The current issue of ORMS Today is now available to INFORMS members in "digital magazine" format. Log in to the Digital Editions Archive and enjoy a new online reading experience.

Software Surveys

Biennial survey of statistical analysis software...
more »

Optimal design of terminal airspace

Scandinavian-based case study focuses on vicinity of airports where the most congestion happens, capacity has its bottleneck and delays occur.

By Valentin Polishchuk

SAS jet takes off from Arlanda Airport in Stockholm, Sweden. The airspace around airports is where most congestion and delays occur.

SAS jet takes off from Arlanda Airport in Stockholm, Sweden. The airspace around airports is where most congestion and delays occur.

Projected growth of air traffic industry is a sign of healthy economic and technological development, as well as an unprecedented challenge to mankind. Since a great deal of air traffic congestion happens during the initial and final phases of flights, super-dense operations (SDO) in terminal areas are a recurring topic in air traffic research. Case in point: Three out of four presentations in the Capacity and Airspace Design session at 2015 SESAR (Single European Sky ATM Research) Innovation Days (the main vehicle through which SESAR disseminates the results of its long-term and innovative research program and which has become a landmark event in the European research calendar) were about terminal maneuvering areas (TMAs).

Indeed, the complexity of traffic pattern near airports creates higher capacity needs, for the same number of aircraft in the air, than in an en route setting (e.g., according to the European ATM Master Plan, as few as 80 movements/hour already lead to high capacity needs in a TMA, while as many as 160 movements/hour create only medium capacity needs en route). In addition, separation standards to avoid wake vortex effects lead to increased sequencing intervals, potentially enforcing time-stretch maneuvers and holding to be executed inside or near the boundary of the TMA. (These issues are mitigated by recent efforts in re-categorization projects on both sides of the Atlantic that strive to define separation standards on per-aircraft-type basis, in contrast to the current system where each aircraft is classified into one of the few categories, and the separation is defined based on the categories of the leading and trailing aircraft.)

Figure 1: Stockholm TMA in the 1950s.

Figure 1: Stockholm TMA in the 1950s.

Figure 2: Stockholm TMA in 2016.

Figure 2: Stockholm TMA in 2016.

Terminal airspace design needs to take into account ground constraints, such as terrain profiles and noise-sensitive neighborhoods. Curved approaches and other techniques are developed in order to smooth air traffic flow in such scenarios. Last but not least, designing the airspace around airports must be done while making educated tradeoffs between cost efficiency and noise impact, traffic complexity and airspace capacity, landing rate restrictions and economic considerations, and many other conflicting objectives. Moreover, when a design has been made, the continuous developments and changes in these and other factors will eventually render the original construction inefficient, making it necessary to redesign the airspace.

Air transportation has a long history of fueling the operations research (O.R.) community with motivation to provide efficient solutions for large-scale optimization problems. A classical O.R. success story is its contribution to airline management, where fleet assignment, aircraft routing, crew rostering and other practical tasks are solved with methods developed by O.R. academics in response to the business demand. Our research looks at another vital ingredient of air transport: air traffic management (ATM).

The current ATM system consists of three major components: skyway design (laying out the “road network” in the sky), flow and capacity management (mapping the filed flight plans demand onto the available network resources) and air traffic control (monitoring the flights and leading them through the airspace sectors). Global growth of air travel, coupled with the ongoing and predicted boost of unmanned aerial vehicles and remotely piloted aircraft, puts an enormous strain on ATM, and both the SESAR and the NextGen (Next Generation Air Transportation Systems, the sister initiative in the United States) envision that the solution to the global challenge will come from the flexible use of airspace, which (in addition to more “political” steps, like sharing resources with the military) puts the flow and capacity management into the heart of the system, and treats both the flight paths and the control sectors as flexible entities rather than rigid structures changeable only on the strategic level (“providing structure where necessary and flexibility where possible”).

In fact, flexible versions of parts of the ATM systems are already implemented and being deployed: Dynamic demand and capacity balancing (and dynamic airspace configuration, its U.S. counterpart) redistributes work among air traffic controllers (ATCOs) as the traffic complexity changes, while FreeFlight and Free Route Airspace (FRASE) allow the aircraft to fly directly from an entry to an exit point of the airspace. This is particularly true in the uncongested Danish-Swedish functional airspace block (FAB), where one can fly freely through the whole block, consisting of as many as three control centers in the two countries.

