Processing Networks

Fluid Models and Stability

J. G. Dai, J. Michael Harrison

• Publisher: Cambridge University Press
• Year: 2020
• Print ISBN: 9781108488891
• eBook ISBN: 9781108805995
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

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.

Table of contents

• Cover
• Half-title
• Title page
• Copyright information
• Dedication
• Contents
• Website
• Preface
• Guide to Notation and Terminology
• 1 Introduction
• 2 Stochastic Processing Networks
• 3 Markov Representations
• 4 Extensions and Complements
• 5 Is Stability Achievable?
• 6 Fluid Limits, Fluid Equations, and Positive Recurrence
• 7 Fluid Equations That Characterize Specific Policies
• 8 Proving Fluid Model Stability Using Lyapunov Functions
• 9 Max-Weight and Back-Pressure Control
• 10 Proportionally Fair Resource Allocation
• 11 Task Allocation in Server Farms
• 12 Multihop Packet Networks
• Appendix A Selected Topics in Real Analysis
• Appendix B Selected Topics in Probability
• Appendix C Discrete-Time Markov Chains
• Appendix D Continuous-Time Markov Chains and Phase-Type Distributions
• Appendix E Markovian Arrival Processes
• Appendix F Convergent Square Matrices
• References
• Index