Anonymous Asynchronous Systems: The Case of Failure Detectors

Due 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 three of these adversaries, namely, asynchrony, failures, and anonymity. This means that, in addition to be asynchronous and crash-prone, the processes have no identity. Trivially, agreement problems (e.g., consensus) that cannot be solved in presence of asynchrony and failures cannot be solved either when adding anonymity. The paper consequently proposes anonymous failure detectors to circumvent these impossibilities. It has several contributions. First it presents three classes of failure detectors (denoted AP, A∩ and A∑) and show that they are the anonymous counterparts of the classes of perfect failure detectors, eventual leader failure detectors and quorum failure detectors, respectively. The class A∑ is new and showing it is the anonymous counterpart of the class ∑ is not trivial. Then, the paper presents and proves correct a genuinely anonymous consensus algorithm based on the pair of anonymous failure detector classes (A∩, A∑) (“genuinely” means that, not only processes have no identity, but no process is aware of the total number of processes). This new algorithm is not a “straightforward extension” of an algorithm designed for non-anonymous systems. To benefit from A∑, it uses a novel message exchange pattern where each phase of every round is made up of sub-rounds in which appropriate control information is exchanged. Finally, the paper discusses the notions of failure detector class hierarchy and weakest failure detector class for a given problem in the context of anonymous systems

Failure detectors encapsulate fairness

Failure detectors have long been viewed as abstractions for the synchronism present in distributed system models. However, investigations into the exact amount of synchronism encapsulated by a given failure detector have met with limited success. The reason for this is that traditionally, models of partial synchrony are specified with respect to real time, but failure detectors do not encapsulate real time. Instead, we argue that failure detectors encapsulate the fairness in computation and communication. Fairness is a measure of the number of steps executed by one process relative either to the number of steps taken by another process or relative to the duration for which a message is in transit. We argue that failure detectors are substitutable for the fairness properties (rather than real-time properties) of partially synchronous systems. We propose four fairness-based models of partial synchrony and demonstrate that they are, in fact, the ‘weakest system models’ to implement the canonical failure detectors from the Chandra-Toueg hierarchy. We also propose a set of fairness-based models which encapsulate the G[subscript c] parametric failure detectors which eventually and permanently suspect crashed processes, and eventually and permanently trust some fixed set of c correct processes.National Science Foundation (U.S.) (Grant CCF-0964696)National Science Foundation (U.S.) (Grant CCF-0937274)Texas Higher Education Coordinating Board (grant NHARP 000512-0130-2007)National Science Foundation (U.S.) (NSF Science and Technology Center, grant agreement CCF-0939370

Looking for the Weakest Failure Detector for kk-Set Agreement in Message-passing Systems: Is Πk\Pi_k the End of the Road?

In the $k$-set agreement problem, each process (in a set of $n$ processes) proposes a value and has to decide a proposed value in such a way that at most $k$ different values are decided. While this problem can easily be solved in asynchronous systems prone to $t$ process crashes when $k>t$, it cannot be solved when $k\leq t$. Since several years, the failure detector-based approach has been investigated to circumvent this impossibility. While the weakest failure detector class to solve the $k$-set agreement problem in read/write shared-memory systems has recently been discovered (PODC 2009), the situation is different in message-passing systems where the weakest failure detector classes are known only for the extreme cases $k=1$ (consensus) and $k=n-1$ (set agreement). This paper introduces a candidate for the general case. It presents a new failure detector class, denoted $\Pi_k$, and shows $\Pi_1=\Sigma\times \Omega$ (the weakest class for $k=1$), and $\Pi_{n-1}={\cal L}$ (the weakest class for $k=n-1$). Then, the paper investigates the structure of $\Pi_k$ and shows it is the combination of two failures detector classes denoted $\Sigma_k$ and $\Omega_k$ (that generalize the previous ``quorums'' and ``eventual leaders'' failure detectors classes). Finally, the paper proves that $\Sigma_k$ is a necessary requirement (as far as information on failure is concerned) to solve the $k$-set agreement problem in message-passing systems. The paper presents also a $\Pi_{n-1}$-based algorithm that solves the $(n-1)$-set agreement problem. This algorithm provides us with a new algorithmic insight on the way the $(n-1)$-set agreeement problem can be solved in asynchronous message-passing systems (insight from the point of view of the non-partitioning constraint defined by $\Sigma_{n-1}$)

The Weakest Failure Detector for Genuine Atomic Multicast

Atomic broadcast is a group communication primitive to order messages across a set of distributed processes. Atomic multicast is its natural generalization where each message m is addressed to dst(m), a subset of the processes called its destination group. A solution to atomic multicast is genuine when a process takes steps only if a message is addressed to it. Genuine solutions are the ones used in practice because they have better performance. Let ? be all the destination groups and ? be the cyclic families in it, that is the subsets of ? whose intersection graph is hamiltonian. This paper establishes that the weakest failure detector to solve genuine atomic multicast is ? = (?_{g,h ? ?} ?_{g ? h}) ? (?_{g ? ?} ?_g) ? ?, where ?_P and ?_P are the quorum and leader failure detectors restricted to the processes in P, and ? is a new failure detector that informs the processes in a cyclic family f ? ? when f is faulty. We also study two classical variations of atomic multicast. The first variation requires that message delivery follows the real-time order. In this case, ? must be strengthened with 1^{g ? h}, the indicator failure detector that informs each process in g ? h when g ? h is faulty. The second variation requires a message to be delivered when the destination group runs in isolation. We prove that its weakest failure detector is at least ? ? (?_{g, h ? ?} ?_{g ? h}). This value is attained when ? = ?

