GLSP under examination and on the specific nature of the failure (that is, do not depends on the instant thj), Equation 8.37 becomes very simple. Let us assume that we are observing a SO long time that, for example, N1,k can be approximated as N1,k=P1(F) = N, where the probability P1(F) is the probability that, assuming to have a failure event, the considered GLSP is involved in the failure and can restored by the first survivability mechanism and analogously N2,k = P2(F) NF and N3,k= [1 - P1(F) - P2(F)] N. With these definitions Equation 8.38 becomes A)1((1(1 (8.38) where TF is the interarrival time of the failure events. <T> is the average unavailability time of the generic GLSP in correspondence to a failure. Besides network availability, when complex survivability strategies are implemented SO that multiple failure can be faced, the so-called resilience factor (RF) is useful to evaluate the effectiveness of a survivability strategy. Let us imagine that a specific survivability strategy is able to face all single link failures (property always true for effective strategies) and a subset of multiple failure events. Calling Sk = {S1,S2,...} the set of all possible sequences of k links selected among the m cable ducts at layer 0, the kth order resilience factor is defined as [26] (8.39) Convergent Network Management and Control Plane where lsp(s) is the cardinality of the set of working GLSPs that are interrupted by the contem- porary failure of all the links in the set Sj lsp,(s) is cardinality of the subset of those GLSPs that are restored without causing ser- vice disruption by the network protection mechanism The normalization factor is derived from the number of links m. The resilience factor of kth order can be also interpreted, if the failure events have the same probability, as the probability that an GLSP is restored in the presence of a random kth order failure event, and complete protection against k contemporary failures imply RFK = 1. Since a network that is able to face k contemporary failures is in