nd LV respectively, where N'1 = NV - N's and LA=LY - LY. A request is represented by a binary vector a and a bandwidth matrix B, where binary variable ak = 1 indicates that the request requires network function k, and ak = 0 otherwise. For simplicity, we use kl to denote the virtual link between network function k and l. We introduce matrix B = { where by denotes the bandwidth requirement of the virtual link kl. Without loss of generality, we assume 1 <k<l<L. We use 0 to denote the bandwidth allocated on substrate link ij, when virtual link kl is mapped onto a substrate path between source S and destination t. This means that substrate link ij is a segment link of the path (s,t), where i, jefs. We introduce a binary variable ms, where mk = 1 stands for network function k mapped onto substrate node S, and ms = 0 otherwise. Furthermore, we introduce a pair-decision variable 2kl =ms.m, which equals 1 only when network functions k and l are mapped onto substrate nodes S and t respectively at the same time, otherwise 2kth = 0. To avoid the quadratic constraint, such relationship among mk, m1, and 2kt can be represented by a triangle inequality [24] in (10.1). (10.1) Since one network function can be only mapped onto one substrate node and the fact that mks and mi are independent variables, we can obtain the value of mk by summing up all the possible values of mi in you We express this relationship in (10.2). Similarly, we can also obtain the equation in (10.3). (10.2) tens, (10.3) KENYSENS, In our system model, the connectivity of virtual network functions is modeled as a multi-commodity flow problem [25]. The equations of (10.4)-(10.6) ensure flow conser- vations, i.e. the amount of flow going into substrate node w equals the amount of flows going out of it, except for w=s, which has only outgoing flows, or w = t, which has only incoming flows. abtsl) (10.4) 10.3 Robust RAN Slicing Network function Original mapping Remapping Substrate node Original substrate path Remapped substrate path Virtual link Single substrate 