re presented. 10.2.2 System Model In this section, we present the system model for robust RAN slicing. We model the substrate network (SN) as a weighted directed graph Gs = (Ns, Ls), where N° and Ls denote the set of substrate nodes and links respectively. A substrate node can be a commodity server or a physical network equipment that provides (virtual) network functions. A substrate link can be softwarized into several virtual links using ports virtualization [23]. Let N's and LS denote the set of failed substrate nodes and links respectively. Here, failed (resp. available) substrate nodes and links are those malfunctioning (resp. properly functioning) commod- ity severs and physical network interfaces, respectively. Similarly, the set of available sub- strate nodes and links is denoted by N's and LS respectively, where N'S We use a binary vector Bi to indicate whether substrate node i possesses the corresponding network functions, where BK = 1 if substrate node i possesses network function k, and BK = 0 otherwise. The dimension of vector Bi is denoted by L. The elements 10 Robust RAN Slicing of vector Bi represent various network functions. For simplicity, we use ij to denote the substrate link between substrate node i and j. The bandwidth of substrate link ij is denoted by bs . We define an indicator aw,ij' WENS, ij E Ls to reflect adjacency of the directed graph Gs = (N's Ls), where aw,ij = 1 if substrate node w is the tail of the directed sub- strate link ij, aw,ij -1 if substrate node w is the head of the directed substrate link ij, and awii==ootherwise. A RAN slice request is also modeled by a weighed directed graph G = (N), Lv), where NV and L" denote the set of requested network functions and virtual links respectively. We assume that network functions used by a specific RAN slice are not shared by other RAN slices for isolation purpose [4]. We use N2 and LY to denote the set of failed network functions and links respectively. Similarly, the set of available substrate nodes and links are denoted by N'D a