大系统中减少延迟的作业并行模型
A Model of Job Parallelism for Latency Reduction in Large-Scale Systems
摘要：
在多个处理核心并行处理计算密集型作业在许多现实世界的应用中是必不可少的。在本文中，我们考虑了一个理想化的模型，作业并行，其中一个作业可以同时由$d$不同的服务器。当$d$服务器完成的工作总量等于作业大小时，就认为作业已完成。研究了并行性对工件平均延迟的影响。具体来说，我们分析了一个系统组成的$n$并行处理器共享服务器中的作业到达根据泊松过程的速率$n λ$（$λ<1$）和每个作业带来了一个指数分布的单位平均工作量。作业到达后，会随机均匀地选择$d$服务器，并同时加入所有选定的服务器。我们通过平均场分析表明，对于固定的$d \geq 2$和大的$n$，服务器的平均占用率是$O(\log (1/(1-λ)))$作为$λ\to 1$相比，$d=1$的$O(1/(1-λ))$平均占用率。因此，我们得到了一个指数级的减少，通过并行作业的响应时间。我们取得了重大进展，严格证明平均场分析。
英文摘要：
Processing computation-intensive jobs at multiple processing cores in parallel is essential in many real-world applications. In this paper, we consider an idealised model for job parallelism in which a job can be served simultaneously by $d$ distinct servers. The job is considered complete when the total amount of work done on it by the $d$ servers equals its size. We study the effect of parallelism on the average delay of jobs. Specifically, we analyze a system consisting of $n$ parallel processor sharing servers in which jobs arrive according to a Poisson process of rate $n λ$ ($λ<1$) and each job brings an exponentially distributed amount of work with unit mean. Upon arrival, a job selects $d$ servers uniformly at random and joins all the chosen servers simultaneously. We show by a mean-field analysis that, for fixed $d \geq 2$ and large $n$, the average occupancy of servers is $O(\log (1/(1-λ)))$ as $λ\to 1$ in comparison to $O(1/(1-λ))$ average occupancy for $d=1$. Thus, we obtain an exponential reduction in the response time of jobs through parallelism. We make significant progress towards rigorously justifying the mean-field analysis.
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