Probabilistic model checking for comparative analysis of automated air traffic control systems

Abstract

Ensuring aircraft stay safely separated is the primary consideration in air traffic control. To achieve the required level of assurance for this safety-critical application, the Automated Airspace Concept (AAC) proposes a network of components providing multiple levels of separation assurance, including conflict detection and resolution. In our previous work, we conducted a formal study of this concept including specification, validation, and verification utilizing the NuSMV and CadenceSMV model checkers to ensure there are no potentially catastrophic design flaws remaining in the AAC design before the next stage of production. In this paper, we extend that work to include probabilistic model checking of the AAC system.1 We are motivated by the system designers requirement to compare different design options to optimize the functional allocation of the AAC components. Probabilistic model checking provides quantitative measures for evaluating different design options, helping system designers to understand the impact of parameters in the model on a given critical safety requirement. We detail our approach to modeling and probabilistically analyzing this complex system consisting of a real-time algorithm, a logic protocol, and human factors. We utilize both Discrete Time Markov Chain (DTMC) and Continuous Time Markov Chain (CTMC) models to capture the important behaviors in the AAC components. The separation assurance algorithms, which are defined over specific time ranges, are modeled using a DTMC. The emergence of conflicts in an airspace sector and the reaction times of pilots, which can be simplified as Markov processes on continuous time, are modeled as a CTMC. Utilizing these two models, we calculate the probability of an unresolved conflict as a measure of safety and compare multiple design options.