates how the operating window slides along the time axis. The first sliding window begins at tINIT and, the optimi-
zation algorithm (to be defined later) is applied in the corresponding time interval [Ts (0), Te (0)]. Next, the sliding window is shifted by
time S, and the current optimizing interval becomes [Ts (1), Te (1)]. Then, we repeat the process until we reach the k th sliding window
such that Te (k ) tFINAL S .
Some parameters are needed to describe the sliding-window approach for each flight f :

•t s :
f
initial starting time, i.e.,

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Fig. 7. Sliding windows from iteration 0 to iteration k with a time length W and a time shift S at each iteration.

T f0 if f
tsf =
P f0 if f

• tsf : the earliest starting time, i.e.,

tsf + tmin if f
tsf =
tsf if f

•t s
f
: the latest starting time, i.e.,

tsf + t max if f
tsf =
tsf + Tmax
p
if f

•t e :
f
initial ending time, i.e.,
– For f , it corresponds to the initial in-block time, which is calculated with regard to initial entry time, STAR route, initial
entry speed, average taxi-in duration;
– For f , it is the exit time of TMA, calculated with regard to initial entry time, STAR route, initial entry speed, average taxi-
in duration, turnaround duration, average taxi-out duration, take-off time, and SID route;
– For f , it is also the exit time of TMA, calculated with regard to earliest off-block time, average taxi-out duration, take-off
time, and SID route.
• tef : the earliest ending time, i.e.,
– For f , it corresponds to the earliest in-block time, which is calculated with regard to earliest entry time in TMA, maximum
entry speed, STAR route, and average taxi-in duration;
– For f , it is the earliest exit time of TMA, calculated with regard to STAR route, earliest entry time in TMA, maximum
entry speed, average taxi-in duration, turnaround time, earliest pushback time, average taxi-out duration, take-off time, and SID
route;
– For f , it is also the earliest exit time of TMA, calculated with regard to earliest off-block time, average taxi-out duration,
take-off time, and SID route.
• tef : the latest ending time, i.e.,
– For f , it corresponds to the latest in-block time, which is calculated with regard to latest entry time in TMA, minimum
entry speed, STAR route, and average taxi-in duration;
– For f , it is the latest exit time of TMA, calculated with regard to STAR route, latest entry time in TMA, minimum entry
speed, average taxi-in duration, turnaround time, latest pushback time, average taxi-out duration, take-off time, and SID route;
– For f , it is also the latest exit time of TMA, calculated with regard to latest off-block time, average taxi-out duration, take-
off time, and SID route.
Fig. 8 gives an overview of the total operations of flight from the entry in TMA until the exit of this TMA.

Each aircraft is classified with one of the following four statuses, based on the positions of the parameters of flight f relative to the
starting and ending times of the current sliding window, k:

• TCompleted flight: t T (k ) . The latest ending time for aircraft f , t , is lower than the beginning time of the k sliding window,
e
f
s e
f

(k ) , which means that aircraft f has already finished its operation before the start of the k sliding window;
th
th

• On-going flight: t T (k ) < t . The beginning time of the k sliding window, T (k ), is between the earliest starting time, t ,
s
f
s e
f th
s s
f

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Fig. 8. Arrival-Departure operations in TMA. A flight goes through several phases: descent following standard terminal arrival route, landing on the
runway and taxiing to the gate, turnaround, push back at the gate, taxiing between the gate and the runway, take-off and initial climb following
standard instrument departure procedure.

and the latest ending time, tef , which means that aircraft f has already been assigned, but it may still impact the next aircraft in
terms of decision variables;
• Active flight: Ts (k ) < tsf tsf
[Ts (k ), Te (k )];
Te (k ). The time decision interval of flight f is included in the sliding window interval

• Planned flight: Te (k ) < tsf . The latest starting time, tsf , is larger than the ending time of the k th sliding window, Te (k ) , which
means that the temporal decision variable interval is not totally included in the time window, so that we could not take decision
for aircraft f in this interval. The flight will be considered later.