FRASE essentially makes en route airways planners (those who decide the highways in the sky) lose their jobs (I once belonged to the cohort, doing my Ph.D. thesis on airways planning in the Department of Applied Math and Statistics at State University of New York at Stony Brook). Upon moving to Sweden, I realized that the focus of route planners should be on TMAs – the airspaces in the vicinity of airports (or air portals, several large airports in a small geographical area) where the most congestion happens, capacity has its bottleneck and delays occur. Even though the clear blue sky might look like it gives essentially infinite room for flying through it, in many places near the airports the ATM systems work at or close to the limit of their capacity. This became the focus of the ODESTA (Optimal Design of Terminal Airspace) project funded by Sweden’s Innovation Agency VINNOVA and run by Linköping University (LiU) in partnership with Luftfartsverket (LFV), the Swedish Air Navigation service provider.

The core of the ODESTA research team consists of Christiane Schmidt, Tobias Andersson Granberg and myself (all affiliated with LiU), along with Billy Josefsson of LFV. Andersson, director of the flight transport and logistics program at LiU, is an expert in mathematical programming. Schmidt, a postdoc in ODESTA, comes from the field of computational geometry – airspace optimization has a solution of geometric tasks at its core. Yours truly, the principal investigator of the project, is an applied mathematician with concentration in operations research (O.R.). Finally, Josefsson is a former ATCO currently working as a manager in automation and human performance with the LFV.

Figure 3: SketchUp model of the 3-D structure of the current sectors over the TMA, made by ATCO students from the LFV’s Entry Point North Air Traffic Services Academy.

Figure 3: SketchUp model of the 3-D structure of the current sectors over the TMA, made by ATCO students from the LFV’s Entry Point North Air Traffic Services Academy.

The project also includes a group of industry and authority experts: Patrik Bergviken (Landvetter, LFV), Robert Graham (head of airport research at EUROCONTROL), Johan Holmer (Trafikverket, the Swedish Traffic Agency), Anders Ledin (Swedavia) and Anne-Marie Ragnarsson (Transportstyrelsen, the Swedish Transportation Authority). Their involvement helps to steer the project in the right direction when it comes to the real world, with all its operational constraints and political regulations, satisfying what actually presents a huge technological challenge.

The project reference group meets twice a year, and at the initial workshop, organized in May 2015, the group advised us to look not only at the grand challenge of optimally solving the airspace design problem in its full generality, but also to explore possibility of finding “quick-and-dirty” improvements that could be implemented without abolishing the current practices in the overall airspace management. The suggestion is very much inline with the general approach in attacking large-scale optimization tasks: Instead of trying to solve the big problem from scratch with some single-shot mega-potent solver, single out several smaller subtasks and optimize each of such components separately (keeping in mind further opportunities to optimize also interfaces between the components). One classical example of successful industry-wide use of this approach within aviation is splitting the fleet management problem (deciding which plane will fly each link on the schedule) into fleet assignment (deciding which aircraft type will fly each link) and aircraft routing (deciding rotations for each aircraft).

Indeed, from a top view, TMA design falls into the broad class of typical O.R. demand-to-resource matching problems. Specifically, the demand for TMA is formed by the flight plans of the aircraft that intend to land in or depart from the TMA. The resources are the runway(s) at the airport(s), the available fly zones, and the surveillance, navigation and control infrastructure, etc. While in principle it is possible to begin solving the airspace design problem from anywhere in the system, one natural approach is to start from a close look at the “outer” and the “inner” boundaries and gradually expand the optimization frontier, culminating in a “meet-in-the-middle” solution that has optimal designs on both sides.

In the TMA case the outer boundary (the “input,” the demand) is defined by the flights through the airspace, and this has been the focus of the research so far. The results obtained by now [1, 2] give a baseline for TMA design assessment, delineate efficiency bottlenecks and determine room for potential improvement.

Specifically, we quantified how many extra miles the aircraft have to fly in the TMA due to the human factor – the fact that each flight must be monitored by ATCOs who have only a limited control capacity. Construction of (parts of) the solution by pushing off the “innermost” structures (the runways) and the design of the “middle-ware” (flight routes and control sectors within the TMA) are topics of forthcoming work in the project.

