We consider a system with $N$ parallel servers where incoming jobs are immediately replicated to, say, $d$ servers. Each of the $N$ servers has its own queue and follows a FCFS discipline. As soon as the first job replica is completed, the remaining replicas are abandoned. We investigate the achievable stability region for a quite general workload model with different job types and heterogeneous servers, reflecting job-server affinity relations which may arise from data locality issues and soft compatibility constraints. Under the assumption that job types are known beforehand we show for New-Better-than-Used (NBU) distributed speed variations that no replication $(d=1)$ gives a strictly larger stability region than replication $(d>1)$. Strikingly, this does not depend on the underlying distribution of the intrinsic job sizes, but observing the job types is essential for this statement to hold. In case of non-observable job types we show that for New-Worse-than-Used (NWU) distributed speed variations full replication ($d=N$) gives a larger stability region than no replication $(d=1)$.

中文翻译：

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冗余系统中可达到的稳定性

我们考虑一个具有 $N$ 个并行服务器的系统，其中传入的作业会立即复制到 $d$ 个服务器。每个 $N$ 服务器都有自己的队列并遵循 FCFS 规则。第一个作业副本完成后，其余副本将被放弃。我们研究了具有不同作业类型和异构服务器的非常通用的工作负载模型的可实现稳定性区域，反映了可能由数据局部性问题和软兼容性约束引起的作业-服务器亲和关系。在事先已知作业类型的假设下，我们展示了新的优于旧的 (NBU) 分布式速度变化，即没有复制 $(d=1)$ 提供比复制 $(d>1)$ 严格更大的稳定区域. 引人注目的是，这并不取决于内在工作规模的潜在分布，但观察工作类型对于此声明的成立至关重要。在不可观察的作业类型的情况下，我们表明，对于新旧比旧 (NWU) 分布式速度变化，完全复制 ($d=N$) 比不复制 $(d=1)$ 提供更大的稳定性区域。