tic distribution. The easier case is that of uniform traffic variation. In this case the random traffic matrix [T] can be written as follows: [T]=x[T0] (8.31) where [To] is the average traffic matrix. x is a random variable with average equal to one and known probability distribution In this case, the problem can be formulated as follows: the network has to be designed SO that the probability that a connection request is rejected is smaller than a certain limit, called PR. The solution is straightforward once the design tool is available. Calling p(x) the prob- ability density of the variable X, it is possible to find a value x0 SO that [p(x)dx=Px (8.32) If the network is dimensioned for the traffic matrix [T] = xo[To], the rejection probability is surely smaller or equal to PR. The situation gets more complex if the traffic matrix depends on more than one random variable, but in line of principle the solution method is the same. Let us assume that [X] is a random matrix, with 2N V 2N2 nonzero elements, and whose average is the identity matrix [I]. Let also assume to know the joined probability density functions of the V ran- dom variables that are elements of [X], called p(x1, X2, Xv). If the traffic matrix can be written as [T] = [X] [To], the method used for the single ran- dom variable can be directly generalized. Naturally it is not easy to derive the model of the traffic matrix and its distribution SO that, in the absence of other information, a Gaussian Convergent Network Management and Control Plane model is often adopted. It is possible to imagine more complex models for the random nature of the traffic, for example, based on Markov chains [21]. In this case, the design gets more complex and we direct the reader to the relevant bibliography for a study of the problem. 8.4.3 Routing Policies-Based Design As we have seen, ILP-based optimization algorithms are quite computationally com- plex, representing in reality, a particular formulation of an NP hard problem. If they are largely used for dimensioning o