Effective transport is vital for a long and narrow country like Sweden, and the relatively low traffic demand gives an opportunity to actually optimize the use of transportation resources. In particular, VINNOVA regularly issues calls for research proposals in the area of transport and environment, and in 2014, LFV and LiU responded to the call by applying for funding for ODESTA. Joint research fits well into the LFV-LiU collaboration agreement signed in 2012 by LFV’s director general and LiU’s vice rector; in addition to research, the agreement covers a joint educational program in which ATCOs receive practical training from LFV along with a bachelor’s degree from LiU. Securing common external research funding was a natural step in strengthening the cooperation. More generally, the teaming up of LFV and LiU was no coincidence but actually a consequence of Swedish government’s (successful) effort to breathe (new) life into the (run down by the textile industry fall) city of Norrköping, to which several governmental establishments (including LFV, Swedish Maritime Administration, Swedish Migration Agency, et al.) were moved from the capital and where a campus of LiU was founded.

ODESTA started in the fall of 2015 and is funded for four years. Introduction of new technologies into ATM practice is a long multistep process that includes simulation and validation prior to deployment. Many follow-up activities are envisioned to continue past ODESTA’s timeframe. The guinea pig for the developed algorithms will be the Stockholm TMA (S-TMA) where Sweden’s largest and third largest airports (Arlanda and Bromma) are situated. A recent study by LFV confirmed the need for the airspace redesign, giving a green light to simulate and validate ODESTA outcomes in the S-TMA. Travelers to the Swedish capital shouldn’t worry, though, that their flight paths will be produced by computer without human oversight. ATM remains a human-centered activity, and our implementations are seen merely as decision support tools aiding human experts in choosing the best out of the infinite number of options (the tools include test environments, graphical user interfaces, and much more).

Interestingly, each earlier effort in airspace design concentrated on only one of the two problems:

  1. Given how the aircraft fly (based on the airways or on historical data), design the sectors around the flight paths that allow for the most effective control of the air traffic flow.
  2. Given the control sectors, find the routes that best fit into the sectors (in particular, the flight paths should not cross between the sectors more often than necessary because every change of the sectors implies a communication overhead of coordinating the change with the ATCOs responsible for the sectors).

ODESTA’s ambition is to surmount this delimitation and address the two problems within a single common optimization framework, providing an algorithmic solution for both problems simultaneously. That is, in its output, the project will provide both the sectors and the routes that together constitute optimal (or close to optimal) solution for the airspace design task.

The most direct result of the research within ODESTA will be models and algorithms for an optimized airspace design. An obvious indirect result is, of course, the redesign of the Stockholm TMA, for which ODESTA will most certainly smoothen the way ahead. Much of the groundwork for an optimal redesign will be performed during the project, and relevant parties will have time and opportunity to discuss issues concerning the redesign at reference group meeting and at the workshops. It may even be the case that an actual redesign will have been made before the project ends, although we deem this as unlikely. If a redesign starts within the timeframe of ODESTA, the reference group and LFV will ensure that knowledge accumulated so far within ODESTA will be part of the process of redesign.

Optimizing the airspace over Stockholm will bring a number of benefits. In ODESTA, we will theoretically show how much the flight paths can be shortened and delays be reduced, thereby reducing noise and emissions, and how much predictability and capacity can be increased. We will also provide means to reach these benefits. We trust that the O.R. expertise developed within the project will also find use in other traffic-congested hotspots around the world, contributing to the mutually beneficial O.R.-industry collaboration.

Valentin Polishchuk ( is an associate professor and senior lecturer of air transportation at Linkoping University, Sweden, and an adjunct professor of computer science at the University of Helsinki.


  1. I. Kostitsyna, M. Löffler and V. Polishchuk, 2015, “Optimizing airspace closure with respect to politicians’ egos,” special issue of Theoretical Computer Science on 7th International Conference on Fun with Algorithms (FUN 2014).
  2. T.A. Granberg, V. Polishchuk and B. Josefsson, 2015, “A Baseline for Terminal Airspace Design Assessment,” in Schaefer, Dirk (editor) Proceedings of the SESAR Innovation Days (2015), EUROCONTROL.