Performance guarantees in communication networks

Abstract

This book is divided into two unequal parts. The first part (230 pages) concerns worst-case performance guarantees in deterministic systems; the second part (140 pages) deals with stochastic systems, and might well have been called Performance estimation in communication networks. Apart fiom the fact that the two parts must needs study the same network elements, such as queues and multiplexers, they have little common ground.Chang explains that this book is the result of courses developed at National Tsing Hua University. If the style of the book reflects the style of the courses then the students should consider themselves lucky, for it is very clearly written. Examples are liberally scattered, and there is a well-paced parallel development of both the theory and the application.I will stress the clarity of his writing throughout. I was less impressed with the technical aspects of the book. There are numerous minor but irritating problems with typesetting, and some of the figures are poorly drawn.First, Part I: deterministic systems. Chapter 1 introduces the fundamental elements that are revisited throughout the book: traffic flows, leaky buckets, multiplexers, work-conserving links, output haf€ic flows, routers (i.e. elements that control an input flow according to some exogenous control process), and networks with or without feedback. It poses the typical problems: for example, given that a flow satisfies a leaky bucket constraint of certain parameters, what is the worst-case delay when the flow passes through a link of given service rate?The leaky bucket is a simple canonical example of a traflic regulator: more generally, one can ask how ttatjic can be regulated to meet any given constraint. Given a traffic flow that satisfies a leaky bucket constraint, one can derive worst-case bounds for the performance of a workconserving link: more generally, one can ask how to tind performance bounds for any given server, given input traffic which satisfies an arbitrary constraint. The rest of Part I answers these two questions.Chapter 2 introduces the abstract (min,+) algebra, which is the proper theoretical construct for answering the two questions above. This algebra allows one to express the behaviour of the network as alinear system. The bulk of this chapter, the most substantial chapter in the book, is concerned with describing the fundamental network elements using the (min,+) algebrathe traf€ic regulator and the server. Among the many examples studied are links with time-varying capacities, links with priorities, links with generalized processor sharing, links which control jitter, and networks with windowed flow control.This chapter also introduces the issue of cell versus packet models.The remaining four chapters of Part I extend these ideas in various ways. Chapter 3 deals with the specification of general traffic constraints, by developing the theory of projections in the (min,+) algebra. Chapter 4 deals with multiclass networks, by developing the theory of (min,+) matrix algebra. Chapter 5 deals with system...

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