On implementing omega in systems with weak reliability and synchrony assumptions

Abstract

We study the feasibility and cost of implementing Ω-a fundamental failure detector at the core of many algorithms-in systems with weak reliability and synchrony assumptions. Intuitively, Ω allows processes to eventually elect a common leader. We first give an algorithm that implements Ω in a weak system S where (a) except for some unknown timely process s, all processes may be arbitrarily slow or may crash, and (b) only the output links of s are eventually timely (all other links can be arbitrarily slow and lossy). Previously known algorithms for Ω worked only in systems that are strictly stronger than S in terms of reliability or synchrony assumptions.We next show that algorithms that implement Ω in system S are necessarily expensive in terms of communication complexity: all correct processes (except possibly one) must send messages forever; moreover, a quadThis paper was originally invited to the special issue of Distributed Computing based on selected papers presented at the 22nd ACM Symposium on Principles of Distributed Computing (PODC 2003). It appears separately due to publication delays. ratic number of links must carry messages forever. This result holds even for algorithms that tolerate at most one crash. Finally, we show that with a small additional assumption to system S-the existence of some unknown correct process whose links can be arbitrarily slow and lossy but fair-there is a communication-efficient algorithm for Ω such that eventually only one process (the elected leader) sends messages. Some recent experimental results indicate that two of the algorithms for Ω described in this paper can be used in dynamically-changing systems and work well in practice [Schiper, Toueg in

Leader Election for Replicated Services Using Application Scores

“…If process j receives a quorum of vote messages (Line 54) indicating the same leader in the same epoch, then process j starts also believing in its leadership and sets its leader and epoch variables, thus Whenever the election does not converge, e.g., too many messages were lost and no quorum sent proposals to process i, a second timeout (retry-timer) is triggered and process i repeats its broadcasts (Line 1), exponentially backing off on each retry. Note that the timeliness implied by waiting for a quorum is not the minimal to enable atomic broadcasts [2,15]. Nevertheless, we have not yet observed the need for weaker timeliness assumptions.…”

“…To solve consensus, it is necessary and sufficient to elect a leader [5,7]. The problem of leader election has been broadly investigated from many viewpoints, from minimizing the synchrony and reliability requirements imposed on links [2,15], to optimizing the Quality of Service of failure detection [8], to electing the leader that can minimize the latency of solving consensus [17]. The ZooKeeper atomic broadcast protocol (Zab) implements a variant of the atomic broadcast primitive called primary order atomic broadcast [13].…”

Failure Detectors Encapsulate Fairness

“…It is shown in [10] that a system with unknown and eventual bounds on relative process speeds and message delay is sufficient to implement ♦P, and thus to implement ♦S. Subsequently, it is shown in [4] that ♦S can be implemented in a system model where all processes execute in lock-step synchrony and there exists some correct process whose links are eventually timely; that is, eventually there is an upper bound on the message delay on these links. In later work, focus shifts to the weakest system model to implement ♦S and an equivalent failure detector Ω [11] (which, eventually and permanently, outputs the id of the same correct process at all correct processes) in environments where up to f processes may crash.…”

Stabilizing leader election in partial synchronous systems with crash failures

“…However, we show that a non-communication-efficient PSSCF solution can be implemented in such systems. Finally, we conclude with the basic system where all links can be asynchronous and lossy (S 0 ): the leader election has neither SSSCF nor PSSCF solution in S 0 [14,9].…”

“…We show that a CE-PSSCF leader election can be done in some weak systems where the SSSCF leader election cannot be done: any system having a timely source that is a process whose all ouput links are timely [14](S 2 ). Using a previous result of Aguilera et al [14], we then recall that communication-efficiency cannot be done if we consider systems having at least one timely source but no fair hub (a hub is a process whose all links are fair lossy) (S 1 ). However, we show that a non-communication-efficient PSSCF solution can be implemented in such systems.…”