This book addresses the stochastic modeling of telecommunication
networks, introducing the main mathematical tools for that purpose,
such as Markov processes, real and spatial point processes and
stochastic recursions, and presenting a wide list of results on
stability, performances and comparison of systems.The authors
propose a comprehensive mathematical construction of the
foundations of stochastic network theory: Markov chains, continuous
time Markov chains are extensively studied using an original
martingale-based approach. A complete presentation of stochastic
recursions from an ergodic theoretical perspective is also
provided, as well as spatial point processes.Using these basic
tools, stability criteria, performance measures and comparison
principles are obtained for a wide class of models, from the
canonical M/M/1 and G/G/1 queues to more sophisticated systems,
including the current "hot topics" of spatial radio networking,
OFDMA and real-time networks.
Contents
1. Introduction.Part 1: Discrete-time Modeling2. Stochastic
Recursive Sequences.3. Markov Chains.4. Stationary Queues.5. The
M/GI/1 Queue.Part 2: Continuous-time Modeling6. Poisson Process.7.
Markov Process.8. Systems with Delay.9. Loss Systems.Part 3:
Spatial Modeling10. Spatial Point Processes.
General
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