Performance modelling of communication networks and computer architectures

Abstract

(Each chapter concludes with Exercises.) Preface. 1. Essentials of Probability Theory. Sample space, events and probability. Conditional probability. Independence. 2. Random Variables and Distributions. Probability distribution functions. Discrete random variable. Continuous random variables. Joint random variables. Conditional distributions. Independence and sums. 3. Expected Values and Moments. Expectation. Generating functions and transforms. Asymptotic properties. 4. Stochastic Processes. Random walks. Markov chains. Markov processes. Reversibility. Renewal theory. 5. Queues. Simple Markovian queues. The M/G/1 queue. The G/G/1 queue. 6. Single Class Queueing Networks. Introduction. Open queueing networks. Closed queueing networks. Mean value analysis. Performance measures for the state-dependent case. The flow equivalent server method. 7. Multi-class Queueing Networks. Service time distributions. Types of service centre. Multi-class traffic model. BCMP theorem. Properties and extensions of BCMP networks. Computational algorithms for BCMP networks. Priority disciplines. Quasi-reversibility. 8. Approximate Methods. Decomposition. Fixed point methods. Diffusion approximation. Maximum entropy methods. 9. Time Delays. Time delays in the single server queue. Time delays in networks of queues. Inversion of the Laplace transforms. Approximate methods. 10. Blocking in Queueing Networks. Introduction. Types of blocking. Two finite queues in a closed network. Aggregating Markovian states. BAS blocking. BBS blocking. Repetitive service blocking. 11. Switching Network Models. Telephone networks. Interconnection networks for parallel processing systems. Models of the full crossbar switch. Multi-stage interconnection networks. Models of synchronous MINS. Models of asynchronous MINS. Interconnection networks in a queueing model. Appendix: Outline Solutions. References. Index. 0201544199T04062001

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