| List of Figures Foreword 1.Queues: The Art of Modelling Part I Markovian Methods 2. Markov Chains and Queues in Discrete Time 1 Definition 2 Classification of States 3 Stationary Distributions 4 Restricted Markov Chains 5 Conditions for Positive Recurrence 6 The M/M/1 queue in discrete time 3. Homogeneous Markov Processes on Discrete State Spaces 1 Definition 2 Stationary Distribution 4. Markovian Queues in Continuous Time 1 The M/M/1 Queue 2 Skip-Free Markov Processes 3 The M/M/∞ Queue 4 The M/M/k Queue 5 The M/M/k/k Queue 6 The M/M/k/k+c/N Queue 5. Markovian Queueing Networks 1 Balance Equations and Reversibility Properties 2 Jackson and Gordon-Newell Networks 3 Symmetric Service Disciplines Part II Semi-Markovian Methods 6 Renewal theory 7 Markov renewal theory 8 Semi-Markovian queues Part III Matrix-Analytic Methods 9 Phase-type distributions 10 Markovian arrival processes 11 The G1/PH/1 queue 12 The BMAP/G/1 queue 13 Discrete time approaches 14 Spatial Markovian arrival processes 15 Appendix References Index |
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