By George Kesidis

This booklet 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 valuable arithmetic and idea to ensure that scholars to appreciate the instruments that optimize laptop networks at the present time.

- Covers either classical (e.g. queueing concept) and smooth (e.g. pricing) facets of networking
- Integrates fabric on communique 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**

So, S,/n is said to be a strongly consistent estimator of p. A proof of the strong LLN, which implies the weak LLN, is given in [44, 621. 12 FIRST-ORDER AUTOREGRESSIVE ESTIMATORS Given a series of samples X, at "times" n E {0,1! ), one may wish to iteratively estimate their mean. To this end, we can define X , as the "current" estimate of the mean. A typical problem in this context is that the underlying distribution of the samples is slowly changing with time. For example, the Transmission Control Protocol (TCP) estimates average packet round-trip times (RTTs) [139] (and "absolute" variation about the estimated average) to calibrate a time-out mechanism for acknowledgements of transmitted packets.

For the LLSE estimator, the constants a and b are chosen so as to minimize the MSE. Show that the LLSE estimator is the conditional expectation E ( X / Y ) when the random variables X and Y are jointly Gaussian with var(Y) > 0 (so, in this case, the best estimator is a linear one). 14 For the gamma distribution. 8) and show that when r E Z+. 15 Use MGFs to prove that the binomial distribution with parameters n and q converges to the Poisson distribution with parameter X as q + 0 and n + x in such a way that nq + A.

That is, consider a discrete random variable Z with range Rz = {c,),"=, and define the events for all j. If the collections of events {Bj),",, and {C,):, are the same (allowing for differences of probability zero), then E(X/Y) = E(XIZ) almost surely. Note that Ry can be different from Rz,in which case E(X1Y) with g $ h. = h(Y) = E(XIZ) = g(Z) almostsurely, 18 REVIEW OF ELEMENTARY PROBABILITY THEORY In general, E ( X / Y )is the function of Y which minimizes the mean-square error (MSE), E [ ( X - h(YH21.