New PDF release: An introduction to communication network analysis

By George Kesidis

ISBN-10: 0470168684

ISBN-13: 9780470168684

This booklet 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 invaluable arithmetic and thought to ensure that scholars to appreciate the instruments that optimize machine networks at the present time.

  • Covers either classical (e.g. queueing conception) 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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4 CONTINUOUS-TIME, TIME-HOMOGENEOUS MARKOV PROCESSES WITH COUNTABLE STATE SPACE We will now define a kind of stochastic process called a Markov process of which the Poisson process is an example; more specifically, a Poisson process is a variety of (transient) pure birth Markov process. A Markov process over a countable state space C is sometimes called a Markov chain. Without loss of generality, we will subsequently take C = Zf . A Markov chain is a kind of random walk on C. It visits a state, stays there for an exponentially distributed amount of time, then makes a transition at random to another state, stays at this new state for an exponentially distributed amount of time, then makes a transition at random to another state, etc.

For n 2 2, x,. , all = clearly, no older samples X k with k < n - 2 affect the MA X,. , for n > 1, where 0 < a < 1 is the "forgetting factor" and X o = Xo. 20) is simply implemented with two additive operations and one bit-shift (the latter to multiply by 1- a). There is a simple trade-off in the choice of a. A small a implies that X, is more responsive to the current samples X k , but this can lead to undesirable oscillations in the AR process A large value of cu means that the AR process will have diminished oscillations ("low-pass'' filter) but will be less responsive to changes in the distribution of the samples X k [136, 1641.

So, Ti+1 - s is exponentially distributed with parameter -q,,, and conditionally independent of s - Ti given {X,, 0 r s). Furthermore, {X,, 0 r < T i ) is similarly conditionally independent of {X,, r 2 T,+l) given X ( s ) = n (by the (n,m)) random variables). 9). 3 at the end of the chapter. 1 Clearly, a Poisson process with intensity X is an example of a Markov chain with transition rates q,, ,,,, - X if rn = 11 + 1, -X if 111 = n. 0 else. 3 The transition rate matrix and transition rate diagram The matrix Q having q,,,,, as its entry in the nth row and rnth column is called the tratlsition rate matrix (or just "rate matrix") of the Markov chain X.

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An introduction to communication network analysis by George Kesidis


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