Book description
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 Modeling
2.
Stochastic Recursive Sequences.
3. Markov Chains.
4.
Stationary Queues.
5. The M/GI/1 Queue.
Part 2:
Continuous-time Modeling
6. Poisson Process.
7. Markov
Process.
8. Systems with Delay.
9. Loss Systems.
Part
3: Spatial Modeling
10. Spatial Point Processes.
