随机处理与匹配网络的变换方法
Transform Method for Stochastic Processing and Matching Networks
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中文总结 AI 辅助
研究现代服务系统拥堵问题中随机处理与匹配网络的稳态分析，提出变换方法，通过直接处理预极限系统克服技术障碍，得出显式函数方程，提供非渐近性能保证，综述其理论进展及实际相关性，为系统设计控制提供有力分析替代。
中文摘要 AI 辅助
现代服务系统，如云数据中心和网约车平台，在大规模运行时面临拥堵挑战。传统运筹学方法通过建模为复杂随机过程分析，存在技术难点且对有限实际系统规模指导有限。本文介绍的变换方法是用于随机处理与匹配网络稳态分析的统一且易处理框架。它直接处理预极限系统克服收敛技术障碍，利用指数测试函数零漂移属性得出队列长度分布变换的显式函数方程，提供非渐近性能保证。自2020年用于数据中心网络负载平衡后不断扩展，本文综述其理论进展并展示在多领域的实际相关性，该方法为系统设计和控制提供了有力分析替代方案。
英文摘要
Modern service systems, ranging from cloud data centers and ride-hailing platforms to healthcare facilities, operate at massive scales where it is important to handle congestion. Queueing theory is used to understand the delay and queue length behavior in these systems. Except in simple queues, it is not possible to obtain a closed form solution for the quantities of interest, and so, one studies the system in certain asymptotic regimes such as the heavy traffic. The transform method, presented in this tutorial, is a framework to understand the steady-state behavior of Stochastic Processing and Matching Networks (SPNs/SMNs). By exploiting the zero-drift property of exponential test functions, the method derives explicit functional equations (acting as a proxy for global balance equations) for the transforms (such as moment-generating functions) of queue-length distributions. These functional equations can be used to either characterize the exact behavior of the system in an asymptotic regime or to obtain non-asymptotic performance bounds on the mean, higher order moments, or tail bounds on the queue lengths. Since its introduction for load-balancing in data center networks, the transform method, as a framework, has been extended to handle various features that arise in different systems, including customer abandonment, state-dependent arrivals, Markov-modulated arrivals, large-system scale, and multi-dimensional networks with multiple bottlenecks. This tutorial presents an overview of the transform method starting with the simplest setting viz., a single server queue. The transform method is introduced as a three step procedure. We then illustrate how the method can be adapted within this three-step framework to handle the aforementioned features.
