By George Kesidis
This e-book is a quantitative textual content, which specializes in the genuine matters in the back of critical modeling and research of communications networks. the writer covers the entire important arithmetic and conception to ensure that scholars to appreciate the instruments that optimize computing device networks this day.
- Covers either classical (e.g. queueing concept) and smooth (e.g. pricing) elements of networking
- Integrates fabric on conversation networks with fabric on modeling/analyzing and designing such networks
- Includes an answer Manual
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Extra info for An introduction to communication network analysis
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:,,. An unbiased, consistent estimate of this variance is To determine the probability of decision error, we will condition on the state of the network: where p2 = 1 - p l .
1 A sample path of the Poisson process. 1. A natural question to ask about a stochastic process X is: What is the distribution of X ( t ) for some specified time t? In other words, what is the (one-dimensional) murginal distribution of the process? We will show that for the Poisson process, X ( t ) is Poisson distributed with mean At. 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.
19 times out of 20'7, the true mean p resides in the interval Consequently, this interval is called the 95% conjidence interval for p. STATISTICAL CONFIDENCE 27 Typically, in practice, the standard deviation a is also not known and mu,t also be estimated from the samples X k . The sample variance is The implicit assumption is that a more general form of central limit theorem holds when the sample standard deviation, is used instead of the true, but unknown, standard deviation a above 11941.