n as a linear equation in the optimization vari- ables of the ILP optimization problem. In particular, it is to remember that with the definitions of Chapter 8, the number of hops of the path followed by the vth connection between nodes i and j can be written as (10.24) Since the hops are all equal (but for the last, but we will neglect this specific case), and the loss due to a traversed OXC are all of the same magnitude, the transmitted power on the link i,j depends only on these two parameters. Following the way we have designed the OXCs, the span loss is compensated by the OXC net gain; thus, the overall ASE noise can be written as (10.25) Next Generation Networking: Enabling Technologies, Architectures, and Performances where the net noise factor of the OXC (NFoxc), the optical bandwidth (Bo), and the span gain (the opposite of the span loss, GT) can be evaluated before the run of the optimization algorithm. The penalties are generally caused in this case by two sources: InB and OutB crosstalk and residual dispersion besides a system margin that has to be taken into account for aging and components specifications variability. As far as crosstalk is considered, it causes a sort of additional noise. This is almost true for the OutB crosstalk, that is a signal completely uncorrelated from the useful channel, while for the InB crosstalk, especially if generated by the channel itself, this could be far from reality. However, we know that if InB crosstalk is a critical element, a worst case approach can be adopted, where the noise approximation is not used and the InB crosstalk power is multiplied by two and subtracted by the useful power to simulate destructive interference. This prudent approach, however, produces a nonlinear constraint and thus cannot be used in an ILP base algorithm. In the case of the Gaussian noise approximation, once given the signal-to-interference ratio Xi for the three causes of crosstalk in a single OXC (X1 for the out-of band crosstalk, X2 for the InB from other channels, and X3 for th