具有个体异构服务器的负载均衡
Load Balancing with Individually Heterogeneous Servers
浏览论文内容
中文总结 AI 辅助
研究具有个体异构服务器的系统中JSQ负载均衡策略的扩散极限，基于测度值过程开发框架统一分析，确定区分不同平局决胜规则性能的关键对象，找到渐近最优的平局决胜规则并通过耦合比较证明结果。
中文摘要 AI 辅助
本文分析了具有多个并行队列的系统中最短队列优先（JSQ）负载均衡策略的扩散极限，其中每个队列由具有潜在不同服务速率的服务器提供服务。先前对JSQ策略的渐近分析假设服务器的服务速率来自有限集，无法捕捉现代数据中心中服务速率可在单个服务器级别变化的情况。对于具有个体异构服务器的系统，跟踪每个可能服务速率的经验队列长度分布变得不可行。为克服这一困难，我们基于测度值过程开发了一个框架，并在一般的平局决胜规则下对所有基于JSQ的负载均衡策略进行统一分析。我们的分析确定了两个关键对象，它们在Halfin-Whitt区域区分不同平局决胜规则的性能，即描述空闲服务器如何在不同服务速率之间分配的极限公平过程和描述到达作业如何在不同服务速率之间分配的极限路由测度。除了刻画不同平局决胜规则的扩散极限外，我们还确定了渐近最小化扩散尺度化作业总数和扩散尺度化等待作业数稳态分布的平局决胜规则。在证明这些结果时，我们开发了基于关键耦合的样本路径比较，它提供了与策略无关的稳态界和下界，以证明渐近最优性。
英文摘要
In this paper, we analyze the diffusion limit of Join-the-Shortest-Queue (JSQ) load balancing policies for a system with many parallel queues where each queue is being served by a server with a potentially different service rate. Prior asymptotic analyses of JSQ policies assumed servers to have service rates from a finite set which does not capture scenarios in modern data centers where service rates can vary at the level of individual servers. For systems with individually heterogeneous servers, tracking the empirical queue length distribution for each possible service rate becomes infeasible. To overcome this difficulty, we develop a framework based on measure-valued processes and provide a unified analysis of all JSQ-based load balancing policies under general tie-breaking rules. Our analysis identifies two key objects that distinguish the performance of different tie-breaking rules in the Halfin--Whitt regime, namely, the limiting fairness process which describes how idle servers are distributed across different service rates and the limiting routing measure which describes how arriving jobs are assigned across different service rates. In addition to characterizing the diffusion limits for different tie-breaking rules, we identify the tie-breaking rule which asymptotically minimizes the steady-state distributions of the diffusion-scaled total number of jobs and the diffusion-scaled number of waiting jobs. In proving these results, we develop crucial coupling-based sample-path comparisons which provide both policy-independent steady-state bounds and lower bounds to prove asymptotic optimality.
