Fast Deterministic Consensus in a Noisy Environment

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.Comment: Typographical errors fixe

Analysis of Timing Based Mutual Exclusion with Random Times

Various timing based mutual exclusion algorithms have been proposed that guarantee mutual exclusion if certain timing assumptions hold. In this paper, we examine how these algorithms behave when the time for the basic operations is governed by random distributions. In particular, we are concerned with how often such algorithms succeed in allowing a processor to obtain a critical section and how this success rate depends on the random variables involved. Correspondingly, we consider how to maximize system throughput. We explore this question in the case where operation times are governed by exponential and gamma distributions, using both theoretical analysis and simulations. 1 Introduction A good design methodology for developing distributed algorithm, as advocated by Liskov [7], is to assume the worst and hope for the best. In assuming the worst, one designs an algorithm which is safe regardless of the amount of time each operation takes. In hoping for the best, one designs th..

Abstract Analysis of Timing-Based Mutual Exclusion with Random Times

Various timing-based mutual exclusion algorithms havebeen proposed that guarantee mutual exclusion if certain timing assumptions hold. In this paper, we examine how these algorithms behave when the time for the basic operations is governed by random distributions. In particular, we are concerned with how often such algorithms succeed in allowing a processor to obtain a critical section and how this success rate depends on the random variables involved. We explore this question in the case where operation times are governed by exponential and gamma distributions, using both theoretical analysis and simulations.