  The commonly used asynchronous bounded delay (ABD) network models assume a
fixed bound on message delay. We propose a probabilistic network model, called
asynchronous bounded expected delay (ABE) model. Instead of a strict bound, the
ABE model requires only a 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. In contrast to ABD networks, ABE
networks cannot be synchronised efficiently. At the example of an election
algorithm, we show that the minimal assumptions of ABE networks are sufficient
for the development of efficient algorithms. For anonymous, unidirectional ABE
rings of known size N we devise a probabilistic leader election algorithm
having average message and time complexity O(N).
