Processing Networks
Fluid Models and Stability

The state of the art in fluid-based methods for stability analysis, giving researchers and graduate students command of the tools.

J. G. Dai (Author), J. Michael Harrison (Author)

9781108488891, Cambridge University Press

Hardback, published 15 October 2020

404 pages
23.4 x 15.6 x 2.3 cm, 0.73 kg

'This book provides an elegant and unified exposition of the general modeling framework of stochastic processing networks (SPNs) and associated theory of stability using fluid models. Much of this material was only previously available in dispersed journal articles. Adopting a continuous-time Markov chain description for SPNs, valid under fairly general assumptions on arrivals, service times and controls, enables a self-contained, accessible treatment. An array of interesting examples and extensions, especially involving applications for telecommunication and data networks, enliven the volume. This monograph will be an invaluable premier resource for graduate students and researchers in computer science, electrical and industrial engineering, applied mathematics and operations management interested in theory and applications of stochastic processing networks.' Ruth J. Williams, University of California, San Diego

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.

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. Multi-hop 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.

Subject Areas: Information technology: general issues [UB], Stochastics [PBWL], Probability & statistics [PBT], Operational research [KJT], Econometrics [KCH]