The status of flight f is updated and changed according to the sliding window being considered. Fig. 9 illustrates the four different
flight statuses and their positions relative to the sliding window. The different time positions of the aircraft and those of the sliding-
window are indicated respectively with blue and red triangles.
At each step, we take into account the active and on-going aircraft in the sliding window interval to be merged and sequenced.
Decisions for the on-going flights have already been made, but these flights still have some influence on the decisions to be made for
the active flights. On the other hand, the conflicts involving completed flights have already been resolved and they cannot have any
impact on the active flights, so they can be cleared out of the decision process and ignored. Then, the optimization window is shifted
by the time step S. The aircraft statuses are updated, a new set of flights waiting to be addressed are considered, and the optimization
process is repeated, as illustrated in Algorithm 1.

Fig. 9. Four flights status, related to the time position of flight f relative to the current sliding window (k).

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Algorithm 1. Sliding-window management

1: procedure SLIDINGWINDOW
2: k 0;
3: Ts (k ) tINIT ;
4: Te (k ) Ts (k ) + W ;
5: Determine each flight status relative to sub-window;
6: FOPT Active and on-going flights ;
7: while Te (k ) < tFINAL do
8: if at least one active flight in FOPT then
9: Subproblem: optimize considering FOPT ;
10: end if
11: Ts (k ) Ts (k ) + S ;
12: Te (k ) Te (k ) + S ;
13: k k + 1;
14: Update each flight status relative to sub-window;
15: Update FOPT ;
16: end while
17: end procedure

3.2. Simulated annealing

Simulated Annealing (SA) (Kirkpatrick et al., 1983) is a meta-heuristic that simulates the annealing of a metal, in which the metal
is heated up and slowly cooled down to move towards an optimal energy state. It can easily be adapted to large-scale problems with
continuous or discrete search spaces. In SA, the objective function to be minimized is analogous to the energy of the physical problem.
A global parameter T is used to simulate the cooling process. A current solution may be replaced by a random “neighborhood”
E
solution accepted with a probability e T , where E is the difference between corresponding function values. We start the cooling
process from a high initial temperature T0 (which can be determined by a heating process or defined by user), the current solution
changes almost randomly at a higher temperature, thus the algorithm is able to trap out of local minima. The decrease of temperature
may follow different laws, such as linear law, geometric law, etc. At each temperature step, a number of iterations are executed. The
probability to accept a degrading solution become smaller and smaller as T decreases. Therefore, at the final stages of the annealing
process, the system will converge to a near-global or global optimum.
Algorithm 2. Neighborhood function

Require: For each flight f, we record its airspace performance, pfa , runway performance, pfr , ground performance, pfg , the total performance is denoted as
pft = pfa + pfr + pfg .
1: The total number of conflicts Pt = f pft ;
2: Generate random number, = random(0,1);
3: if Pt > 0 then
4: sum 0;
5: target Pt × ;
6: i 1;
7: while sum < target do
8: sum sum+ pit ;
9: i i + 1;
10: end while
11: else
12: Choose randomly one flight i in the flight set;
13: end if
14: if i then
15: if pia > 0 then choose with equal probability between the entering time and the entering speed in the TMA, then choose randomly one value between 0 and
the maximum allowed deviation;
16: else if pir > 0 then choose with equal probability among the entering time in the TMA,the entering speed in the TMA, and the landing runway;
17: else choose randomly the entering time in f;
18: end if
19: else if i do
20: if pig > 0 then
21: choose randomly the pushback time in f;
22: else
23: choose with equal probability between the pushback time change and the take-off runway change;
24: end if
25: end if

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Table 3
An example of aircraft terminal performance (in minutes).
Flight F1 F2 F3 F4 F5
Terminal performance 50 65 52 34 6

