Analyzing eventual leader election protocols for dynamic systems by probabilistic model checking

Leader election protocols have been intensively studied in distributed computing, mostly in the static setting. However, it remains a challenge to design and analyze these protocols in the dynamic setting, due to its high uncertainty, where typical properties include the average steps of electing a leader eventually, the scalability etc. In this paper, we propose a novel model-based approach for analyzing leader election protocols of dynamic systems based on probabilistic model checking. In particular, we employ a leading probabilistic model checker, PRISM, to simulate representative protocol executions. We also relax the assumptions of the original model to cover unreliable channels which requires the introduction of probability to our model. The experiments confirm the feasibility of our approach

Probabilistic verification of hierarchical leader election protocols in dynamic systems

Leader election protocols are fundamental for coordination problems—such as consensus—in distributed computing. Recently, hierarchical leader election protocols have been proposed for dynamic systems where processes can dynamically join and leave, and no process has global information. However, quantitative analysis of such protocols is generally lacking. In this paper, we present a probabilistic model checking based approach to verify quantitative properties of these protocols. Particularly, we employ the compositional technique in the style of assume-guarantee reasoning such that the sub-protocols for each of the two layers are verified separately and the correctness of the whole protocol is guaranteed by the assume-guarantee rules. Moreover, within this framework we also augment the proposed model with additional features such as rewards. This allows the analysis of time or energy consumption of the protocol. Experiments have been conducted to demonstrate the effectiveness of our approach

Time-Varying Graphs and Dynamic Networks

The past few years have seen intensive research efforts carried out in some apparently unrelated areas of dynamic systems -- delay-tolerant networks, opportunistic-mobility networks, social networks -- obtaining closely related insights. Indeed, the concepts discovered in these investigations can be viewed as parts of the same conceptual universe; and the formal models proposed so far to express some specific concepts are components of a larger formal description of this universe. The main contribution of this paper is to integrate the vast collection of concepts, formalisms, and results found in the literature into a unified framework, which we call TVG (for time-varying graphs). Using this framework, it is possible to express directly in the same formalism not only the concepts common to all those different areas, but also those specific to each. Based on this definitional work, employing both existing results and original observations, we present a hierarchical classification of TVGs; each class corresponds to a significant property examined in the distributed computing literature. We then examine how TVGs can be used to study the evolution of network properties, and propose different techniques, depending on whether the indicators for these properties are a-temporal (as in the majority of existing studies) or temporal. Finally, we briefly discuss the introduction of randomness in TVGs.Comment: A short version appeared in ADHOC-NOW'11. This version is to be published in Internation Journal of Parallel, Emergent and Distributed System

Self-Stabilization in the Distributed Systems of Finite State Machines

The notion of self-stabilization was first proposed by Dijkstra in 1974 in his classic paper. The paper defines a system as self-stabilizing if, starting at any, possibly illegitimate, state the system can automatically adjust itself to eventually converge to a legitimate state in finite amount of time and once in a legitimate state it will remain so unless it incurs a subsequent transient fault. Dijkstra limited his attention to a ring of finite-state machines and provided its solution for self-stabilization. In the years following his introduction, very few papers were published in this area. Once his proposal was recognized as a milestone in work on fault tolerance, the notion propagated among the researchers rapidly and many researchers in the distributed systems diverted their attention to it. The investigation and use of self-stabilization as an approach to fault-tolerant behavior under a model of transient failures for distributed systems is now undergoing a renaissance. A good number of works pertaining to self-stabilization in the distributed systems were proposed in the yesteryears most of which are very recent. This report surveys all previous works available in the literature of self-stabilizing systems

