n Process j is not deadlocked when Q(j,i) <= W(i) for all i. n Then we are optimistic and assume that process j will require no more resources to complete its task n It will thus soon return all of its allocated resources. Thus: W(i) = W(i) + A(j,i) for all i n If this assumption is incorrect, a deadlock may occur later n This deadlock will be detected the next time the deadlock detection algorithm is invoked