To generate a neighborhood solution, instead of simply choosing randomly a flight f in the active-flight set, we use a method
similar to the so-called roulette-wheel selection. We note for each aircraft the number of conflicts and the time of congestion as its air
and ground performance respectively. Air performance involves link and node conflicts, and ground performance involves runway,
taxiway network and terminals congestions. Let us take the example of Fig. 6, in Table 3, we note the total time during which an
aircraft is overlapping with other flights. For example, the overlapping time between the flight F1 and all the other flights is 50 min;
for F5 it is only 6 min.
Considering this overload period, it is better to first change the decisions of aircraft which are mostly involved in congestion
(F2, F3, F1) than the ones with less impact (F5 ) in order to mitigate the terminal congestion. The performance metric can help us to
better focus on the most charged and congested periods. The fact that our neighborhood definition is based on the air and ground
flight performance increases the likelihood that a flight involved in many conflicts, or experiencing severe congestions, will be
chosen. As shown in Fig. 10, in the neighborhood selection, firstly, we record different performance indicators for each aircraft. Then,
we choose a flight using a roulette wheel selection method based on the conflict performance. Next, we target this flight to decide
which decision variable to be changed. Lastly, we choose randomly a discretized value for the related decision variable. To sum-
marize, a detailed description is shown in Algorithm 2.
The SA terminates the execution if either the maximum number of transitions or the minimum temperature are reached.
Fig. 11 summarizes the overall optimization process. The simulation process takes the decision proposed by the optimization
algorithm and simulates the associated flight in order to produce the objective function and the vector of performance. The objective
function and the performance indicators provided by the simulation process guide the optimization module to search for better
solution. The time sliding window manager updates flight status and puts them into the two previous mentioned modules. The
optimization and simulation processes are repeated.
In the next section, we apply the simulated annealing algorithm combined with time decomposition approach to resolve the
integrated terminal airspace management problem and airport capacity management problem.

4. Results

In this section we present some test problems and analyze the associated results. We tested our methodology on a four-hour real
data case at Paris CDG Airport. Numerical results with different settings of (user-defined) algorithm parameters were presented and
discussed. The overall process is run on a 2.50 GHz core i7 CPU, under Linux operating system PC based on Java code.

4.1. Real data analysis

A busy winter day on February 18th, 2016 was chosen as our data set. Fig. 12 shows the initial terminal and taxi network
occupancy over the day, the line color green, blue, orange, and pink respectively represent Terminal 1, Terminal 2, Terminal 3 and
taxi network occupancy. Terminal 1 consists of a central circular terminal building and seven satellites with boarding gates, thus
cannot handle many aircraft and keeps a stable low traffic over the day. Air France operates from Terminal 2, and CDG is the
principal hub for Air France (hub airport is used by one airline to concentrate passenger traffic and flight operations at a given
airport), thus Terminal 2 is the main terminal of CDG that serves the majority of aircraft. Therefore we observed much more traffic
flows in Terminal 2 compared to the other two terminals. Terminal 3 mainly hosts charter and low-cost airlines, is mainly composed
of hangars for night parking, therefore the departure flights leave the terminal early in the morning and the arrival flights come late at
night, forming the curve in orange color shown in Fig. 12. Peak hour with a maximum gate occupancy was reached between 8 am and

Fig. 10. Neighborhood generation. We first target one aircraft using a roulette wheel selection based on number of conflicts. Then, we modify one of
its decision variables with regard to the type of aircraft and its performance indicators.

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Fig. 11. Overall optimization process summary.

Fig. 12. Initial terminals and taxi network occupancy on February 18th, 2016. Terminal 2 is the main terminal in CDG and receives much more
traffic flows compared to the other two terminals.

10 am in Terminal 2. Then the terminal occupancy decreased sharply, which consecutively leaded to a peak in the taxi network. Here
we extracted the flight data of the most dense time period in the day from 6 am to 10 am as our test problem. A total of 332 flights
were operated at CDG, including 177 departures and 155 arrivals, 109 flights were arrival-departures. We have in total 67 Heavy and
265 Medium aircraft. The fleet mix ratio on this period is 20% for Heavy aircraft and 80% for Medium aircraft. The parameters
chosen for specifying the optimization problem and the resolution algorithm are respectively given in Tables 4 and 5.
We tackle the integrated airport and TMA optimization problem at a macroscopic level, the aim is to show that the proposed
algorithm can react in the right direction facing airport capacity reduction. Due to lack of data, we cannot apply our method to a
historic situation. Moreover, directly comparing the optimized results with the historic situation would somehow be difficult, due to

Table 4
User-defined parameter values specifying the optimization problem.
Parameter Value