Design, Formal Modeling, and Validation of Cloud Storage Systems using Maude

To deal with large amounts of data while offering high availability, throughput and low latency, cloud computing systems rely on distributed, partitioned, and replicated data stores. Such cloud storage systems are complex software artifacts that are very hard to design and analyze. We argue that formal specification and model checking analysis should significantly improve their design and validation. In particular, we propose rewriting logic and its accompanying Maude tools as a suitable framework for formally specifying and analyzing both the correctness and the performance of cloud storage systems. This chapter largely focuses on how we have used rewriting logic to model and analyze industrial cloud storage systems such as Google's Megastore, Apache Cassandra, Apache ZooKeeper, and RAMP. We also touch on the use of formal methods at Amazon Web Services.This work is based on research sponsored by the Air Force Research Laboratory and the Air Force Office of Scientific Research, under agreement number FA8750-11-2-0084. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation thereon. This work is also based on research supported by the National Science Foundation under Grant Nos. NSF CNS 1409416 and NSF CNS 1319527.Ope

Byzantine fault-tolerant agreement protocols for wireless Ad hoc networks

Tese de doutoramento, Informática (Ciências da Computação), Universidade de Lisboa, Faculdade de Ciências, 2010.The thesis investigates the problem of fault- and intrusion-tolerant consensus in resource-constrained wireless ad hoc networks. This is a fundamental problem in distributed computing because it abstracts the need to coordinate activities among various nodes. It has been shown to be a building block for several other important distributed computing problems like state-machine replication and atomic broadcast. The thesis begins by making a thorough performance assessment of existing intrusion-tolerant consensus protocols, which shows that the performance bottlenecks of current solutions are in part related to their system modeling assumptions. Based on these results, the communication failure model is identified as a model that simultaneously captures the reality of wireless ad hoc networks and allows the design of efficient protocols. Unfortunately, the model is subject to an impossibility result stating that there is no deterministic algorithm that allows n nodes to reach agreement if more than n2 omission transmission failures can occur in a communication step. This result is valid even under strict timing assumptions (i.e., a synchronous system). The thesis applies randomization techniques in increasingly weaker variants of this model, until an efficient intrusion-tolerant consensus protocol is achieved. The first variant simplifies the problem by restricting the number of nodes that may be at the source of a transmission failure at each communication step. An algorithm is designed that tolerates f dynamic nodes at the source of faulty transmissions in a system with a total of n 3f + 1 nodes. The second variant imposes no restrictions on the pattern of transmission failures. The proposed algorithm effectively circumvents the Santoro- Widmayer impossibility result for the first time. It allows k out of n nodes to decide despite dn 2 e(nk)+k2 omission failures per communication step. This algorithm also has the interesting property of guaranteeing safety during arbitrary periods of unrestricted message loss. The final variant shares the same properties of the previous one, but relaxes the model in the sense that the system is asynchronous and that a static subset of nodes may be malicious. The obtained algorithm, called Turquois, admits f < n 3 malicious nodes, and ensures progress in communication steps where dnf 2 e(n k f) + k 2. The algorithm is subject to a comparative performance evaluation against other intrusiontolerant protocols. The results show that, as the system scales, Turquois outperforms the other protocols by more than an order of magnitude.Esta tese investiga o problema do consenso tolerante a faltas acidentais e maliciosas em redes ad hoc sem fios. Trata-se de um problema fundamental que captura a essência da coordenação em actividades envolvendo vários nós de um sistema, sendo um bloco construtor de outros importantes problemas dos sistemas distribuídos como a replicação de máquina de estados ou a difusão atómica. A tese começa por efectuar uma avaliação de desempenho a protocolos tolerantes a intrusões já existentes na literatura. Os resultados mostram que as limitações de desempenho das soluções existentes estão em parte relacionadas com o seu modelo de sistema. Baseado nestes resultados, é identificado o modelo de falhas de comunicação como um modelo que simultaneamente permite capturar o ambiente das redes ad hoc sem fios e projectar protocolos eficientes. Todavia, o modelo é restrito por um resultado de impossibilidade que afirma não existir algoritmo algum que permita a n nós chegaram a acordo num sistema que admita mais do que n2 transmissões omissas num dado passo de comunicação. Este resultado é válido mesmo sob fortes hipóteses temporais (i.e., em sistemas síncronos) A tese aplica técnicas de aleatoriedade em variantes progressivamente mais fracas do modelo até ser alcançado um protocolo eficiente e tolerante a intrusões. A primeira variante do modelo, de forma a simplificar o problema, restringe o número de nós que estão na origem de transmissões faltosas. É apresentado um algoritmo que tolera f nós dinâmicos na origem de transmissões faltosas em sistemas com um total de n 3f + 1 nós. A segunda variante do modelo não impõe quaisquer restrições no padrão de transmissões faltosas. É apresentado um algoritmo que contorna efectivamente o resultado de impossibilidade Santoro-Widmayer pela primeira vez e que permite a k de n nós efectuarem progresso nos passos de comunicação em que o número de transmissões omissas seja dn 2 e(n k) + k 2. O algoritmo possui ainda a interessante propriedade de tolerar períodos arbitrários em que o número de transmissões omissas seja superior a . A última variante do modelo partilha das mesmas características da variante anterior, mas com pressupostos mais fracos sobre o sistema. Em particular, assume-se que o sistema é assíncrono e que um subconjunto estático dos nós pode ser malicioso. O algoritmo apresentado, denominado Turquois, admite f < n 3 nós maliciosos e assegura progresso nos passos de comunicação em que dnf 2 e(n k f) + k 2. O algoritmo é sujeito a uma análise de desempenho comparativa com outros protocolos na literatura. Os resultados demonstram que, à medida que o número de nós no sistema aumenta, o desempenho do protocolo Turquois ultrapassa os restantes em mais do que uma ordem de magnitude.FC

