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Autonomous air traffic management (ATM) operations for urban air mobility(UAM) will necessitate the use of distributed protocols for decentralizedcoordination between aircraft. As UAM operations are time-critical, it will beimperative to have formal guarantees of progress for the distributed protocolsused in ATM. Under asynchronous settings, message transmission and processingdelays are unbounded, making it impossible to provide deterministic bounds onthe time required to make progress. We present an approach for formallyguaranteeing timely progress in a Two-Phase Acknowledge distributed knowledgepropagation protocol by probabilistically modeling the delays using theories ofthe Multicopy Two-Hop Relay protocol and the M/M/1 queue system. The guaranteestates a probabilistic upper bound to the time for progress as a function ofthe probabilities of the total transmission and processing delays being lessthan two given values. We also showcase the development of a library of formaltheories, that is tailored towards reasoning about timely progress indistributed protocols deployed in airborne networks, in the Athena proofassistant.

Formal Guarantees of Timely Progress for Distributed Knowledge Propagation