In a recent paper the $γ$-Boost scheduling policy was shown to minimize the tail of the response time distribution in a light-tailed M/G/1-queue. This policy schedules jobs using a boosted arrival time, defined as the arrival time of a job minus its boost, where the boost of a job depends on its exact job size. The $γ$-Boost policy can also be used when only partial job size information is available, such as the type of an incoming job. In such case the boost $b_i$ of a job depends solely on its type $i$ and $γ$-Boost was shown to optimize the tail among all boost policies, where a boost policy is fully determined by the $b_i$ values. In the partial information setting $γ$-Boost relies on two types of information: job types and arrival times. This paper focuses on the problem of minimizing the tail in a light-tailed M/G/1-queue in the partial job size information setting when the scheduler only makes use of the job types and {\it does not exploit arrival times}. Prior work showed that in case of $2$ job types the so-called Nudge-$M$ policy minimizes the tail in a large class of scheduling policies. In this paper we introduce the $γ$-CounterBoost policy in the partial information setting with $d \geq 2$ job types and prove that it minimizes the tail in an even broader class of scheduling policies called Contextual CounterBoost policies. The $γ$-CounterBoost policy reduces to the Nudge-$M$ policy in case of $d=2$ job types.

翻译：在近期一篇论文中，$γ$-Boost 调度策略被证明能在轻尾 M/G/1 队列中最小化响应时间分布的尾部。该策略使用提升到达时间（定义为作业到达时间减去其提升值）来调度作业，其中作业的提升值取决于其确切大小。当仅能获取部分作业大小信息（例如传入作业的类型）时，也可采用 $γ$-Boost 策略。在此情况下，作业的提升值 $b_i$ 仅取决于其类型 $i$，并且 $γ$-Boost 被证明能在所有提升策略中优化尾部性能，其中提升策略完全由 $b_i$ 值确定。在部分信息设定下，$γ$-Boost 依赖于两类信息：作业类型和到达时间。本文聚焦于在轻尾 M/G/1 队列中最小化尾部的问题，此时调度器仅利用作业类型信息而{\it 不利用到达时间}。先前研究表明，对于 $2$ 种作业类型的情况，所谓的 Nudge-$M$ 策略能在一大类调度策略中最小化尾部。本文针对 $d \geq 2$ 种作业类型的部分信息设定引入了 $γ$-CounterBoost 策略，并证明它能在更广泛的调度策略类（称为上下文 CounterBoost 策略）中最小化尾部。对于 $d=2$ 种作业类型的情况，$γ$-CounterBoost 策略退化为 Nudge-$M$ 策略。