Brief announcement: The Asynchronous Bounded-Cycle model

In this paper, we introduce the Asynchronous Bounded-Cycle (ABC) model, which considerably relaxes the Θ-Model proposed by Le Lann and Schmid. The ABC model just bounds the ratio of the number of forward and backward messages in certain cycles in the space-time diagram of an asynchronous execution. It hence avoids any reference to end-to-end delays, allows individual messages to have arbitrary delays, and does not involve global synchrony conditions. We show that clock synchronization and lock-step rounds can easily be implemented and proved correct in the ABC model, even in the presence of Byzantine failures. Moreover, we show that any correct Θ-algorithm also works correctly in the ABC model. Our proof is based on a novel technique for assigning message delays to asynchronous executions, which is of independent interest.