ate that final network cost is quite near the optimum when proceeding in this way [6], while the computational complexity is sensibly reduced. Besides in terms of computation complexity, this approach has the practical advantage to allow simulation of different survivability mechanisms by designing the working part of the network only once. We will exploit this feature in the last part of the chapter, when we will compare differ- ent survivability strategies maintaining the same traffic and network. These hypotheses are a sufficient base to lay the foundation for a general network design method based on ILP. In order to do that we have to built a general description of the network that is suitable for the scope. 8.4.2.2 Network Model for ILP In a multilayer network model, a set of topology and traffic variables can be defined at the same way at infrastructure layer (layer 0 in our model), at the optical layer (layer 1) and at the MPLS layer (layer 2). We will call them with the same symbol with a suitable prefix. The layer prefix will be written on the left of the symbol, SO that it is not confused with indices representing elements of a matrix. For example, the number of nodes will be indicated with ON if we are considering the infrastructure layer, with 1N if we are considering the optical layer, and 2N if we are dealing with the MPLS layer. Naturally variables at different layers are related, in this case ON 1N = 2N. The topology will be described by two matrixes: the adjacency matrix [sA], whose dimensions are SN X N (s = 0, 1, 2), and the link matrix [L], which exists only at the physi- cal layer. The element saii of the adjacency matrix is 1 if at the sth layer the nodes i and j are connected via a layer direct connection, otherwise it is zero. The element lij of the link matrix contains the length of the physical cable connecting nodes i and j at layer 0 if this cable exists, otherwise it is zero. The traffic is defined through a traffic matrix [T] of dimension 2N X 2N that contains the request of traffic 