By George Kesidis

ISBN-10: 0470168684

ISBN-13: 9780470168684

This publication is a quantitative textual content, which specializes in the true concerns at the back of severe modeling and research of communications networks. the writer covers the entire invaluable arithmetic and thought to ensure that scholars to appreciate the instruments that optimize desktop networks this present day.

- Covers either classical (e.g. queueing thought) and sleek (e.g. pricing) facets of networking
- Integrates fabric on conversation networks with fabric on modeling/analyzing and designing such networks
- Includes an answer Manual

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**Additional info for An introduction to communication network analysis**

**Sample text**

X 2 , X3. . , o2 var(X) E(X - EX)' < x. STATISTICAL CONFIDENCE where X -- X , and (T > 0. Finally. suppose that the mean exists and is finite. i t . p E = XI EX < x. Define the cumulative sum S,, for r? + X L + . . + X,,. > 1 and note again that ES,, = np and var(S,) = ng2. Thus, for all n . 1. For all 2, E R, That is. converges in distribution to a standard (mean 0 and variance I ) Gaussian. 16 at the end o f this chapter. 2 Confidence intervals Suppose that 77 identically distributed samples X I , X2.

Q, , < 0. That is, a Markov chain is said to enter state n at time T and subsequently visit state n for S seconds if X ( T - ) # n, X ( t ) = n for all T 5 t < S T, and X ( S T ) # n. Also, define the assumed finite set of states + + to which a transition is possible directly from n. , r 0 for all rn $ I U {n). Now let T,be the time of the zth state transition with To constant on intervals [TZp1. , ~ ( 0is) the initial distribution of the stochastic process X ic so CONTINUOUS-TIME. TIME-HOMOGENEOUS MARKOV PROCESSES WITH COUNTABLE STATE SPACE 43 An alternative description of how a Markov chain X with t m e doma~nE' make\ from state to state will now be given.

INDEPENDENT RANDOM VARIABLES To this end. y, = f l f2. Thus, the CDF of the sum is Exchanging the first integral on the right-hand side with a derivative with respect to z , the PDF of X 1 X 2 is + of f l and f 2 which is denoted f = f l * f 2 . Thus, f is the con~~olution In this context. moment generating functions can be used to simplify calculations. Let the MGF of X , be + Note that rn, is basically the (bilateral) Laplace transform [164] of ,f,. The MGF of XI X 2 is where the last equation holds because of the independence of X I and X 2 .

### An introduction to communication network analysis by George Kesidis

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