Revisiting the Election Problem in Asynchronous Distributed Systems

This paper is about the weakest failure detector to solve the Election problem in asynchronous distributed systems. We first discuss the relationship between the Election problem and the Consensus problem in asynchronous distributed systems with unreliable failure detectors. Chandra and Toueg have stated that Consensus is solvable in asynchronous systems with unreliable failure detectors. But, in contrast to the Consensus problem, the Election problem is impossible to solve with unreliable failure detectors even with a single crash failure. More precisely, the weakest failure detector that is needed to solve this problem is a Perfect Failure Detector, which is strictly stronger than the weakest failure detector that is needed to solve Consensus.

While lots of consensus algorithms have been proposed for crash-prone asynchronous message-passing systems enriched with a failure detector of the class Ω (the class of eventual leader failure detectors), very few algorithms have been proposed for systems enriched with a failure detector of the class P (the class of perfect failure detectors). Moreover, (to the best of our knowledge) the early decision and stopping notion has not been investigated in such systems. This paper presents an early-deciding/stopping P-based consensus algorithm. A process that does not crash decides (and stops) in at most min(f+2, t+1) rounds, where t is the maximum number of processes that may crash, and f the actual number of crashes (0≤ f≤ t). Differently from what occurs in a synchronous system, a perfect failure detector notifies failures asynchronously. This makes the design of an early deciding (and stopping) algorithm not trivial. Interestingly enough, the proposed algorithm meets the lower bound on the number of rounds for early decision in synchronous systems. In that sense, it is optimal. The paper then presents an original algorithm that implements a perfect failure detector in the Theta model, an interesting model that achieves some form of synchrony without relying on physical clocks. Hence, the stacking of these algorithms provides an algorithm that solves consensus in the Theta model in min(f+2, t+1) communication rounds, i.e., in two rounds when there are no failures, which is clearly optimal.

A non-blocking implementation of a concurrent object is an implementation that does not prevent concurrent accesses to the internal representation of the object, while guaranteeing the deadlock-freedom progress condition without using locks. Considering a failure free context, G. Taubenfeld has introduced (DISC 2013) a simple modular approach, captured under a new problem called the it fair synchronization problem, to transform a non-blocking implementation into a starvation-free implementation satisfying a strong fairness requirement. This paper extends this approach in several directions. It first generalizes the fair synchronization problem to read/write asynchronous systems where any number of processes may crash. Then, it introduces a new failure detector and uses it to solve the fair synchronization problem when processes may crash. This failure detector, denoted QP (Quasi Perfect), is very close to, but strictly weaker than, the perfect failure detector. Last but not least, the paper shows that the proposed failure detector QP is optimal in the sense that the information on failures it provides to the processes can be extracted from any algorithm solving the fair synchronization problem in the presence of any number of process crash failures.

This paper defines the Non-Blocking Atomic Commitment problem in a message-passing asynchronous system and determines a failure detector to solve the problem. This failure detector, which we call the modal failure detector star, and which we denote by M*, is strictly weaker than the perfect failure detector P but strictly stronger than the eventually perfect failure detector ◇P. The paper shows that at any environment, the problem is solvable with M*.

It is shown that, in a precise sense, if there is no bound on the number of faulty processes in a system with unreliable but fair communication, Uniform Distributed Coordination (UDC) can be attained if and only if a system has perfect failure detectors. This result is generalized to the case where there is a bound t on the number of faulty processes. It is shown that a certain type of generalized failure detector is necessary and sufficient for achieving UDC in a context with at most t faulty processes. Reasoning about processes' knowledge as to which other processes are faulty plays a key role in the analysis.

Due to the multiplicity of loci of control, a main issue distributed systems have to cope with lies in the uncertainty on the system state created by the adversaries that are asynchrony, failures, dynamicity, mobility, etc. Considering message-passing systems, this paper considers the uncertainty created by the net effect of asynchrony and process crash failures in systems where the processes are anonymous (i.e., processes have no identity and locally execute the same algorithm). Trivially, agreement problems such as consensus, that cannot be solved in non-anonymous asynchronous systems prone to process failures, cannot be solved either if the system is anonymous. The paper investigates failure detectors that allow processes to circumvent this impossibility. It has several contributions. It first presents four failure detectors (denoted AP, $${\overline{AP}}$$ , AΩ, and AΣ) and show that they are the “identity-free” counterparts of perfect failure detectors, eventual leader failure detectors, and quorum failure detectors, respectively. AΣ is new and showing that AΣ and Σ have the same computability power in a non-anonymous system is not trivial. The paper also shows that the notion of failure detector reduction is related to the computation model. Then, the paper presents and proves correct a uniform anonymous consensus algorithm based on the failure detector pair (AΩ, AΣ) (“uniform” means here that not only processes have no identity, but no process is aware of the total number of processes). This new algorithm is not a simple “straightforward extension” of an algorithm designed for non-anonymous systems. To benefit from AΣ, it uses a novel broadcast facility which encapsulates an AΣ-based message exchange pattern that provides the processes with an interesting intersection property on the set of messages they have exchanged. Finally, the paper discusses the notions of failure detector hierarchy, weakest failure detector for anonymous consensus, and the implementation of identity-free failure detectors in anonymous systems.

A distributed algorithm is crash quiescent if it eventually stops sending messages to crashed processes. An algorithm can be made crash quiescent by providing it with either a crash notification service or a reliable communication service. Both services can be implemented in practical environments with failure detectors. Therefore, crash-quiescent failure detection is fundamental to system-wide crash quiescence. We establish necessary and sufficient conditions for crash-quiescent failure detection in partially synchronous environments where a bounded, but unknown, number of consecutive messages can be arbitrarily late or lost. Without a correct majority of processes, not even the weakest oracle for fault-tolerant consensus, ⋄W, can be implemented crash quiescently. With a correct majority, however, the eventually perfect failure detector, ⋄P, is possible. Our ⋄P algorithm is correct in all runs, but improves performance via crash quiescence in any run with a correct majority. We also present a refinement of our ⋄P algorithm to mitigate the overhead of achieving crash quiescence; the resulting bit complexity per utilized link is asymptotically better than or equal to that of non-crash-quiescent counterparts.

Communication-optimal eventually perfect failure detection in partially synchronous systems

A Leader is a Coordinator that supports a set of processes to cooperate a given task. This concept is used in several domains such as distributed systems, parallelism and cooperative support for cooperative work. In completely asynchronous systems, there is no solution for the election problem satisfying both of safety and liveness properties in asynchronous distributed systems. Therefore, to solve the election problem in those systems, one property should be weaker than the other property. If an election algorithm strengthens the safety property in sacrifice of liveness property, it would not nearly progress. But on the contrary, an election algorithm strengthening the liveness property in sacrifice of the safety property would have the high probability of violating the safety property. In this paper, we presents a safety strengthened Leader Election protocol with an unreliable failure detector and analyses it in terms of safety and liveness properties in asynchronous distributed systems.

We describe two system models that allow the implementation of dependable applications in asynchronous systems. We provide assumptions that are sufficiently weak to be satisfied by real distributed systems. Nevertheless, we can show that important problems of dependable computing are still solvable. For mobile systems we weaken the assumptions even more and show that it is still possible to solve the consensus problem using eventually perfect failure detectors using communication via stubborn channels.