The Impact of RDMA on Agreement

Remote Direct Memory Access (RDMA) is becoming widely available in data centers. This technology allows a process to directly read and write the memory of a remote host, with a mechanism to control access permissions. In this paper, we study the fundamental power of these capabilities. We consider the well-known problem of achieving consensus despite failures, and find that RDMA can improve the inherent trade-off in distributed computing between failure resilience and performance. Specifically, we show that RDMA allows algorithms that simultaneously achieve high resilience and high performance, while traditional algorithms had to choose one or another. With Byzantine failures, we give an algorithm that only requires n \geq 2f_P + 1 processes (where f_P is the maximum number of faulty processes) and decides in two (network) delays in common executions. With crash failures, we give an algorithm that only requires n \geq f_P + 1 processes and also decides in two delays. Both algorithms tolerate a minority of memory failures inherent to RDMA, and they provide safety in asynchronous systems and liveness with standard additional assumptions.

What Good are Probabilistic Specifications and What Probabilistic Specifications are Good?

Patrick Eugster

The number of probabilistic approaches to ``classic'' distributed systems problems such as reliable broadcast, consensus, or leader election, has further increased recently. Probabilistic algorithms, possibly starting from probabilistic system models, have been motivated by the need for practicable solutions to such problems, circumventing bottlenecks and limitations inherent to distributed computing. While many approaches coming out of this revival of probabilistic approaches are indeed pathbreaking, it is legitimate to question the usefulness of certain efforts, which claim some form of probabilistic reliability, yet fail to provide clear specifications of the proposed algorithms. In this paper, we point out the inherent difficulties related to the specification of the behavior of probabilistic algorithms through various examples.

2003

Transformations in distributed computations and applications to set agreement

Bastian Pochon

In a distributed application, high-availability of a critical online service is ensured despite failures by duplicating the vital components of the server. Whilst guaranteeing the access to the server at all times, duplication requires particular care, so as to maintain a consistent state amongst all components. A distributed computation plays a key-role in preserving the consistency of the state in this case. Indeed, one of the fundamental forms of distributed computation is distributed agreement. In a distributed agreement problem, the components of the system, called processes, are supposed to all propose a value and eventually decide on a common value that depends on the proposed values. Designing correct distributed agreement algorithms relies on a mathematical model abstracting the details of the underlying physical model. In practice, there are many models, inspired from various types of physical failures. Coping with one type of failures rather than another one, for a distributed agreement algorithm, is not of equal difficulty. Indeed some types are intrinsically harder to cope with than other ones. The thesis studies how distributed algorithms can be transformed from one model to another one. The idea is to design distributed agreement algorithms in models in which the task is made as easiest and least error-prone as possible, and execute the transformed algorithms in models imposed by the underlying physical constraints. We investigate another aspect of transforming distributed computations, the notion of reducibility amongst distributed computations. Reducibility offers an elegant way for deducing lower or upper bounds on the complexity of a distributed algorithm from complexity bounds that have been proved elsewhere, about a different distributed computation or in a different model. For investigating reducibility, the thesis considers two very general classes of models: synchronous models, in which the communication delay and the process execution speed are known and bounded, and asynchronous models, in which the communication delay and the process execution speed are unknown and potentially unbounded. The thesis investigates reducibility of a distributed agreement problem called set agreement. Precisely, we consider the early-deciding variant of set agreement, in which processes must decide as fast as they can in any execution. We prove a lower bound on the complexity of early-deciding set agreement in the synchronous model. The proof works by reducing the impossibility of set agreement in the asynchronous model to the desired lower bound. In some cases, complexity bounds must still be derived with ad-hoc arguments, for example when there is no apparent connection with existing results. The thesis presents an alternative approach to reducibility, namely the connection of distributed computing with algebraic topology. Within this framework, we derive a lower bound for the complexity of early-deciding set agreement in the synchronous model. For all the lower bounds that we derive in the thesis, we show that these bounds are tight, by presenting for each lower bound an algorithm matching the complexity of the lower bound.

EPFL2006

The Time-Complexity of Local Decision in Distributed Agreement

Partha Dutta, Rachid Guerraoui, Bastian Pochon

Agreement is at the heart of distributed computing. In its simple form, it requires a set of processes to decide on a common value out of the values they propose. The time-complexity of distributed agreement problems is generally measured in terms of the number of communication rounds needed to achieve a global decision; i.e., for all non-faulty (correct) processes to reach a decision. This paper studies the time-complexity of local decisions in agreement problems, which we de¯ne as the number of communication rounds needed for at least one correct process to decide. We explore bounds for early local decision, that depend on the number f of actual failures (that occur in a given run of an algorithm), out of the maximum number t of failures tolerated (by the algorithm). We ¯rst consider the synchronous message-passing model where we give tight local decision bounds for three variants of agreement: consensus, uniform consensus and (non-blocking) atomic commit. We use these results to (1) show that, for consensus, local decision bounds are not compatible with global decision bounds (roughly speaking, they cannot be reached by the same algorithm), and (2) draw the ¯rst sharp line between the time-complexity of uniform consensus and atomic commit. Then we consider the eventually synchronous model where we give tight local decision bounds for synchronous runs of uniform consensus. (In this model, consensus and uniform consensus are similar, atomic commit is impossible, and one cannot bound the number of rounds to reach a decision in non-synchronous runs of consensus algorithms.) We prove a counter-intuitive result that the early local decision bound is the same as the early global decision bound. We also give a matching early deciding consensus algorithm that is signi¯cantly better than previous eventually synchronous consensus algorithms.

2007

Transformations in distributed computations and applications to set agreement

Bastian Pochon

EPFL2006