Davide Cherubini - PhD Thesis - UniCA Eprints

6.4 LP models(a) Disaggregated flows(b) Aggregated flowsFigure 6.1: Aggregating flows per source nodeit is possible to rewrite the GRP as follows:z = min(u max ) (6.44)∑x f ij · isf + ∑ flowij h ≤ u max · c ij ∀(i, j) ∈ A (6.45)f∈F h∈N⎧∑⎪⎨ − ∑ f∈F (h) df + is f i = hflowji h − flowij h = dj:(j,i)∈Aj:(i,j)∈A⎪⎩− is f if i ≠ h, i = E(f), f ∈ F (h)0 otherwise(6.46)flowij h ≥ 0 ∀(i, j) ∈ A, ∀h ∈ N (6.47)is f ∈ [0, d f ] ∀f ∈ F (6.48)(6.49)Survivability ConstraintsThe survivability constraints with flow aggregation can now be introduced withthe example of figure 6.2.The failure of the undirected edge l = p − q involves two directed arcs l + =(p → q) and l − = (q → p).The IS-IS protocol will reroute the corresponding flows affected by the fail throughthe network and part of them might traverse the link (i, j) as shown in figure57