The maximum possible throughput (or the rate of job completion) of a multi-server system is typically the sum of the service rates of individual servers. Recent work shows that launching multiple replicas of a job and canceling them as soon as one copy finishes can boost the throughput, especially when the service time distribution has high variability. This means that redundancy can, in fact, create synergy among servers such that their overall throughput is greater than the sum of individual servers. This work seeks to find the fundamental limit of the throughput boost achieved by job replication and the optimal replication policy to achieve it. While most previous works consider upfront replication policies, we expand the set of possible policies to delayed launch of replicas. The search for the optimal adaptive replication policy can be formulated as a Markov Decision Process, using which we propose two myopic replication policies, MaxRate and AdaRep, to adaptively replicate jobs. In order to quantify the optimality gap of these and other policies, we derive upper bounds on the service capacity, which provide fundamental limits on the throughput of queueing systems with redundancy.

中文翻译：

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通过冗余的协同作用：自适应复制策略和基本限制

多服务器系统的最大可能吞吐量（或作业完成率）通常是各个服务器的服务率之和。最近的工作表明，启动一个作业的多个副本并在完成一个副本后立即取消它们可以提高吞吐量，特别是在服务时间分配具有高度可变性的情况下。这实际上意味着冗余可以在服务器之间产生协同作用，从而使它们的整体吞吐量大于单个服务器的总和。这项工作旨在找到通过作业复制实现的吞吐量提升的基本限制，以及实现该目标的最佳复制策略。尽管大多数以前的工作都考虑了前期复制策略，但我们将可能的策略集扩展到延迟启动副本。可以将最佳自适应复制策略的搜索公式化为马尔可夫决策过程，通过该过程，我们提出了两个近视复制策略MaxRate和AdaRep，以自适应地复制作业。为了量化这些策略和其他策略的最佳差距，我们得出了服务容量的上限，这为具有冗余的排队系统的吞吐量提供了基本限制。