Stochastic Modeling and Analysis of Telecoms Networks

Overview

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 ...

See more details below
Hardcover
$172.38
BN.com price
(Save 6%)$185.00 List Price
Other sellers (Hardcover)
  • All (7) from $147.38   
  • New (6) from $147.38   
  • Used (1) from $172.37   

Overview

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.

Read More Show Less

Product Details

  • ISBN-13: 9781848212381
  • Publisher: Wiley
  • Publication date: 3/27/2012
  • Series: ISTE Series , #513
  • Edition number: 1
  • Product dimensions: 6.20 (w) x 9.30 (h) x 1.10 (d)

Table of Contents

Preface ix

Chapter 1. Introduction 1

1.1. Traffic, load, Erlang, etc1

1.2. Notations and nomenclature 7

1.3. Lindley and Bene?s 10

1.4. Notes and comments 18

PART 1: DISCRETE-TIME MODELING 21

Chapter 2. Stochastic Recursive Sequences 23

2.1. Canonical space 24

2.2. Loynes’s scheme 30

2.3. Coupling 34

2.4. Comparison of stochastic recursive sequences 40

2.5. Notes and comments 43

Chapter 3. Markov Chains 45

3.1. Definition and examples 45

3.2. Strong Markov property 49

3.3. Classification of states 52

3.4. Invariant measures and invariant probability 60

3.5. Effective calculation of the invariant probability 75

3.6. Problems 77

3.7. Notes and comments 80

Chapter 4. Stationary Queues 83

4.1. Single server queues 84

4.2. Processor sharing queue 104

4.3. Parallel queues 106

4.4. The queue with S servers 117

4.5. Infinite servers queue 124

4.6. Queues with impatient customers 127

4.7. Notes and comments 146

Chapter 5. The M/GI/1 Queue 149

5.1. The number of customers in the queue 149

5.2. Pollacek-Khinchin formulas 153

5.3. Sojourn time 156

5.4. Tail distribution of the waiting time 158

5.5. Busy periods 160

PART 2: CONTINUOUS-TIME MODELING 167

Chapter 6. Poisson Process 169

6.1. Definitions 170

6.2. Properties 176

6.3. Discrete analog: the Bernoulli process 181

6.4. Simulation of the Poisson process 183

6.5. Non-homogeneous Poisson process 185

6.6. Cox processes 189

6.7. Problems 189

6.8. Notes and comments 191

Chapter 7. Markov Process 193

7.1. Preliminaries 193

7.2. Pathwise construction 195

7.3. Markovian semi-group and infinitesimal generator 199

7.4. Martingale problem 215

7.5. Reversibility and applications 220

7.6. Markov Modulated Poisson Processes 226

7.7. Problems 232

7.8. Notes and comments 234

Chapter 8. Systems with Delay 237

8.1. Little’s formula 237

8.2. Single server queue 241

8.3. Multiple server queue 245

8.4. Processor sharing queue 252

8.5. The M/M/∞ queue 253

8.6. The departure process 254

8.7. Queuing networks 255

8.8. Problems 265

8.9. Notes and comments 268

Chapter 9. Loss Systems 271

9.1. General 271

9.2. Erlang model 274

9.3. The M/M/1/1 + C queue 276

9.4. The “trunk” effect 279

9.5. Engset model 280

9.6. IPP/M/S/S queue 281

9.7. Generalized Erlang models 285

9.8. Hierarchical networks 289

9.9. A model with balking 294

9.10. A call center with impatient customers 301

9.11. Problems 303

9.12. Notes and comments 304

PART 3: SPATIAL MODELING 307

Chapter 10. Spatial Point Processes 309

10.1. Preliminary 309

10.2. Stochastic geometry 310

10.3. Poisson process 311

10.4. Stochastic analysis 326

10.5. Problems 336

10.6. Notes and comments 337

Appendix A. Mathematical Toolbox 339

A.1. Probability spaces and processes 339

A.2. Conditional expectation 347

A.3. Vector spaces and orders 352

A.4. Bounded variation processes 356

A.5. Martingales 363

A.6. Laplace transform 378

A.7. Notes and comments 379

Bibliography 381

Index 385

Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star

(0)

4 Star

(0)

3 Star

(0)

2 Star

(0)

1 Star

(0)

Your Rating:

Your Name: Create a Pen Name or

Barnes & Noble.com Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & Noble.com that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & Noble.com does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at BN.com or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation

Reminder:

  • - By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
  • - Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on BN.com. It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

 
Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)