Discretization time step, T 5s

Discretization speed step, vf 0.01V f0
Maximum delay of RTA at TMA, Tmax 30 min
Minimum delay of RTA at TMA, Tmin −5 min
Maximum pushback delay, Tmax p 15 min
Minimum allowable speed, V f
min 0.9V f0
Maximum allowable speed, V fmax 1.1V f0
Conflicts weighting coefficient, a 1
Overload weighting coefficient, s 1
Delay weighting coefficient, d 0.001

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Table 5
Empirically-set parameter values of the simulated annealing algorithm with
time decomposition approach.
Parameter Value

Geometrical temperature reduction coefficient 0.99

Number of iterations at each temperature step 100
Initial rate of accepting degrading solutions 0.15
Final temperature 10 6T0
Time length of the sliding window 2h
Time shift of the sliding window 0.5 h

the simplifications and assumptions from the model. In this paper, we build the initial occupancy curve by simulating the process
using the initial flight data (initial entering time, initial entering speed, initial pushback time, etc.). We use this curve as baseline case,
and impose a reasonable capacity limit, which is fair to compare with the results from the optimization process.
Two major aspects were discussed in the rest of the section: First, different levels of degradations of the terminal capacity and taxi
network capacity were imposed to verify the impact on flight delays and on other airport components. Second, we studied the
benefits of runway assignment on reducing flight delays in peak hour when two runways are facing imbalanced throughput.

4.2. Influence of reduced airport capacity to flight delays

First, we investigated how the different levels of degradation of the terminal occupancy and taxi network occupancy would
influence the traffic. Two capacity parameters, the imposed maximum terminal capacity, Ot , and the imposed maximum taxi network
capacity, On , were defined to investigate the airport congestion problem. In the case of terminal overload, we chose to study the
traffic on Terminal 2, because it is much more occupied than the other two terminals and has an important peak hour.
As shown in Fig. 13, the dark gray line and the light gray line respectively represented the initial terminal occupancy and the
initial taxi network occupancy. The initial maximum gate occupancy for this period was 90. Therefore, we chose Ot = 80, 75, and 70

Fig. 13. Maximum terminal capacity tests, with Ot = 80, 75, 70, and Ot = 70, Tmax = 60 min respectively. Comparison of initial occupancy and
optimized occupancy for terminal and taxi network.

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Fig. 14. Decisions comparison for different maximum terminal capacity Ot .

respectively. We first set a threshold of Ot = 80. After running the algorithm, the maximum capacity was reduced and kept below the
threshold as illustrated in Fig. 13(a). A decrease of the taxi network occupancy was observed as well. Then we decreased the capacity
to Ot = 75, in a short period the traffic exceeded this threshold as shown in Fig. 13(b). When the imposed capacity continued
decreasing to Ot = 70, we encountered a bottleneck and the maximum capacity cannot be reduced anymore. This was due to the
inherent maximum allowed RTA delays that we can change. To make a further test, we set the maximum RTA change, Tmax , to be
60 min instead of 30 min. After launching the algorithm, as shown in Fig. 13(d), this terminal overload was totally absorbed with the
cost of more than 20 aircraft whose time deviations were more than 30 min as shown in Fig. 14(a). We also observed that the RTA
distribution shifted to the right as Ot decreases, while pushback delay were not influenced significantly as illustrated in Fig. 14(b).
Similarly, the imposed capacity was applied to taxi network. As shown in Fig. 15, the initial maximum taxi network occupancy on
this period was 35. We set a threshold of On = 25, 20 and 15 to launch three tests separately. In Fig. 15, the dark blue line and the
light blue line represented the optimized terminal occupancy and taxi network occupancy respectively. In Fig. 15(a), On = 25 was
easily reached for the whole period after optimization, also a decrease of maximum terminal occupancy was observed, even when we
didn’t put any constraints on Ot . A sharp increase or decrease of gate occupancy would consecutively increase taxi network capacity
as well. As our strategy was to delay the aircraft arrival, the curve was shifted to the right compared to the initial occupancy curve.
With On = 20 in Fig. 15(b), we could see that the traffic overload cannot be absorbed, there was still a maximum taxi network
occupancy of 22 around 10 am With On = 15 in Fig. 15(c), the limited flight delays cannot absorb the taxi occupancy either, and the
maximum value remained almost the same as with On = 20 . To make a further test, we set the maximum RTA change, Tmax , to be
60 min instead of 30 min. After launching the algorithm, as shown in Fig. 15(d), this taxi network overload cannot be absorbed either,
in contrast to the terminal overload. This is because only one congestion period was found in the terminal occupancy, while taxi
network encountered several levels of congestion in different time periods, thus more unstable and difficult to mitigate under a
certain threshold. When we took a look at the decision changes in Fig. 16, the RTA delay and pushback delay distribution shifted to
the right when On decreased, which indicated that there were more delays for both arrivals and departures. In such case, the
algorithm kept aircraft as much as possible at the gate and slowed down arriving aircraft in order to reduce the number of aircraft on
the taxi network. Limited capacity of the taxi network caused more flight delays.

