1. Introduction
Global air traffic passenger demand is expected to increase 250% in the next 20 years [
1]. To accommodate such air traffic growth, the air traffic management system strives to provide the airports and the sectors the traffic capacities needed to ensure arrival traffic punctuality, while having ecologically and economically friendly flights. At the same time, high levels of air traffic safety must be maintained. Reducing arrival delays is one of the most important functions of a ground arrival management (AMAN) system, which provides air traffic controllers with automation support for sequencing and spacing.
AMAN design requirements depend on the characteristics of a given arrival air traffic flow and its surrounding environment, e.g., runway and airspace capacity, weather conditions, air routes, and other geographical constraints. In the United States, the Traffic Management Advisory [
2] was deployed in air traffic control centers in the 1990s, while its enhanced versions, the Time-Based Flow Management [
3] and Terminal Sequencing and Spacing [
4], take into account future airborne-based operations [
5]. These systems contribute to consistency in sequencing and time-spacing of arrival traffic in en-route and terminal airspace areas. In Europe, the ongoing SESAR project has facilitated collaboration among European countries and contributed to the development of “Enhanced” AMAN, which coordinates arrival time-schedules covering wider ranges of airspace than in the case of conventional operations [
6]. Focusing on the busy terminal area, metaheuristics active solutions for efficient aircraft scheduling and re-routing were proposed to enable real-time optimization within a small computation time [
7]. In the Asia-Pacific strategic air traffic flow management region, the Long Range Air Traffic Flow Management has been devised to provide a basis for research into applications beyond current system time-frames [
8]. Ongoing Japanese research and development on “Extended” AMAN (E-AMAN) aims to achieve efficient arrival traffic flow at Tokyo International Airport [
9]. To analyze bottlenecks that future arrival traffic flow may bring, mathematical models are useful to predict causes and provide solutions for reducing arrival delay times. In this light, we apply queue-based modeling for arrivals at a single airport and discuss new procedures and technologies that support air traffic controllers in handling arrival traffic at congested airports. Our proposed queuing approach provides closed-form analytical results about flight delay bottlenecks in the airspace area around the airport.
Several studies have modeled aircraft arrival and departure operations using queuing-based models. Air traffic in a sector is modeled in [
10] as an
M/
M/
s queue where the sector capacity
s is defined as the number of aircraft transiting this sector at any time. This
M/
M/
s queue is coupled to an
M/
M/1 queue that generates communication messages to be handled by air traffic controllers. Modi [
10] established relations between the rate of communication messages for air traffic controllers and the aircraft arrival rate in the sector. A network of queues is employed to model a system of multiple airports in [
11,
12]. In [
11], the propagation of delays is analyzed in a system of airports by means of
queues. In [
12], a Jacksonian network with
queues is used to model the entirety of air traffic over US airspace. The results show that this modeling approach approximates well a Monte Carlo simulation of the same system. Aircraft departures at a single airport are analyzed in [
13] by means of a
queuing model. With the runway schedule as input, the model outputs the expected runway waiting time for an aircraft prior to departure. This model was applied in a case study for Newark Liberty International Airport to predict taxi-out times. In [
14], a queuing model is used to estimate the taxi-out time at Boston’s Logan Airport. The arrival process at an airport is analyzed in [
15,
16], with particular focus on runway-related delays. In [
15], the expected waiting time for aircraft arriving on a single runway is determined using an
queuing model. Simple bounds for the expected waiting time are determined by comparison to the
and
models. However, the authors did not make use in their case study of operational data or compare their results against actual data. In [
16], the US National Airspace System is modeled as a network of queues, with the TRACON sectors being modeled as an
queue. All the above models assume that arrivals and/or service times follow exponential or Erlang distributions. However, when analyzing actual air traffic data, these assumptions do not hold. In fact, it is often difficult to fit traffic data on known distributions. In addition, these models assume that operations, e.g., arrivals at a runway, occur one by one. Thus, the authors often make use of single-server queuing models. However, when considering the time aircraft use (fly within) airspace, several aircraft can be flown at the same time in an airspace. To model this, we assume a multi-server queue. As such, we consider a
queuing model that characterizes better the actual traffic data.
Given the above, the present paper proposes a queue-based modeling approach to estimating flight arrival delays and the impact of decreasing flight separation in the context of E-AMAN. We applied our models to arrival traffic at Tokyo International Airport, which is the world’s fifth busiest airport with respect to passenger traffic. Our analysis builds on a data-driven analysis of actual flight plans and arrival flight track data. The contribution of this paper is twofold. First, we propose an analytical approach for estimating aircraft time delays in an extended area around a destination airport, while taking into account current aircraft separation and airspace capacity restrictions. Second, we analyze the impact on aircraft delays when considering novel arrival procedures that can accommodate increased arrival traffic volumes by reducing the minimum aircraft separation.
This paper is organized as follows.
Section 2 introduces air traffic operations at Tokyo International Airport, and characterizes the arrival traffic data recorded in 2016 and 2017. This data analysis supports the models subsequently presented.
Section 3 proposes a queue-based modeling approach in which the aircraft arrival process is formulated as a
queuing model. Based on the data-driven analysis, probability distributions of the inter-arrival time and service time are estimated. In
Section 4, the
queuing model is applied in estimating aircraft arrival delay time as a function of the distance from the airport. The estimation results permit analysis of the relationship between arrival rate and aircraft waiting time. In
Section 5, we analyze the positive impact on the airspace capacity of reducing inter-arrival time within the arrival traffic flow. In this context, aircraft delay time is estimated by means of the proposed queue-based approach.
