By George Kesidis
This e-book is a quantitative textual content, which makes a speciality of the genuine matters at the back of severe modeling and research of communications networks. the writer covers all of the priceless arithmetic and concept to ensure that scholars to appreciate the instruments that optimize machine networks at the present time.
- Covers either classical (e.g. queueing idea) and smooth (e.g. pricing) elements of networking
- Integrates fabric on communique 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
1. 17), which gives the desired result for s = 0. For s :> 0, take a real E such that So, where the second-to-last equality is the Markov property. So. 19).
The total holding time in state n is exponentially distributed with parameter -(I,,, and therefore, by the memoryless property, Vn is also exponentially distributed with parameter -(I,,,. Thus, We will now explain the terms of the right-hand side. The first term represents the probability that the Markov chain X makes only a single transition (from n to m) in interval of time (s, s E]. Recall that the probability that X makes a transition to state m from state n is - ( ~ ~ , ~ The / qsymbol ~ , ~ O(E)("little oh of E " ) represents a function satisfying + lim-4 ~ )= 0.
X ( r ) = k) = P(X(t) = 71 1 X(S)= m)P(X(s)= m / X(r) = k)P(X(r)= k) where the second equality is the Markov property. In the second-to-last expression, we clearly see the transition from some initial state to k at time r, then to state m at time s (s - r seconds later), and finally to to state n at time t ( t - s seconds later). Our objective in the remainder of this section is to compute the transition probability matrix P ( t ) in terms of the known transition rate matrix Q. , the square matrix with 1's in every diagonal entry and 0's in every off-diagonal entry.
An introduction to communication network analysis by George Kesidis