Chasing the Weakest Failure Detector for k-Set Agreement in Message-passing Systems

This paper continues our quest for the weakest failure detector which allows the k-set agreement problem to be solved in asynchronous message-passing systems prone to any number of process failures. It has two main contributions which (we hope) will be instrumental to complete this quest. The first contribution is a new failure detector (denoted ∏∑x,y). This failure detector has several noteworthy properties. (a) It is stronger than ∑x which has been shown to be necessary. (b) It is equivalent to the pair (∑, Ω) when x = y = 1 (from which it follows that ∏∑1,1 is optimal to solve consensus). (c) It is equivalent to the pair (∑n−1, Ωn−1) when x = y = n − 1 (from which it follows that ∏∑n−1, n−1) is optimal for (n − 1)-set agreement). (d) It is strictly weaker than the pair (∑x,Ωy) (which has been investigated in previous works) for the pairs (x, y) such that 1 < y < x < n. (e) It is operational: the paper presents a ∏∑x,y-based algorithm that solves k-set agreement for k ⩾ xy. The second contribution of the paper is a proof that, for 1 < k < n − 1, the eventual leaders failure detector k (which eventually provides each process with the same set of k process identities, this set including at least one correct process) is not necessary to solve k-set agreement problem. More precisely, the paper shows that the weakest failure detector for k-set agreement and k cannot be compared

À la recherche du détecteur de fautes minimal pour le k-accord

Ce rapport de stage de master recherche en informatique présente des travaux effectués dans le domaine des systèmes distribués asynchrones. Il s'agit d'études visant à déterminer le plus faible détecteur de faute permettant de résoudre le problème du k-accord dans un système distribué asynchrone où les processus communiquent par passage de messages et où un nombre arbitrairement grand de défaillances peuvent survenir

Information Infrastructures in Distributed Environments: Algorithms for Mobile Networks and Resource Allocation

A distributed system is a collection of computing entities that communicate with each other to solve some problem. Distributed systems impact almost every aspect of daily life (e.g., cellular networks and the Internet); however, it is hard to develop services on top of distributed systems due to the unreliable nature of computing entities and communication. As handheld devices with wireless communication capabilities become increasingly popular, the task of providing services becomes even more challenging since dynamics, such as mobility, may cause the network topology to change frequently. One way to ease this task is to develop collections of information infrastructures which can serve as building blocks to design more complicated services and can be analyzed independently. The first part of the dissertation considers the dining philosophers problem (a generalization of the mutual exclusion problem) in static networks. A solution to the dining philosophers problem can be utilized when there is a need to prevent multiple nodes from accessing some shared resource simultaneously. We present two algorithms that solve the dining philosophers problem. The first algorithm considers an asynchronous message-passing model while the second one considers an asynchronous shared-memory model. Both algorithms are crash fault-tolerant in the sense that a node crash only affects its local neighborhood in the network. We utilize failure detectors (system services that provide some information about crash failures in the system) to achieve such crash fault-tolerance. In addition to crash fault-tolerance, the first algorithm provides fairness in accessing shared resources and the second algorithm tolerates transient failures (unexpected corruptions to the system state). Considering the message-passing model, we also provide a reduction such that given a crash fault-tolerant solution to our dining philosophers problem, we implement the failure detector that we have utilized to solve our dining philosophers problem. This reduction serves as the first step towards identifying the minimum information regarding crash failures that is required to solve the dining philosophers problem at hand. In the second part of this dissertation, we present information infrastructures for mobile ad hoc networks. In particular, we present solutions to the following problems in mobile ad hoc environments: (1) maintaining neighbor knowledge, (2) neighbor detection, and (3) leader election. The solutions to (1) and (3) consider a system with perfectly synchronized clocks while the solution to (2) considers a system with bounded clock drift. Services such as neighbor detection and maintaining neighbor knowledge can serve as a building block for applications that require point-to-point communication. A solution to the leader election problem can be used whenever there is a need for a unique coordinator in the system to perform a special task

A Failure Detector for k-Set Agreement in Asynchronous Dynamic Systems

The k-set agreement problem is a generalization of the consensus problem where processes can decide up to k different values. Very few papers have tackled this problem in dynamic networks, and to the best of our knowledge, every algorithm proposed so far for k-set agreement in dynamic networks assumed synchronous communications. Exploiting the formalism of the Time-Varying Graph model, this paper proposes a new failure detector Sigma-bottom-k, based on Sigma-k and Sigma-bottom, for solving k-set agreement in asynchronous dynamic networks. We present two algorithms that implement this new failure detector, making assumptions on the number of process failures and graph connectivity. We also provide an algorithm for solving k-set agreement using Sigma-bottom-z , under an assumption on the relative values of k and z