Section 6 discusses how this proposed queue-based approach contributes to the design of E-AMAN procedures and technologies. Additionally, our future work on the mathematical modeling of the aircraft arrival process is discussed, as are further extensions of the study. Finally,
Section 7 provides conclusions and outlines our plans for future work.
5. Analyzing the Impact of Increased Airspace Capacity by Decreasing Minimum Aircraft Separation
In this section, we analyze the impact of increased airspace capacity
using the
model. Considering
allows that three aircraft are served (i.e., allowed to be present) at the same time in a single airspace. As explained in
Section 4.2,
represents the situation where two aircraft co-occupy the assigned airspace, keeping a 5 NM minimum separation distance while flying in an airspace of 10 NM length. If
is allowed in the same operation, the arrival aircraft separation can be reduced to less than 5 NM, e.g, two arrival pairs maintain a 3 NM separation while one pair maintains a 4 NM separation. Applying RECAT for current arrival sequencing with current aircraft types at Tokyo International Airport theoretically enables us to realize airspace capacity
if accurate time-spacing is achieved. To increase the airspace capacity, arrival time-separation needs to be controlled more precisely.
Table 5 and
Table 6 show the estimated aircraft arrival delay when
, as assumed for current operation and for Metering operation.
Figure 14 compares the estimates for current operations and Metering operations under
and
. Comparing with the results of
, the
results show a remarkable reduction in arrival delay time, especially in the case of the airspace areas
and
. The respective arrival delays in areas
and
under current operations are
and
s, while under Metering operations the respective arrival delays are
and
s, as shown in
Table 5 and
Table 6. These results show that decreasing the minimum aircraft separation has a positive impact not only by increasing runway throughput, but also by decreasing arrival delay times in key airspace areas. The next section discusses how these benefits can be delivered.
6. Discussion
When arriving aircraft are flying far from the destination airport, the arrival traffic flow is controlled by airspace and airport capacity constraints. Close to the destination airport, flow control shifts to time-based arrival management in order to realize the required inter-arrival times between assigned aircraft arrival times. Applying a minimum inter-arrival aircraft time allows for an increased runway throughput. In this case, however, the most important questions are as follows: (i) How does decreasing inter-arrival aircraft time impact aircraft arrival delays? (ii) How can the arrival delay time be minimized while accommodating increasing air traffic demands? Below, we provide insight on these questions.
To address the first question, our queuing model for arrival traffic, with model parameters derived by analyzing actual flight data, yielded the following preliminary results: decreasing inter-arrival time is one of the most powerful solutions for reducing arrival delay times occurring in airspace bottleneck areas, and . Arrival delays can be remarkably reduced while allowing an increasing number of aircraft arrivals, as long as time-based separation can accommodate (i.e., three aircrafts present in a single airspace area at the same time), and as long as inter-aircraft separation can be reduced from that observed under current operations, i.e., a new wake vortex category is applied.
The second question can be addressed in a discussion of the transition point at which arrival management efficiently shifts from traffic flow control to time-based operation. Here, our arrival time delay estimates (see
Figure 14) allow us to judge the transition point by smoothly interpolating the plots between
and
, as shown in
Figure 15. This estimation shows that the most efficient transition will be realized around 70 NM distance from the airport.
Conventionally, improving automation levels in the future arrival management, i.e., applying aircraft self-separation and/or advanced AMAN, are discussed targeting increasing runway throughput, as shown in
Section 4.2. However, their impacts on the overall arrival traffic flow have not been studied yet. This paper provides a quantitative approach which estimates bottlenecks and arrival delay time in the traffic flow as impacts of increasing runway throughput. Feasible solutions were clarified to achieve increasing arrival rate up to 120% (36 arrivals in an hour) while reducing arrival delay time for a case study airport. These results provide a meaningful practical value in the on-going process of developing global standards on the automation system design in air transport. The authors’ future work will estimate the maximum potential of arrival rates considering the automation levels and runway occupancy time at the airport under the latest air traffic data in 2019 corresponding the new configurations of airspace and air routes at the airport. The bottlenecks and feasible solutions will be clarified based on the proposed data-driven queuing approach.
Although the
model is advantageous in clarifying these questions, mathematical restrictions prevent application of such models for operations in which the stability condition
is not satisfied. As expressed in Equation (
2), if the system workload
is not less than 1, then the queue becomes unstable and the estimated delay time for incoming aircraft tends to become extraordinarily long. The second restriction of the
model is the approximation accuracy of the estimated delay given by Equation (
3): for a fixed
c, the delay approximation provided in Equation (
3) is asymptotically correct as
approaches 1 [
18], regardless of the values of
and
. Moreover, even for moderate values of
, Equation (
3) has been shown to be a good approximation, provided
and
[
18]. As shown in
Table 3,
Table 4,
Table 5 and
Table 6, the
queues considered for all 29 airspace areas satisfy the queue stability requirement. However, the
value is not always close to 1, making the approximation of the delay less accurate, particularly in airspace far from the airport. To improve delay estimation accuracy, our future work will apply other queue-based modeling, and will compare estimation results with a macroscopic analysis of aircraft arrival by means of
queuing models.