We propose a natural generalisation of asynchronous bounded delay (ABD) network models. The commonly used ABD models assume a known bound on message delay. This assumption is often too strict for real-life applications. To this end we introduce a novel probabilistic network model, called asynchronous bounded expected delay (ABE), which requires a known bound on the expected message delay. While the conditions of ABD networks restrict the set of possible executions, in ABE networks all asynchronous executions are possible, but executions with extremely long delays are less probable. The ABE model captures asynchrony that occurs in sensor networks and ad-hoc networks.
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