Contents lists available at ScienceDirect Transportation Research Part C journal homepage: www.elsevier.com/locate/trc Three-dimensional conflict count models for unstructured and layered airspace designs Emmanuel Sunil ⁎ , Joost Ellerbroek, Jacco M. Hoekstra, Jerom Maas Faculty of Aerospace Engineering, Delft University of Technology, Kluyverweg 1, 2629 HS Delft, The Netherlands ARTICLE INFO Keywords: Airspace safety Airspace design Conflict probability Conflict rate Air Traffic Management (ATM) ABSTRACT This paper presents analytical models that describe the safety of unstructured and layered en route airspace designs. Here, ‘unstructured airspace’ refers to airspace designs that offer opera- tors complete freedom in path planning, whereas ‘layered airspace’ refers to airspace concepts that utilize heading-altitude rules to vertically separate cruising aircraft based on their travel directions. With a focus on the intrinsic safety provided by an airspace design, the models com- pute instantaneous conflict counts as a function of traffic demand and airspace design para- meters, such as traffic separation requirements and the permitted heading range per flight level. While previous studies have focused primarily on conflicts between cruising aircraft, the models presented here also take into account conflicts involving climbing and descending traffic. Fast- time simulation experiments used to validate the modeling approach indicate that the models estimate instantaneous conflict counts with high accuracy for both airspace designs. The simu- lation results also show that climbing and descending traffic caused the majority of conflicts for layered airspaces with a narrow heading range per flight level, highlighting the importance of including all aircraft flight phases for a comprehensive safety analysis. Because such trends could be accurately predicted by the three-dimensional models derived here, these analytical models can be used as tools for airspace design applications as they provide a detailed understanding of the relationships between the parameters that influence the safety of unstructured and layered airspace designs. 1. Introduction The sustained growth of air traffic in recent years has stressed several components of the current Air Traffic Management (ATM) system to near saturation levels. This is particularly true for en route airspace design where continued reliance on the fixed airway network has significantly reduced flight efficiencies (Doble et al., 2008). This is because airway navigation often force aircraft to deviate from direct trajectories, which during peak demand periods can trigger artificial traffic concentrations and increased delays (Magill et al., 1998; Dell’Olmo and Lulli, 2003). Their use in Europe, for instance, has been linked to the 20% increase in en route delays in 2016, even though traffic demand grew by only 2.4% during the same time period (Performance Review Commission, 2016). Similar statistics reported in many other parts of the world have motivated several studies to explore alternate options for organizing en route traffic(Rebollo and Balakrishnan, 2014; SESAR Consortium, 2007; Joint Planning and Development Office, 2007). To overcome the capacity limitations posed by airway routing, some researchers have proposed a transition to less rigid route https://doi.org/10.1016/j.trc.2018.05.031 Received 23 December 2017; Received in revised form 24 April 2018; Accepted 30 May 2018 ⁎ Corresponding author. E-mail address: e.sunil@tudleft.nl (E. Sunil). Transportation Research Part C 95 (2018) 295–319 0968-090X/ © 2018 Elsevier Ltd. All rights reserved. T