search Input: the solution of the reduced problem x ;the neighborhood size k; Output: the local minimal solution x*; 1: Set x* = x,i=1; 2: while i and iter MAXITER do X" = intlinprog (P|N;(x)): if " CTX then Set i = 1,x* = LocalSearch (P,x", k); Seti = i + 1; end if iter = iter + 1. 10: end while Local search is the same as the general VNS process in [29] to find the local optimal x*. VNS systematically exploits the solution space based on the following observation [29]: a local minimum with respect to one neighborhood structure is necessarily but insufficient condition for the local minimum of another neighbourhood, i.e. a local minimum within the ith neighborhood Nj(x') is not necessarily within the (i + 1)th neighborhood Ni+1(x). In VNS, the neighborhood size, which is denoted by i, increases from 1 to k. Given a solutionx' of the reduced problem, we explore the ith neighborhood Nj(x') to obtain the best solution x". The loop of local search continues if x" is found to be better than the incumbent solution x' (line 4); then another local search re-centers around x" and begins again with the first neighborhood N(); otherwise, if there is no improvement on the objective function value, the neighborhood size is increased by 1. The local search process proceeds until the total iterations, which is denoted by iter, exceed the MAX - ITER, i.e. the maximum allowed iterations. Numerical Results 10.4.1 Performance Metrics Performance metrics include the failure rate of requests (RF, defined in (10.39)), the average load of substrate links (U , defined in (10.40)), and the average time of mapping a request. The total number of substrate links is denoted by ILSI The initialized substrate link band- width within the substrate node pair (i,j) is denoted by by the number of failed requests (10.39) number of arrived requests (10.40) 10 Robust RAN Slicing 10.4.2 Simulation Scenarios and Settings We model the arrivals of slice requests, occurrence of VNF failures, and substrate link fail- ures as Poisson processes with arrival