Davide Cherubini - PhD Thesis - UniCA Eprints

6.4 LP modelsModel for GRPz = min(u max ) (6.57)∑is f · x f ij +∑p h ≤ u max · c ij ∀(i, j) ∈ A (6.58)f∈F∑h∈P(f)h:(i,j)∈P(h)p h = d f − is f ∀f ∈ F (6.59)p h ≥ 0 ∀h ∈ P(f) (6.60)is f ∈ [0, d f ] ∀f ∈ F (6.61)Survivability ConstraintsIn this model the 100% degree of survivability is realized by means of explicitLSPs, found as solution of the model, and implemented in the router configurationas backup secondary paths. Each backup path, represented by a new variable q h ,is common for all the working primary paths obtained for each commodity f.The recovery scheme used is the path restoration technique.As can be seen from the equations 6.62, 6.63, 6.64, 6.65, and 6.66 the survivabilityconstraints are quite complex in this case and the model requires particularsolving techniques such as Column Generation [62].∑h∈P(f), l∈P(h)∑f∈Fp h ≤∑h∈P(f), l∉P(h)is f · x f,lij + ∑h:(i,j)∈P(h), l∉P(h)q h ∀f ∈ F, ∀l ∈ A (6.62)(p h + q h ) ≤ u max · c ij ∀(i, j), l ∈ A (6.63)q h ≤ d f(h) · y h ∀h ∈ P(f) (6.64)y h ∈ {0, 1} ∀h ∈ P(f) (6.65)∑y h ≤ 1 ∀f ∈ F (6.66)h∈P(f)Equation 6.62 states that the flow to be rerouted (p h ) has to be smaller thanthe capacity of the backup path (q h ).Constraint 6.63 represents the flow conservation equation for arc (i, j). The firstterm is the IS-IS traffic flowing along the arc when the edge l fails, while the second63