  It is well known that the consensus problem cannot be solved
deterministically in an asynchronous environment, but that randomized solutions
are possible. We propose a new model, called noisy scheduling, in which an
adversarial schedule is perturbed randomly, and show that in this model
randomness in the environment can substitute for randomness in the algorithm.
In particular, we show that a simplified, deterministic version of Chandra's
wait-free shared-memory consensus algorithm (PODC, 1996, pp. 166-175) solves
consensus in time at most logarithmic in the number of active processes. The
proof of termination is based on showing that a race between independent
delayed renewal processes produces a winner quickly. In addition, we show that
the protocol finishes in constant time using quantum and priority-based
scheduling on a uniprocessor, suggesting that it is robust against the choice
of model over a wide range.
