使用串联服务器进行速度扩展

Speed Scaling with Multiple Servers Under A Sum Power Constraint

The problem of scheduling jobs and choosing their respective speeds with multiple servers under a sum power constraint to minimize the flow time + energy is considered. This problem is a generalization of the flow time minimization problem with multiple unit-speed servers, when jobs can be parallelized, however, with a sub-linear, concave speedup function $k^{1/α}, α>1$ when allocated $k$ servers, i.e., jobs experience diminishing returns from being allocated additional servers. When all jobs are available at time $0$, we show that a very simple algorithm EQUI, that processes all available job…

Speed Scaling On Parallel Servers with MapReduce Type Precedence Constraints

A multiple server setting is considered, where each server has tunable speed, and increasing the speed incurs an energy cost. Jobs arrive to a single queue, and each job has two types of sub-tasks, map and reduce, and a {\bf precedence} constraint among them: any reduce task of a job can only be processed once all the map tasks of the job have been completed. In addition to the scheduling problem, i.e., which task to execute on which server, with tunable speed, an additional decision variable is the choice of speed for each server, so as to minimize a linear combination of the sum of the flow …

Scheduling for Multi-Phase Parallelizable Jobs

With multiple identical unit speed servers, the online problem of scheduling jobs that migrate between two phases, limitedly parallelizable or completely sequential, and choosing their respective speeds to minimize the total flow time is considered. In the limited parallelizable regime, allocating $k$ servers to a job, the speed extracted is $k^{1/α}, α>1$, a sub-linear, concave speedup function, while in the sequential phase, a job can be processed by at most one server with a maximum speed of unity. A LCFS based algorithm is proposed for scheduling jobs which always assigns equal speed to th…

多服务器SRPT具有速度扩展功能，极具竞争力

Multiple Server SRPT with speed scaling is competitive

流行的最短剩余处理时间（SRPT）算法是否可以在多台服务器上实现恒定的竞争比，当服务器速度相对于流时间加能耗度量可调（速度缩放）时？这个问题已经有一段时间没有解决了，众所周知，在没有速度缩放的情况下会产生负面结果。本文的主要结果是表明，多服务器SRPT可以是恒定的竞争，与竞争比，只取决于服务器的功率使用功能，而不是对作业/服务器的数量或作业大小（不像当速度缩放是不允许的）。当所有的工作大小是统一的，我们表明，循环路由是最佳的，可以达到相同的竞争比，最有名的算法为单服务器的问题。最后，我们证明了一类贪婪的分派政策，包括政策，路线最少的负载或最短的队列，不承认一个恒定的竞争比。当工件到达是随机的，泊松到达和独立同分布。作业大小，我们表明，随机路由和一个简单的门静态速度缩放算法实现了恒定的竞争比。

网络速度缩放中的竞争比与网络无关

Stochastic Network Speed Scaling with Competitive Ratios Independent of the Network

针对网络速度缩放问题，提出一种通过凸规划路由并以固定速度运行服务器的算法，其竞争比仅依赖功率函数，对$P(s)=s^2$至多为黄金比例，并证明现有路由规则可能远非最优。

最长等待时间优先广播调度

Longest Wait First for Broadcast Scheduling

我们认为在线算法的广播调度。在基于拉取的广播模型中，在服务器处存在$n$单位大小的信息页面，并且对于页面的请求在线到达。当服务器传输一个页面$p$时，所有对该页面的未完成请求都将得到满足。最长等待优先算法（LWF）是一种自然的算法，已被证明具有良好的经验性能。在本文中，我们做了两个主要贡献的分析LWF和广播调度。\begin{itemize} \item We give an intuitive and easy to understand analysis of LWF which shows that it is $O(1/\eps^2)$-competitive for average flow-time with $(4+\eps)$ speed. Using a more involved analysis, we show that LWF is $O(1/\eps^3)$-competitive for average flow-time with $(3.4+ε)$ speed. \item We show that a natural extension of LWF is O(1)-speed O(1)-competitive for more general objective functions such as average delay-factor an…