超越缩放：重负载下双选择幂均值场模型的可计算误差界
Beyond Scaling: Calculable Error Bounds of the Power-of-Two-Choices Mean-Field Model in Heavy-Traffic
AI总结：
该研究针对双选择幂负载均衡算法，结合斯坦因方法与状态空间集中技术，推导重负载下均值场模型的渐近紧可计算误差界，通过数值和模拟验证其在中小规模系统中有效。
摘要：
本文提供了一种推导重负载下均值场模型可计算近似误差的方法，重点针对著名的负载均衡算法——双选择幂（Po2）。该方法结合了线性化均值场模型的斯坦因方法和基于几何尾界的状态空间集中（SSC）。具体而言，我们将状态空间划分为两个区域：均值场平衡附近的邻域及其补集。首先，我们利用尾界证明稳态概率超出该邻域的概率很小。接着，我们使用线性化均值场模型和斯坦因方法刻画生成元差异，该差异构成近似误差的主导项。从该主导项出发，我们能够得到渐近紧的可计算误差界，而非文献中多数结果那样的量级缩放结果。最后，我们将理论界与数值评估进行比较，以证明我们结果的有效性。我们注意到，模拟结果表明，该界甚至在小型系统（如仅含数百个服务器的系统）中也有效。
英文摘要：
This paper provides a recipe for deriving calculable approximation errors of mean-field models in heavy-traffic with the focus on the well-known load balancing algorithm---power-of-two-choices (Po2). The recipe combines Stein's method for linearized mean-field models and State Space Concentration (SSC) based on geometric tail bounds. In particular, we divide the state space into two regions, a neighborhood near the mean-field equilibrium and the complement of that. We first use a tail bound to show that the steady-state probability being outside the neighborhood is small. Then, we use a linearized mean-field model and Stein's method to characterize the generator difference, which provides the dominant term of the approximation error. From the dominant term, we are able to obtain an asymptotically-tight bound, a calculable bound, not order-wise scaling results like most results in the literature. Finally, we compare the theoretical bound with numerical evaluations to show the effectiveness of our results. We note that the simulation results show that the bound is valid even for small size systems such as a system with only hundred servers.
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。
