PROBABILISTIC TIMED AUTOMATA ANALYSIS OF AIR TRAFFIC CONTROL SYSTEMS

Abstract

A research project unites intelligent air-traffic-management system development with the strict mathematical evaluation of control-action coordination interfaces between pilots and controllers. The controller–pilot interface must receive formal specifications just like flight-control software since it represents a unified reactive system. Every system interaction receives probabilistic timed automaton modeling because it represents both real-time operational constraints and the random occurrence of human errors and equipment breakdowns. The Z formal specification language enables writing contracts that link observable external actions to their required pre-conditions and post-conditions which humans and machines can verify. The system interface modules that represent human operators and graphical displays and underlying avionics logic and supervisory safety agents are connected to perform weak branching bisimulation which proves behavioral equivalence under timing uncertainty.

The model demonstrates that the controller commands along with machine feedback and supervisory vetoes and pilot acknowledgements can be represented with twenty global states in a model that includes every significant timing and fault scenario. The automated verification system measures a low probability of mission success as well as operator slips that increase overall risk and identifies critical time-divergent execution paths that reveal hidden design vulnerabilities. Interface engineers can modify timing guards and revise visual cues and embed cognitive-load adaptations without disrupting the existing formal proofs because the graphical display and hidden logic have been proven equivalent. The study transforms the controller–pilot interface into an air-traffic-management ecosystem component which receives mathematical certification and sets the stage for future interfaces that adapt to workload data while providing safety guarantees that machines can verify.