4.3. Influence of runway assignment to flight delays

We investigated the benefits of arrival runway assignment and departure runway assignment on reducing flight delays in peak
hour when two runways are facing imbalanced throughput.
Paris TMA arrival routes use a four-corner procedure as shown in Fig. 1 in Section 2. In Table 6, southern flows from OKIPA and
BANOX mainly use the southern landing runway 26L. Northern flows from MOPAR use more 26L as well, flows from LORNI land
more at the northern runway 27R. Moreover, the flows coming from South sometimes land on the northern runway, and vice versa. In
practice, landing runway changes can be achieved by controllers’ tactical vectoring. The departure runway changes are related to a
more detailed level of ground operations, i.e., how alternate taxi routes are assigned. Thus, in this paper, we only focus on the benefits

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Fig. 15. Maximum taxi network capacity tests, with On = 25, 20, 15, and On = 15, Tmax = 60 min respectively. Comparison of initial occupancy
and optimized occupancy for terminal and taxi network.

Fig. 16. Decisions comparison for different maximum taxi network capacity On .

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Table 6
Landing traffic flow distribution with regard to flight entry point in TMA and landing runway on February 18th, 2016.
27R 26L Total

MOPAR 39 (6%) 77 (13%) 116 (19%)

LORNI 131 (21%) 73 (12%) 204 (33%)
OKIPA 32 (5%) 165 (27%) 197 (32%)
BANOX 15 (3%) 80 (13%) 95 (16%)
Total 217 (35%) 395 (65%) 612 (100%)

of departure runway changes in imbalanced runway throughput situation.

First, we want to investigate how runway changes can bring benefits to reduce flight delays. We set three cases:

• Case 1: Both landing runway and take-off runway are decision variables;
• Case 2: Take-off runway is a decision variable, landing runway is predefined and fixed;
• Case 3: Landing runway is a decision variable, take-off runway is predefined and fixed.
Fig. 17 gave an example of one sliding window optimization evolution; it showed the value of two criteria (number of conflict and
total delays) at the end of each temperature step during the cooling process of SA. Solid lines represented the number of conflicts and
dashed lines denoted the total delays in minutes. The number of conflicts in Case 1 converged faster than the other two cases. Case 1
and Case 2 reached conflict-free solution almost at the same time, while in Case 3 conflict-free solution cannot be found. Seven SID
conflicts with in total 160 s loss of separation still remained, due to the fact that once the take-off runway was fixed, one can only
adjust pushback time to resolve conflicts, thus it was more difficult to find a feasible solution in the given pushback delay period. This
result showed that take-off runway assignment did not only balance runway throughput, but may also reduce controllers’ potential
maneuvers in peak hour for the SID airspace. As for total delays, before conflict-free solutions were found, delay criteria, for three
cases, stayed at a high level to offer more possibilities for the algorithm to search in the state space to establish first a conflict free
solution. Then, the delay criterion started decreasing. We can observe that Case 1 reached the lowest delay, while Case 2 remained
the highest.
Fig. 18 showed the runway throughput for landings and take-offs. The period 7 am–8 am corresponded to the higher landing
throughput, then after the turnaround process, the period 9 am–10 am corresponded to the higher departure throughput. We ob-
served a more balanced traffic for each runway in Case 1 without reducing the throughput. Fig. 19 showed the distribution of flights
RTA and pushback delays. In Case 1, a total of 102 arrival flights (66%) modified their RTA within 5 min. While in Case 2 and 3, more
RTA delays were required compared to Case 1, only 46% of the flights RTA was less than 5 min, and 54% in Case 3. Without the take-
off runway changes, much more pushback delays were requested. Pushback delay didn’t change as significantly as RTA delay,

Fig. 17. Evolution of the two criteria for different runway decisions.

