This book addresses the stochastic modeling of telecommunicationnetworks, introducing the main mathematical tools for that purpose, such as Markov processes, real and spatial point processes andstochastic recursions, and presenting a wide list of results onstability, performances and comparison of systems.
The authors propose a comprehensive mathematical construction ofthe foundations of stochastic network theory: Markov chains, continuous time Markov chains are extensively studied using anoriginal martingale-based approach. A complete presentation ofstochastic recursions from an ergodic theoretical perspective isalso provided, as well as spatial point processes.
Using these basic tools, stability criteria, performance measuresand comparison principles are obtained for a wide class of models, from the canonical M/M/1 and G/G/1 queues to more sophisticatedsystems, including the current „hot topics“ of spatialradio 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.
The authors propose a comprehensive mathematical construction ofthe foundations of stochastic network theory: Markov chains, continuous time Markov chains are extensively studied using anoriginal martingale-based approach. A complete presentation ofstochastic recursions from an ergodic theoretical perspective isalso provided, as well as spatial point processes.
Using these basic tools, stability criteria, performance measuresand comparison principles are obtained for a wide class of models, from the canonical M/M/1 and G/G/1 queues to more sophisticatedsystems, including the current „hot topics“ of spatialradio 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.
