For a single server system, Shortest Remaining Processing Time (SRPT) is a size-based policy that is optimal in the sense that, regardless of the job size distribution, it minimizes the number of jobs in the system at each point in time. However, one reason that size-based policies such as SRPT are rarely deployed in practice is that the exact processing times of jobs are usually not known to the scheduler. In this paper, we will discuss scheduling a single-server system when accurate information about the jobs' processing times is not available. When the SRPT policy uses estimated processing times, the underestimation of large jobs can significantly degrade performance. When the estimation error distribution is known, the Gittins' Index policy is known to be optimal in minimizing the mean sojourn time in an M/G/1 queue. For a multiplicative error model, we first characterize the Gittins' Index policy for any estimation error distribution. We then use insights from the Gittins' Index policy to construct a simple heuristic, Size Estimate Hedging (SEH), that only uses jobs' estimated processing times for scheduling while exhibiting near-optimal performance.

中文翻译：

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具有估计作业大小的单服务器调度的近乎最佳策略

对于单个服务器系统，最短剩余处理时间（SRPT）是基于大小的策略，从某种意义上说，它是最佳的，无论作业大小分布如何，它都会使系统在每个时间点的作业数量最小化。但是，实际上很少部署基于大小的策略（如SRPT）的一个原因是，调度程序通常不知道作业的确切处理时间。在本文中，我们将讨论在无法获得有关作业处理时间的准确信息时调度单服务器系统。当SRPT策略使用估计的处理时间时，低估大型作业可能会严重降低性能。当估计误差分布已知时，已知Gittins索引策略在最小化M / G / 1队列中的平均停留时间方面是最佳的。对于乘法误差模型，我们首先对所有估计误差分布表征Gittins指数策略。然后，我们利用Gittins索引策略中的洞察力来构建简单的启发式规模估计对冲（SEH），它仅使用作业的估计处理时间进行调度，同时表现出近乎最佳的性能。