Career: fundamental lower bound and tradeoff problems in networking

Issued as final reportNational Science Foundation (U.S.

Simple Bivalency Proofs of the Lower Bounds in Synchronous Consensus Problems

A fundamental problem of fault-tolerant distributed computing is for the reliable processes to reach a consensus. For a synchronous distributed system of n processes with up to t crash failures and f failures actually occur, we prove using a straightforward bivalency argument that the lower bound for reaching uniform consensus is (f + 2)-rounds in the case of 0 < f ⤠t â2, and a new lower bound for early-stopping consensus is min (t + 1, f + 2)-rounds where 0 ⤠f ⤠t. Both proofs are simpler and more intuitive than the traditional methods such as backward induction. Our main contribution is that we solve the open problem of proving that bivalency can be applied to show the (f + 2)-rounds lower bound for synchronous uniform consensus.Singapore-MIT Alliance (SMA

LIPIcs, Volume 251, ITCS 2023, Complete Volume

LIPIcs, Volume 251, ITCS 2023, Complete Volum

Lower Bounds for Achieving Synchronous Early Stopping Consensus with Orderly Crash Failures

In this paper, we discuss the consensus problem for synchronous distributed systems with orderly crash failures. For a synchronous distributed system of n processes with up to t crash failures and f failures actually occur, first, we present a bivalency argument proof to solve the open problem of proving the lower bound, min (t + 1, f + 2) rounds, for early-stopping synchronous consensus with orderly crash failures, where t < n - 1. Then, we extend the system model with orderly crash failures to a new model in which a process is allowed to send multiple messages to the same destination process in a round and the failing processes still respect the order specified by the protocol in sending messages. For this new model, we present a uniform consensus protocol, in which all non-faulty processes always decide and stop immediately by the end of f + 1 rounds. We prove that the lower bound of early stopping protocols for both consensus and uniform consensus are f + 1 rounds under the new model, and our proposed protocol is optimal.Singapore-MIT Alliance (SMA

State Machine Replication:from Analytical Evaluation to High-Performance Paxos

Since their invention more than half a century ago, computers have gone from being just an handful of expensive machines each filling an entire room, to being an integral part of almost every aspect of modern life. Nowadays computers are everywhere: in our planes, in our cars, on our desks, in our home appliances, and even in our pockets. This widespread adoption had a profound impact in our world and in our lives, so much that now we rely on them for many important aspects of everyday life, including work, communication, travel, entertainment, and even managing our money. Given our increased reliance on computers, their continuous and correct operation has become essential for modern society. However, individual computers can fail due to a variety of causes and, if nothing is done about it, these failures can easily lead to a disruption of the service provided by computer system. The field of fault tolerance studies this problem, more precisely, it studies how to enable a computer system to continue operation in spite of the failure of individual components. One of the most popular techniques of achieving fault tolerance is software replication, where a service is replicated on an ensemble of machines (replicas) such that if some of these machines fail, the others will continue providing the service. Software replication is widely used because of its generality (can be applied to most services) and its low cost (can use off-the-shelf hardware). This thesis studies a form of software replication, namely, state machine replication, where the service is modeled as a deterministic state machine whose state transitions consist of the execution of client requests. Although state machine replication was first proposed almost 30 years ago, the proliferation of online services during the last years has led to a renewed interest. Online services must be highly available and for that they frequently rely on state machine replication as part of their fault tolerance mechanisms. However, the unprecedented scale of these services, which frequently have hundreds of thousands or even millions of users, leads to a new set performance requirements on state machine replication. This thesis is organized in two parts. The goal of the first part is to study from a theoretical perspective the performance characteristics of the algorithms behind state machine replication and to propose improved variants of such algorithms. The second part looks at the problem from a practical perspective, proposing new techniques to achieve high-throughput and scalability. In the first part, we start with an analytical analysis of the performance of two consensus algorithms, one leader-free (an adaptation of the fast round of Fast Paxos) and another leader-based (an adaptation of classical Paxos). We express these algorithms in the Heard-Of round model and show that using this model it is fairly easy to determine analytically several interesting performance metrics. We then study the performance of round models in general. Round models are perceived as inefficient because in their typical implementation, the real-time duration of rounds is proportional to the (pessimistic) timeouts used on the underlying system. This contrasts with the failure detector or the partial synchronous system models, where algorithms usually progress at the speed of message reception. We show that there is no inherent gap in performance between the models, by proposing a round implementation that during stable periods advances at the speed of message reception. We conclude the first part by presenting a new leader election algorithm that chooses as leader a well-connected process, that is, a process whose time needed to perform a one-to-majority communication round is among the lowest in the system. This is useful mainly in systems where the latency between processes is not homogeneous, because the performance of leader-based algorithms is particularly sensitive to the performance and connectivity of the process acting as a leader. The second part of the thesis studies different approaches to achieve high-throughput with state machine replication. To support the experimental work done in this part, we have developed JPaxos, a fully-featured implementation of Paxos in Java. We start by looking at how to tune the batching and pipelining optimizations of Paxos; using an analytical model of the performance of Paxos we show how to derive good values for the bounds on the batch size and number of parallel instances. We then propose an architecture for implementing replicated state machines that is capable of leveraging multi-core CPUs to achieve very high-levels of performance. The final contribution of this thesis is based on the observation that most implementations of state machine replication have an unbalanced division of work among threads, with one replica, the leader, having a significantly higher workload than the other replicas. Naturally, the leader becomes the bottleneck of the system, while other replicas are only lightly loaded. We propose and evaluate S-Paxos, which evenly balances the workload among all replicas, and thus overcomes the leader bottleneck. The benefits are two-fold: S-Paxos achieves a higher throughput for a given number of replicas and its performance increases with the number of replicas (up to a reasonable number)