大规模系统中未知负载的学习与均衡
Learning and balancing unknown loads in large-scale systems
AI总结：
针对大规模服务器池中未知时变负载，提出内外环阈值学习与分配机制，证明其可使负载均衡，并发展非流体极限方法处理快速调整与 Coxian 服务时间。
摘要：
考虑一个由相同服务器池组成的系统，其中服务时间服从指数分布的任务以非齐次 Poisson 过程到达。准入阈值用于内部控制回路，将到达任务分配给服务器池；同时，在外部控制回路中，一种学习机制随时间调整该阈值，使其与系统未知的 offered load（提供负载）保持一致。在多服务器情形下，我们证明：在每个服务器池的归一化提供负载受到适当约束的时间区间内，该学习机制达到均衡，并由此带来负载的均衡分布。此外，当服务时间服从 Coxian 分布的任务以恒定速率到达，且阈值仅依据系统中的任务总数进行调整时，我们建立了类似结果。本文提出的新型证明技术不同于传统的流体极限分析，能够处理第一种学习机制由占用过程规模趋于零的偏移所触发的快速变化。此外，我们的方法无需依赖详细状态描述符的流体极限，即可刻画具有 Coxian 分布服务时间的系统的渐近行为。
英文摘要：
Consider a system of identical server pools where tasks with exponentially distributed service times arrive as a time-inhomogenenous Poisson process. An admission threshold is used in an inner control loop to assign incoming tasks to server pools while, in an outer control loop, a learning scheme adjusts this threshold over time to keep it aligned with the unknown offered load of the system. In a many-server regime, we prove that the learning scheme reaches an equilibrium along intervals of time where the normalized offered load per server pool is suitably bounded, and that this results in a balanced distribution of the load. Furthermore, we establish a similar result when tasks with Coxian distributed service times arrive at a constant rate and the threshold is adjusted using only the total number of tasks in the system. The novel proof technique developed in this paper, which differs from a traditional fluid limit analysis, allows to handle rapid variations of the first learning scheme, triggered by excursions of the occupancy process that have vanishing size. Moreover, our approach allows to characterize the asymptotic behavior of the system with Coxian distributed service times without relying on a fluid limit of a detailed state descriptor.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
