重流量下广义交换机中的最优调度
Optimal Scheduling in Generalized Switch in Heavy Traffic
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中文总结 AI 辅助
针对广义交换机中已知作业持续时间的最优调度问题，提出最小均衡桶（SEB）策略，通过基于持续时间的桶和均衡服务结构同时优先小作业并减少资源浪费，实现重流量下最优平均响应时间。
中文摘要 AI 辅助
广义交换机是一个高度灵活的排队模型，涵盖了多类别、多服务器和多资源排队系统以及各种随机网络。尽管针对该模型已经开发了许多调度策略，但它们几乎全部针对未知作业持续时间的情形。如何在广义交换机中最优地利用已知的作业持续时间仍然是一个未解决的问题。此外，在两种情形下，优化平均响应时间也仍然是一个未解决的问题。我们首次提出了一种策略，即我们的最小均衡桶（SEB）策略，以保证广义交换机中重流量最优的平均响应时间。设计最优调度策略的关键挑战在于，我们必须同时优先处理小作业并最小化资源浪费，同时还要符合广义交换机的服务选项。SEB通过将作业分组到基于持续时间的桶中，并强制执行一种“均衡”的服务结构来克服这一挑战，该结构保持每个桶的平衡，同时仍然优先处理最小的作业。我们证明了SEB的重流量最优性。仿真进一步证实了受SEB启发的启发式算法的有效性。
英文摘要
The generalized switch is a highly flexible queueing model, covering multiclass, multiserver, and multiresource queueing systems as well as a wide variety of stochastic networks. Although many scheduling policies have been developed for this model, they almost entirely address unknown job duration settings. How to optimally use known job durations in the generalized switch has remained open. Moreover, optimizing mean response time remains open in both settings. We introduce the first policy to guarantee heavy-traffic optimal mean response time in the generalized switch, our Smallest Equalizing Bucket (SEB) policy. The key challenge in designing an optimal scheduling policy is that we must simultaneously prioritize small jobs and also minimize resource waste, all while fitting within the generalized switch's service options. SEB overcomes this challenge by grouping jobs into duration-based buckets and enforcing an "equalizing" service structure that keeps each bucket balanced while still prioritizing the smallest jobs. We prove SEB's heavy-traffic optimality. Simulations further confirm the effectiveness of SEB-inspired heuristics.
