Probabilistic models for computer networks: Tools and solved problems

✍ Scribed by José Alberto Hernández, Pablo Serrano

• Publisher: lulu.com
• Year: 2015
• Tongue: English
• Leaves: 199
• Category: Library

✦ Synopsis

Probabilistic models for computer networks: Tools and solved problems overviews the main probabilistic tools and theory used in the performance analysis and modelling of modern computer networks and communication systems. With over one hundred examples and solved problems, the reader will be introduced to Poisson processes, Markov chains and queueing theory in an intuitive manner. Important theorems and tools are followed by easy network-based examples, showing the reader their applicability in real scenarios. This book is highly recommended for students in their final years of a degree in engineering, and for Ph.D. students willing to strengthen their skills in the evaluation of network performance.

✦ Table of Contents

Probability review
Random variables
Probability Density Functions
Expectation and variance
Some useful PDFs
Conditional and joint probability
Conditional expectation
The Bayes' theorem
The Central Limit Theorem
Further problems
The exponential random variable
Definition
Simulation and estimation
The memoryless property
Minimum of several exponential random variables
Comparison of several exponential random variables
Further problems
The Poisson process
Counting processes
Stationary and independent increments
The Poisson process
Inter-arrival times of events
Waiting times
Conditional distribution of arrivals
Aggregation and sampling of Poisson processes
The theorem of Palm-Khintchine
Further problems
Discrete-Time Markov Chains
Introduction by example
States and transitions between states
Problem formulation
The Markov property and the Chapman-Kolmogorov equations
Sojourn times
Reachability and types of states
Steady-state analysis
First-passage times
Further problems
Continuous-Time Markov Chains
CTMCs by example
The infinitesimal generator
Definition and Chapman-Kolmogorov equations
The transient behaviour of a CTMC
Steady-state analysis and balance equations
First-passage times
Further problems
Classical queueing theory
Introduction by example
Definition and Kendall's notation
Little's theorem
The classical M/M/1 queue
The M/M/1/K queueing system
The M/M/c queueing system
Other non-classical Markovian queueing systems
Further problems
Open queueing networks
Introduction
Burke's theorem
Analysis of two M/M/1 queues in tandem
Types of networks and Jackson's theorem
Extended analysis for other open networks and Kleinrock's approximation
Further problems
Index