Heavy Traffic Limits for Join-the-Shortest-Estimated-Queue Policy Using Delayed Information
Heavy Traffic Limits for Join-the-Shortest-Estimated-Queue Policy Using Delayed Information
复制标题
使用延迟信息的加入最短估计队列策略的大流量限制
DOI：
10.1287/moor.2020.1056
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
David Lipshutz
中科院分区：
文献类型：
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作者：
R. Atar;David Lipshutz
我们考虑了一个并行队列网络的负载平衡问题，其中关于队列状态的信息是受延迟影响的。在此设置中，采用在应用于队列的当前状态时表现良好的路由策略在应用于队列的延迟状态时可能表现得相当差。将此视为部分观察下的控制问题，我们建议使用当前队列长度的估计作为加入最短队列策略的输入。对于一类一般的估计方案，在繁忙的交通条件下，我们证明了扩散尺度过程收敛到一个所谓的扩散模型的解，在这个模型中，朝着这个目标的重要一步是确定估计的队长经历状态空间崩溃。在某些情况下，我们的扩散模型是由一个新的带反射的随机时滞方程给出的，其中Skorokhod边界项随时滞出现。我们用自然估计方案的例子来说明我们的结果，讨论了它们的可实现性，并用模拟比较了它们的相对性能。
We consider a load-balancing problem for a network of parallel queues in which information on the state of the queues is subject to a delay. In this setting, adopting a routing policy that performs well when applied to the current state of the queues can perform quite poorly when applied to the delayed state of the queues. Viewing this as a problem of control under partial observations, we propose using an estimate of the current queue lengths as the input to the join-the-shortest-queue policy. For a general class of estimation schemes, under heavy traffic conditions, we prove convergence of the diffusion-scaled process to a solution of a so-called diffusion model, in which an important step toward this goal establishes that the estimated queue lengths undergo state-space collapse. In some cases, our diffusion model is given by a novel stochastic delay equation with reflection, in which the Skorokhod boundary term appears with delay. We illustrate our results with examples of natural estimation schemes, discuss their implementability, and compare their relative performance using simulations.