How fast can eventual synchrony lead to consensus?

It is well known that the consensus problem can be solved in a distributed system if, after some time T/sub S/, no process fails and there is some upper bound /spl delta/ on how long it takes to deliver a message. We know of no existing algorithm that guarantees consensus among N processes before time T/sub S/+O(N/spl delta/). We show that consensus can be achieved by time T/sub S/+O(/spl delta/).