Can the popular shortest remaining processing time (SRPT) algorithm achieve a constant competitive ratio on multiple servers when server speeds are adjustable (speed scaling) with respect to the flow time plus energy consumption metric? This question has remained open for a while, where a negative result in the absence of speed scaling is well known. The main result of this paper is to show that multi-server SRPT with speed scaling can be constant competitive, with a competitive ratio that only depends on the power-usage function of the servers, but not on the number of jobs/servers or the job sizes (unlike when speed scaling is not allowed). When all job sizes are unity, we show that round-robin routing is optimal and can achieve the same competitive ratio as the best known algorithm for the single server problem. Finally, we show that a class of greedy dispatch policies, including policies that route to the least loaded or the shortest queue, do not admit a constant competitive ratio. When job arrivals are stochastic, with Poisson arrivals and i.i.d. job sizes, we show that random routing and a simple gated-static speed scaling algorithm achieves a constant competitive ratio.

中文翻译：

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具有速度扩展能力的多服务器SRPT具有竞争力

当服务器速度相对于流量时间和能耗指标是可调整的（速度缩放）时，流行的最短剩余处理时间（SRPT）算法能否在多台服务器上实现恒定的竞争比？这个问题已经存在了一段时间，众所周知，在没有速度缩放的情况下会产生负面结果。本文的主要结果表明，具有速度缩放功能的多服务器SRPT可以保持恒定的竞争性，竞争率仅取决于服务器的电源使用功能，而不取决于作业/服务器的数量或服务器的数量。作业大小（与不允许进行速度缩放的情况不同）。当所有工作规模都统一时，我们证明了循环路由是最佳的，并且可以与单服务器问题的最佳算法达到相同的竞争比。最后，我们显示出一类贪婪的分发策略，包括路由到负载最小或队列最短的策略，都不允许恒定的竞争比率。当工作到达是随机的时，泊松到达和iid工作大小，我们证明了随机路由和简单的门控静态速度缩放算法可以实现恒定的竞争比。