By George Kesidis

ISBN-10: 0470168684

ISBN-13: 9780470168684

This booklet is a quantitative textual content, which specializes in the genuine concerns in the back of severe modeling and research of communications networks. the writer covers all of the worthy arithmetic and concept to ensure that scholars to appreciate the instruments that optimize desktop networks this present day.

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

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

**Sample text**

Also suppose that a batch of ir samples X,, 1 5 i 5 n , is taken while the network is in a single state but that state is not known. Finally, suppose it is known that the probability that the network is in state 1 is 111 and that ~ 1 , = ~ E(X, 1 network state j ) for krlown values p,, J E ( 1 . 2 ) . Without loss of generality, take p~ < 112. We wish to infer from the sample data X , the state of the network. More specifically, we wish to minimize the probability of error P, in our decision. To do this, note that by the REVIEW OF ELEMENTARY PROBABILITY THEORY central limit theorem, given that the network is in state j , the sample mean is approximately normally distributed with mean p, and variance u:,,.

20 REVIEW OF ELEMENTARY PROBABILITY THEORY This is the MGF of a gamma (Erlang) distributed random variable with parameters X and n E Z+and PDF for z > 0. 8 Suppose that, for i = 1 , 2 , the random variable X i is Gaussian distributed with mean p, and variance a:. Also suppose that X I and X 2 are independent. l6), the MGF of X1 + X2 is + which we recognize as a Gaussian MGF. 6. 10 CONDITIONAL INDEPENDENCE the events A and C are said to be independent given B. , events A and C are (unconditionally) independent if P(A ( C ) = P(A).

Rrr) L E Z+. n E 1: = Z', rrj E I,,}. 2 A sample path of a Markov chain. ,. ,. 9)), let n = X ( s ) and let i be the number of transitions of X prior to the present time s . Clearly, the random variables i, n, and Ti (the last transition time prior to s) can be discerned from {X,, 0 5 r s) and can therefore be considered "given" as well. 2. Note that exp(q,,,x) depends on { X , , 0 5 r through n = X ( s ) . So, Ti+1 - s is exponentially distributed with parameter -q,,, and conditionally independent of s - Ti given {X,, 0 r s).

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

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