Approaches for stochastic safety analysis arising in ATM application

This paper studies the stochastic safety analysis and resolution problems for Air Traffic Management (ATM) systems. Two approaches to estimating the aircraft safety are introduced: a Multi- level Markov Chain (MMC) approximation method for probabilistic prediction of the aircraft conflict, and an Air Traffic Density Estimation (ATDE) approach, which is a simulation-based method for predicting congestions in the airspace within a period of time. Using the estimated aircraft safety, we formulate an optimal trajectory planning problem and develop an efficient solution algorithm for resolving the conflicts. Numerical examples arising in ATM systems are presented to evaluate and compare the two conflict detection approaches along with the developed conflict resolution algorithm.