Conformal Mapping for Optimal Network Slice Planning based on Canonical Domains

The evolution towards 5G consists of managing highly dynamic networks and making decisions related to the provisioning of networks in an as-a-service and cost-aware fashion. This is translated by 5G verticals that are dedicated to specific services, applications or use cases fulfilling the constant demand of vertical industries. In this vein, to achieve the high-level goals defined by operators and service providers, and to answer to the elasticity and low-latency specifications of the upcoming 5G mobile system, the optimal placement of Virtual Network Functions (VNF) must cope with the non-uniform service demands and the irregular nature of network topologies. This paper addresses this issue by mapping the non-uniform distribution of signaling messages in the physical domain to a new uniform environment (i.e., canonical domain) whereby the placement of core functions is more feasible and efficient by means of Schwartz-Christoffel conformal mappings. The experimentation results, compared to some baseline approaches, have proven the efficiency of the conformal mapping based placement in allocating the virtual resources (i.e., virtual CPU and virtual storage) with regard to the optimal end-to-end delay, cost and activated Virtual Machines (VMs). Another interesting contribution is that all placement decisions are based on a realistic spatio-temporal user-centric model, which defines both the mobility of User Equipments (UEs) and the underlying service usage.