Certification

An Introduction to Communication Network Analysis by George Kesidis

By George Kesidis

This e-book is a quantitative textual content, which specializes in the genuine matters at the back of critical modeling and research of communications networks. the writer covers the entire important arithmetic and thought to ensure that scholars to appreciate the instruments that optimize machine networks at the present time.

  • Covers either classical (e.g. queueing thought) and glossy (e.g. pricing) points of networking
  • Integrates fabric on communique networks with fabric on modeling/analyzing and designing such networks
  • Includes an answer Manual

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Extra resources for An Introduction to Communication Network Analysis

Example text

CHAPTER 2 MARKOV CHAINS A stochastic (or random) process is a collection of random variables indexed by a parameter in a domain. In this book, this parameter will be interpreted as time (stochastic processes describing images can be indexed by more than one spatial parameter and those describing video will have joint spatial and temporal indexes). , { X ( t ) ( t E Z+) is a discrete time stochastic process when X ( t ) is a random variable for all t E Z+. If the time parameter t takes values over R or PPf (or any real interval), the stocha5tic process is said to be continuous time.

For this reason, X is sometimes called the intensity (or "mean rate" or just "rate") of the Poisson process X . 1. X ( t ) is Poisson distributed with parameter At. 18). By integrating by parts, we get - Lrn ( ~ t ) ~ e - ~ ~:;X;i + i! e dz . After successively integrating by parts in this manner, we get 2 P ( X ( t ) I, Z ) = i! -At + . + ( w e - * ' l! + La he-h~ dz MARKOV CHAINS Now note that { X ( t )= i ) and { X ( t ) I i - 1) are disjoint events and { X ( t )= i ) U { X ( t )I i - 1) = { X ( t ) I i).

These properties are fundamental to the subsequent construction of Markov chains. 1. ). This is the memoryless property and its simple proof is left as an exercise. So, in this sense, given X > y, the lifetime has "forgotten" that X > y. 3 at the end of the chapter) and only geometrically distributed random variables have this property among all discretely distributed random variables. Now suppose that X I and X2 are independent and exponentially distributed random variables with parameters XI and X2, respectively.

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