Contributions on agreement in dynamic distributed systems

139 p.This Ph.D. thesis studies the agreement problem in dynamic distributed systems by integrating both the classical fault-tolerance perspective and the more recent formalism based on evolving graphs. First, we developed a common framework that allows to analyze and compare models of dynamic distributed systems for eventual leader election. The framework extends a previous proposal by Baldoni et al. by including new dimensions and levels of dynamicity. Also, we extend the Time-Varying Graph (TVG) formalism by introducing the necessary timeliness assumptions and the minimal conditions to solve agreement problems. We provide a hierarchy of time-bounded, TVG-based, connectivity classes with increasingly stronger assumptions and specify an implementation of Terminating Reliable Broadcast for each class. Then we define an Omega failure detector, W, for the eventual leader election in dynamic distributed systems, together with a system model, , which is compatible with the timebounded TVG classes. We implement an algorithm that satisfy the properties of W in M. According to our common framework, M results to be weaker than the previous proposed dynamic distributed system models for eventual leader election. Additionally we use simulations to illustrate this fact and show that our leader election algorithm tolerates more general (i.e., dynamic) behaviors, and hence it is of application in a wider range of practical scenarios at the cost of a moderate overhead on stabilization times

On the Limits and Practice of Automatically Designing Self-Stabilization

A protocol is said to be self-stabilizing when the distributed system executing it is guaranteed to recover from any fault that does not cause permanent damage. Designing such protocols is hard since they must recover from all possible states, therefore we investigate how feasible it is to synthesize them automatically. We show that synthesizing stabilization on a fixed topology is NP-complete in the number of system states. When a solution is found, we further show that verifying its correctness on a general topology (with any number of processes) is undecidable, even for very simple unidirectional rings. Despite these negative results, we develop an algorithm to synthesize a self-stabilizing protocol given its desired topology, legitimate states, and behavior. By analogy to shadow puppetry, where a puppeteer may design a complex puppet to cast a desired shadow, a protocol may need to be designed in a complex way that does not even resemble its specification. Our shadow/puppet synthesis algorithm addresses this concern and, using a complete backtracking search, has automatically designed 4 new self-stabilizing protocols with minimal process space requirements: 2-state maximal matching on bidirectional rings, 5-state token passing on unidirectional rings, 3-state token passing on bidirectional chains, and 4-state orientation on daisy chains