  This paper is devoted to deterministic consensus in synchronous dynamic
networks with unidirectional links, which are under the control of an
omniscient message adversary. Motivated by unpredictable node/system
initialization times and long-lasting periods of massive transient faults, we
consider message adversaries that guarantee periods of less erratic message
loss only eventually: We present a tight bound of $2D+1$ for the termination
time of consensus under a message adversary that eventually guarantees a single
vertex-stable root component with dynamic network diameter $D$, as well as a
simple algorithm that matches this bound. It effectively halves the termination
time $4D+1$ achieved by an existing consensus algorithm, which also works under
our message adversary. We also introduce a generalized, considerably stronger
variant of our message adversary, and show that our new algorithm, unlike the
existing one, still works correctly under it.
