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Redundancy scheduling with scaled Bernoulli service requirements
Queueing Systems ( IF 0.7 ) Pub Date : 2019-06-22 , DOI: 10.1007/s11134-019-09621-2
Youri Raaijmakers , Sem Borst , Onno Boxma

Redundancy scheduling has emerged as a powerful strategy for improving response times in parallel-server systems. The key feature in redundancy scheduling is replication of a job upon arrival by dispatching replicas to different servers. Redundant copies are abandoned as soon as the first of these replicas finishes service. By creating multiple service opportunities, redundancy scheduling increases the chance of a fast response from a server that is quick to provide service, and mitigates the risk of a long delay incurred when a single selected server turns out to be slow. The diversity enabled by redundant requests has been found to strongly improve the response time performance, especially in case of highly variable service requirements. Analytical results for redundancy scheduling are unfortunately scarce however, and even the stability condition has largely remained elusive so far, except for exponentially distributed service requirements. In order to gain further insight in the role of the service requirement distribution, we explore the behavior of redundancy scheduling for scaled Bernoulli service requirements. We establish a sufficient stability condition for generally distributed service requirements and we show that, for scaled Bernoulli service requirements, this condition is also asymptotically nearly necessary. This stability condition differs drastically from the exponential case, indicating that the stability condition depends on the service requirements in a sensitive and intricate manner.

中文翻译:

具有扩展伯努利服务要求的冗余调度

冗余调度已成为改进并行服务器系统响应时间的强大策略。冗余调度的关键特性是通过将副本分派到不同的服务器来复制到达的作业。一旦这些副本中的第一个完成服务,冗余副本就会被放弃。通过创建多个服务机会,冗余调度增加了快速提供服务的服务器的快速响应的机会,并降低了当单个选定服务器变慢时产生的长时间延迟的风险。已发现冗余请求启用的多样性极大地提高了响应时间性能,特别是在高度可变的服务需求的情况下。然而,遗憾的是,冗余调度的分析结果很少,到目前为止,除了指数分布的服务需求外,甚至稳定性条件在很大程度上仍然难以捉摸。为了进一步了解服务需求分布的作用,我们探索了针对缩放伯努利服务需求的冗余调度行为。我们为普遍分布的服务需求建立了一个充分的稳定性条件,并且我们表明,对于可扩展的伯努利服务需求,这个条件也是渐近必要的。这种稳定性条件与指数情况有很大不同,表明稳定性条件以一种敏感而复杂的方式依赖于服务需求。为了进一步了解服务需求分布的作用,我们探索了针对缩放伯努利服务需求的冗余调度行为。我们为普遍分布的服务需求建立了一个充分的稳定性条件,并且我们表明,对于可扩展的伯努利服务需求,这个条件也是渐近必要的。这种稳定性条件与指数情况有很大不同,表明稳定性条件以一种敏感而复杂的方式依赖于服务需求。为了进一步了解服务需求分布的作用,我们探索了针对缩放伯努利服务需求的冗余调度行为。我们为普遍分布的服务需求建立了一个充分的稳定性条件,并且我们表明,对于可扩展的伯努利服务需求,这个条件也是渐近必要的。这种稳定性条件与指数情况有很大不同,表明稳定性条件以一种敏感而复杂的方式依赖于服务需求。这个条件也是渐近必要的。这种稳定性条件与指数情况有很大不同,表明稳定性条件以一种敏感而复杂的方式依赖于服务需求。这个条件也是渐近必要的。这种稳定性条件与指数情况有很大不同,表明稳定性条件以一种敏感而复杂的方式依赖于服务需求。
更新日期:2019-06-22
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