Processing Networks: Fluid Models and Stability (Hardcover)

This state-of-the-art account unifies material developed in journal articles over the last 35 years, with two central thrusts: It describes a broad class of system models that the authors call 'stochastic processing networks' (SPNs), which include queueing networks and bandwidth sharing networks as prominent special cases; and in that context it explains and illustrates a method for stability analysis based on fluid models. The central mathematical result is a theorem that can be paraphrased as follows: If the fluid model derived from an SPN is stable, then the SPN itself is stable. Two topics discussed in detail are (a) the derivation of fluid models by means of fluid limit analysis, and (b) stability analysis for fluid models using Lyapunov functions. With regard to applications, there are chapters devoted to max-weight and back-pressure control, proportionally fair resource allocation, data center operations, and flow management in packet networks. Geared toward researchers and graduate students in engineering and applied mathematics, especially in electrical engineering and computer science, this compact text gives readers full command of the methods.

這本最新的專書整合了過去35年來在期刊文章中發展的材料，主要有兩個核心內容：首先，它描述了一類被作者稱為「隨機處理網絡」（SPNs）的系統模型，其中包括排隊網絡和帶寬共享網絡作為重要特例；其次，在這個背景下，它解釋並演示了一種基於流體模型的穩定性分析方法。其中的核心數學結果是一個定理，可以概括為：如果從SPN中衍生的流體模型是穩定的，那麼SPN本身也是穩定的。詳細討論了兩個主題：（a）通過流體極限分析推導流體模型，以及（b）使用李亞普諾夫函數對流體模型進行穩定性分析。在應用方面，書中有章節專門討論最大權重和反壓控制、比例公平資源分配、數據中心運營以及分組網絡中的流量管理。這本緊湊的書籍針對工程和應用數學領域的研究人員和研究生，特別是電氣工程和計算機科學領域的讀者，使他們完全掌握這些方法。