in terms of LSPs to route in the MPLS layer, its element Tij represents in particular the number of LSPs to route between node i and node j of the MPLS layer (layer 2). If the traffic forecast is not sufficiently reliable, the matrix [T] has to be derived from the traffic statistics with a statistical model. For the moment we will assume that [T] is given, we will analyze in the next section a draft method to manage traffic uncertainly. We will call TM = Max(Tij), (i = 1,..., 2N), (j = 1,..., 2N) the maximum number of LSPs requests starting from node i towards another node. Generally TM is a small number since we imagine to design a transport network where the LSPs are high speed (e.g., 1 Gbit/s). In any case TM M, which is the maximum number of LSPs required between the same nodes. Telecommunication Networks Seattle Chicago Kansa City New York City Sunnyvale Denver Washington, DC Atlanta Los Angeles Houston FIGURE 8.25 Reduced version of the North American network used for the examples of this chapter. The link length is assumed equal to the highway distance between the corresponding cities. The maximum number TM of LSPs to be routed between a couple of nodes is given by TM = Max(T)M). The routing is represented by the routing matrixes [sR], [A]. The matrixes [sR] = 1, 2) have dimensions 2N X 2N sN X SN TM and it is defined as follows: the ele- ment Vijkdv is one if the vth LSP request between the nodes i and j transit through the link k-d at the layer S. In principle this is a huge matrix, but in reality it is very sparse. For example, in a network like the pan American network of Figure 8.25 with 10 nodes at all the layers, supposing TM = 3, it seems a matrix with about 30,000 elements. However, in the network we have chosen as an example and in general in any network, it is possible to set a maximum number of hops per LSP and it is quite small (generally much smaller than N). For example, optimizing with random traffic the network of Figure 8.25 the maximum number of hops results to be 3 at optical layer and 