Threshold protocols in survivor set systems

• Published in: Distributed computing 2010-10, Vol.23 (2), p.135-149
• Main Authors: Junqueira, Flavio P., Marzullo, Keith, Herlihy, Maurice, Penso, Lucia Draque
• Format: Article
• Language: English
• Subjects: Algorithms; Computer Communication Networks; Computer Hardware; Computer Science; Computer Systems Organization and Communication Networks; Failure; Fault tolerance; Replication; Software Engineering/Programming and Operating Systems; Theory of Computation; Thresholds; Transformations; Transforms; Voters
• ISSN: 0178-2770; 1432-0452
• DOI: 10.1007/s00446-010-0107-3

Many replication protocols employ a threshold model when expressing failures they are able to tolerate. In this model, one assumes that no more than t out of n components can fail, which is a good representation when failures are independent and identically distributed (IID). In many real systems, however, failures are not IID, and a straightforward application of threshold protocols yields suboptimal results. Here, we examine the problem of transforming threshold protocols into survivor-set protocols tolerating dependent failures. Our main goal is to show the equivalence between the threshold model and the core/survivor set model. Toward this goal, we develop techniques to transform threshold protocols into survivor set ones. Our techniques do not require authentication, self-verification or encryption. Our results show in one case that we can transform a threshold protocol to a subset by spreading a number of processes across processors. This technique treats a given threshold algorithm as a black box, and consequently can transform any threshold algorithm. However, it has the disadvantage that the transformation is not possible for all sets of survivor sets. The second technique instead focuses on transforming voters : functions that evaluate to a value out of a set of tallied values in a replication protocol. Voters are an essential part of many fault-tolerant protocols, and we show a universal way of transforming them. With such a transformation we expect that a large number of protocols in the literature can be directly transformed with our technique. It is still an open problem, however, if the two models are equivalent, and our results constitute an important first step in this direction.