Air Traffic Management based on 4D Trajectories: A Reliability Analysis using Multi-State Systems Theory

Abstract

Abstract The current Air Traffic Management (ATM) functional approach is changing. Both SESAR (Single European Sky ATM Research) and NEXTGEN (Next Generation Air Transportation System) support the four-dimension (4D) trajectory implementation within their operational concepts. Apart from the three classical spatial dimensions, ‘time’ is now integrated as an additional fourth dimension, which will restrict aircraft flights over indicated waypoints along the trajectory. 4D trajectories can be understood as complex Multi-State Systems (MSS) that rely on environmental, internal and usage conditions. A reliability analysis of the waypoints and time windows that describe the 4D trajectory may allow airline operators and air traffic service providers to establish performance indicators and compliance metrics. This paper develops a model to evaluate potential ‘malfunctions’ of a 4D trajectory, based on the MSS reliability theory. This is a natural extension of classical binary-state evaluation: trajectories present different performance levels and several failure modes (a degradation range). The operational reliability assessment, which is achieved with Monte Carlo simulation and random processes (Markov) methods, offers a framework to predict how probable is for the trajectory to enter a degraded state. We use this analysis to quantify the 4D trajectory level of variability and to propose corrective measures to solve potential trajectory degradations or unplanned situations. The methodology is validated through a practical case study. The main contribution of this paper is to provide a methodology to evaluate the robustness of 4D trajectories and to deal with their perturbation, which is a cornerstone in traffic synchronization and conflict resolution.