We consider a large-scale service system where incoming tasks have to be instantaneously dispatched to one out of many parallel server pools. The dispatcher uses a threshold for balancing the load and keeping the maximum number of concurrent tasks across server pools low. We demonstrate that such a policy is optimal on the fluid and diffusion scales for a suitable threshold value, while only involving a small communication overhead. In order to set the threshold optimally, it is important, however, to learn the load of the system, which may be uncertain or even time-varying. For that purpose, we design a control rule for tuning the threshold in an online manner. We provide conditions which guarantee that this adaptive threshold settles at the optimal value, along with estimates for the time until this happens.

中文翻译：

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基于自学阈值的负载均衡

我们考虑一个大型服务系统，其中传入的任务必须立即分派到许多并行服务器池中的一个。调度程序使用阈值来平衡负载并将跨服务器池的最大并发任务数保持在较低水平。我们证明了这样的策略在流体和扩散尺度上对于合适的阈值是最佳的，而只涉及很小的通信开销。然而，为了优化设置阈值，了解系统的负载很重要，这可能是不确定的，甚至是随时间变化的。为此，我们设计了一个控制规则，以在线方式调整阈值。我们提供了保证该自适应阈值稳定在最佳值的条件，以及发生这种情况之前的时间估计。