Performance Modelling of Communication Networks and Computer Architectures (International Computer S, 1st edition
Authors: Peter G. Harrison, Naresh M. Patel
Venue:  (1992)

From the Book:PREFACE: Communication systems are becoming ever more complex as technological advances permit ever faster transmission over links of ever greater capacity. In telecommunications networks the information transmitted is generally in binary digital form, representing computer data, voice or video. Considerable resources and effort will be expended in coming years to allow interactive transcontinental and intercontinental collaboration through the sharing of information of these types. This will require the transmission of vast quantities of data in fractions of a second, particularly in the case of video where very many bits are needed to define each screen and many screens must be transmitted every second. Communication networks are organized hierarchically as Local Area Networks (LANs) for local communication, e.g. within a building, Metropolitan Area Networks (MANs), which contain georgraphically close nodes, e.g. within a city, and Wide Area Networks (WANs) for communication over longer distances up to thousands of miles. There may also be other levels in the hierarchy, for example using satellites. Communication between any two nodes in such a system may involve many intermediate nodes and meet contention from diverse traffic from many sources. The number of nodes in a network may run into thousands: they have diverse characteristics ranging from a local workstation to a gateway between sub-networks, and the links between nodes may also be of different types, e.g. Ethernet, radio, fibre-optic. The design of efficient communication systems, giving at least a minimum specified level of performance, is therefore of paramount importance. Similarly, the world'sinsatiableappetite for high performance computing, supported by enormous advances in VLSI technology, has led to the development of a range of parallel computer architectures. These may involve a small of a range of parallel computer architectures. These may involve a small or large number of processors cooperating to solve a problem in parallel, based on the partitioning of some algorithm. As with telecommunications systems, parallel computers can be extremely complex and again involve thousands of nodes which can be 'active' processors or 'passive' resources, such as memory modules or communication paths. Indeed, in a large parallel architecture, the central components are the interconnection networks (INs) between collections of nodes. These INs must be high speed and have high bandwidth, for example to facilitate fast memory accesses. Once again, the design of efficient parallel computer architectures is demanding of the utmost importance. Performance models of computer and communication systems have been studied for many years with a view to assisting optimization and guiding the design of new generations. To date, however, they have seen only limited use in practice: it has so far been reasonably effective to tune an optimization or new design using educated guesses and experimentation with existing similar systems--even though this process is often unreliable and requires expensive, exclusive use of the resources. Now, however, with dramatic increase in complexity associated with the systems of the future, such intuitive understanding of system behaviour is much harder to acquire. Hence formal models of performance are necessary for efficient and reliable design and/or optimization. There are two main types of model available for this purpose: simulation and stochastic, the latter also often being referred to as analytic. Ideally, simulation should be used in combination with the analytical approach. This book considers stochastic (queueing-based) models and is intended as a course text for computer science courses at the advanced undergraduate and Masters degree levels, as a reference for researchers in the field and as a handbook for professionals in the business of performance evaluation and design of computer architectures. It may also be relevant to courses in electrical engineering, operations research and applied probability, especially if these focus on telecommunications or computer applications. The emphasis is on modelling contention systems, which are mainly represented by queues or networks of queues. This provides a good abstract description of many physical systems, but there are other aspects of telecommunication networks which are not considered in any detail, for example network protocols and congestion control strategies. Nevertheless, the mathematical techniques described can be applied to such problems and there are a host of references in the literature that can do just this. The book has been written so as to be as self-contained as possible and the prerequisites for reading it are pre-university mathematics and some informal 'feel' for probability, for example as might be acquired in playing 'games of chance'. The material is presented in a rigorous way, appropriate to an academic course of lectures, but is structured so that the less mathematically sophisticated reader can often omit technical details yet still gain a thorough informal understanding. The intention is that the reader should rarely have to consult other texts to fill in the details of any model considered. For example, Chapter 4 covers the main properties of stochastic processes that form the foundations of most analytic models of computer/communication systems. At the same time, the book does not claim to be encyclopaedic and certain model types are not considered, for example those using Petri-nets. The book is organized into 11 chapters, as outlined below, which interlink in various ways to provide a number of ways of reading (depending also on the degree of mathematical sophistication of the reader) and possible course structures. The first chapter gives an introduction to the conventional notion of probability and can be regarded in two ways: as a summary of the formal, axiomatic definition or at an intuitive level. Random variables are introduced in Chapter 2 and the main results on expectations--which can provide an alternative formalism for probability theory--are presented in Chapter 3. Chapter 4 is devoted to stochastic processes and may be used as a 'built-in' reference to stochastic processes and may be used as a 'built-in' reference for basic properties used in later chapters. Markov processes and renewal processes are considered in some depth and the notion of reversibility, a powerful technique in queueing theory, is introduced. In fact, the mathematically experienced reader with a background in probability may skip all of the first four chapters on a first reading, using them only when referred to later if necessary. Chapter 5 considers single queues and their application to computer/communication systems; networks of queues are studied in Chapter 6. This analysis is extended to queueing networks with multiple classes of customers in Chapter 7 and the now ell-known algorithms for solving such 'product form' networks are derived. Up to this point, the results obtained for queues and networks of queues are exact, but in real problems, networks are often too complex for their solutions to be numerically tractable and the assumptions required for solutions rarely hold. Chapter 8 therefore considers approximate, more efficient, methods of solution. In Chapter 9, distributions of time delays in networks are considered. This has become an important issue recently with the development of transaction processing systems for which benchmareks specifying quantiles for response times have been defined. Chapter 10 is devoted to blocking, which is another vital phenomenon which cannot be modelled by a product form network. Blocking occurs when the service of one queue is inhitited by another queue (of finite capacity) being full. This situation occurs in open queueing systems which contain finite capacity queues, for example in a communication network of nodes with finite buffers. Finally, the techniques described in a communication network of nodes with finite buffers. Finally, the techniques describes in the book are applied to model the performance of interconnetion networks which areise in parallel computer systems and in telephone exhanges. Each chapter is supported by a set of exercises which serve to test the understanding of the reader, give practice for written examinations, elaborate on certain issues arising in the chapter and help a practitioner apply modelling techniques to real problems. Selected solutions are provided for about two thirds of the exercises at the end of the book. The exercises are given ratings, following Donald Knuth's notation, as follows: 00 = very easy (can be done immediately) 10 = simple exercises (up to two minutes) 20 = moderately difficult (up to 20 minutes) 30 = more difficult (up to an hour) 40 = very difficult (no time limit) There are several courses that could be based upon this book, ranging from performance analysis in computer science to telecommunications to stochastic processes and their applications in these areas. Two courses on perfrormance modelling are proposed--one introductory, the other advanced--and the later chapters of the book could provide material to cover the performance aspects of courses on distributed systems and (parallel) computer architecture. The more theoretical material could be used as the main test for a course on stochastic processes, but would most likely be supported by other books unless this course were slanted toward communication and computing applications. Acknowledgements This book is based partly on lectures given by Peter Harrison at Imperial College over several years, supported by Naresh Patel until he joined Tandem Computers Inc., in 1990. We therefore thank the students of these lectures for pointing out the deficiencies of earlier expositions, either directly or indirectly. Many of the authors' own results described in the later chapters were obtained the the course of a research project supported by the Science and Engineering Research Council of the United Kingdom under grant number GR/E/54986. More specifically, it is a pleasure to thank Tony Field for his enthusiasm and suggestions during our collaboration over several years and Edgwige Pitel for her scrupulous comments on parts of the manuscript.