Stochastic Modeling and Analysis of Telecoms Networks

Table of Contents

 

 

 

Preface

 

Chapter 1. Introduction

1.1. Traffic, load, Erlang, etc.

1.2. Notations and nomenclature

1.3. Lindley and Beneš

1.4. Notes and comments

 

PART 1: DISCRETE-TIME MODELING

 

Chapter 2. Stochastic Recursive Sequences

2.1. Canonical space

2.2. Loynes’s scheme

2.3. Coupling

2.4. Comparison of stochastic recursive sequences

2.5. Notes and comments

 

Chapter 3. Markov Chains

3.1. Definition and examples

3.2. Strong Markov property

3.3. Classification of states

3.4. Invariant measures and invariant probability

3.5. Effective calculation of the invariant probability

3.6. Problems

3.7. Notes and comments

 

Chapter 4. Stationary Queues

4.1. Single server queues

4.2. Processor sharing queue

4.3. Parallel queues

4.4. The queue with S servers

4.5. Infinite servers queue

4.6. Queues with impatient customers

4.7. Notes and comments

 

Chapter 5. The M/GI/1 Queue

5.1. The number of customers in the queue

5.2. Pollacek-Khinchin formulas

5.3. Sojourn time

5.4. Tail distribution of the waiting time

5.5. Busy periods

 

PART 2: CONTINUOUS-TIME MODELING

 

Chapter 6. Poisson Process

6.1. Definitions

6.2. Properties

6.3. Discrete analog: the Bernoulli process

6.4. Simulation of the Poisson process

6.5. Non-homogeneous Poisson process

6.6. Cox processes

6.7. Problems

6.8. Notes and comments

 

Chapter 7. Markov Process

7.1. Preliminaries

7.2. Pathwise construction

7.3. Markovian semi-group and infinitesimal generator

7.4. Martingale problem

7.5. Reversibility and applications ...