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Fig. 18. Landing runways (27R and 26L) throughput comparison for Case 1 and Case 2, and take-off runways (27L and 26R) throughput comparison
for Case 1 and Case 3.

Fig. 19. RTA and pushback delay decision changes distribution with take-off and landing runway assignment (Case 1), with only landing runway
assignment (Case 2), and with only take-off runway assignment (Case 3).

Table 7
Total RTA delay and pushback delay comparison.
Total RTA delay (in minutes) Total pushback delay (in minutes)

Case 1 897 443

Case 2 1425 501
Case 3 1293 696

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Table 8
Computational time for various problem sizes. The total number of flights are the sum of type “Active” and “On-going”.
Time period All Dep. Arr. Medium Heavy Run time (s)

6:00–8:00 164 101 63 134 (82%) 30 (18%) 51

6:30–8:30 238 137 101 202 (85%) 36 (15%) 85
7:00–9:00 234 123 111 194 (83%) 40 (17%) 88
7:30–9:30 241 119 122 196 (81%) 45 (19%) 93
8:00–10:00 266 127 139 212 (80%) 54 (20%) 103
8:30–10:30 259 121 138 200 (77%) 59 (23%) 104
9:00–11:00 229 106 123 175 (76%) 54 (24%) 85

because we had a low demand between 6 am and 9 am, the major departure flows occurred between 9 am and 10 am. Regarding the
total RTA delay and pushback delay, as shown in Table 7, a decrease of 37 % (from 1425 min to 897 min) RTA delay was reached for
Case 1 compared to Case 2. A decrease of 36 % (from 696 min to 443 min) pushback delay was reached for Case 1 compared to Case
3.
The average computational time of our optimization algorithm was 13 min with in total of 10 sliding windows. As shown in
Table 8, the average CPU time for each window was less than 2 min, which is very promising for tackling such a complicated problem
in practice.

5. Conclusions

To address the connected airport and terminal airspace management problems, this paper proposed a model to manage the
arrival, surface and departure problems at the macroscopic level. The objective was to resolve conflicts in the terminal airspace, to
reduce airside capacity overload, and to reduce flight delays. First, we proposed a TMA route network structure and a high level
airport abstraction model. Then, a time sliding-window approach combined with a simulated annealing algorithm was applied to
solve the problem. The approach was implemented in the case of Paris CDG airport and showed some potential benefits: First,
reduced terminal capacity until a certain threshold was efficiently mitigated by RTA and pushback time changes. When the imposed
capacity was more reduced, the overload could not be mitigated anymore, and the airport could not absorb more demand without
imposing delays out of the maximum range. Similarly to terminal occupancy, a decrease of the maximum taxi network capacity could
be mitigated by delaying arrivals. Second, landing runway assignment and take-off runway assignment in peak hour with imbalanced
runway throughputs could significantly reduce the flight delays. Moreover, the conflicts in the airspace could be resolved also, which
may imply that the runway change did not create many more controller’s workload.
The next steps for this research would integrate a more precise microscopic level to optimize the ground movements by con-
sidering individual flights and gates. Uncertainties about the flight arrival time, pushback time and taxi duration should be taken also
into account as well.

Acknowledgments

This work has been partially supported by Civil Aviation University of China (CAUC), by China Scholarship Council (CSC) and by
the National Science Foundation of Tianjin through Grant No. 17JCYBJC43100. The authors would like to thank Serge Roux for his
assistance with data and technical support. The authors would like to thank SNA-RP/CDG-LB for providing the traffic data. The
authors thank the anonymous reviewers for their insightful comments.

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