An introduction to communication network analysis by George Kesidis

By George Kesidis

This ebook is a quantitative textual content, which makes a speciality of the true concerns in the back of critical modeling and research of communications networks. the writer covers the entire worthwhile arithmetic and thought to ensure that scholars to appreciate the instruments that optimize desktop networks at the present time.

  • Covers either classical (e.g. queueing idea) and sleek (e.g. pricing) features 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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Extra resources for An introduction to communication network analysis

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So, we focus our attention on continuous-time Markov chains in this chapter. Discrete-time Markov chains are briefly MARKOV CHAINS covered at the end of the chapter. Refer to [20, 1 18, 1 19, 161, 1931 for further details concerning Markov processes. 1 MEMORYLESS PROPERTY OF THE EXPONENTIAL DISTRIBUTION In this section, the salient properties of exponentially distributed random variables are discussed. 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.

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. ;,, associate an cxponentzall~distributed random varidble 7 ,( r , 1 1 1 ) with parameter q,, ,,, > 0 ( recall thic means ES,( r r .

The extent to which the random variable Y discriminates the samples LJ E R. 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.

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