### Related Works  
SFC Deployment is an NP-hard problem [25]. Several exact optimization models, and sub-optimal heuristics, have been proposed in recent years. [PERSON] et al. [26] defined a protocol for optimal VNF placement based on SDN traffic rules and an exact optimization algorithm. This work solves the optimal VNF placement, migration, and routing problem, modeling various system and network metrics as costs and user satisfaction. HPAC [27] is a heuristic proposed by the same authors to scale the solutions of [26] for bigger topologies based on the Gomory-Hu tree transformation of the network. Their call for future work includes the need for the dynamic triggering of adaptation like monitoring user demands, network loads, and other system parameters. [PERSON] et al. [28] present a resource allocation and VNF placement optimization model for vCDN and a two-phase offline heuristic for solving it in polynomial time. This work models server availability through an empirical probabilistic model and optimizes this score alongside the VNF deployment costs. Their algorithm produces near-optimal solutions in minutes for a Network Function Virtualization Infrastructure (NFVI) deployed on a substrate network made of even 600 physical machines. They base the dimensioning criteria on extensive video streaming VNF QoE-aware benchmarking. Authors in [20] keep track of resource utilization in the context of an optimization model for multi-cloud placement of VNF chains. Utilization statistics per node and network statistics per link are taken into account inside a simulation/optimization framework for VNF placement in vCDN in [29]. This offline algorithm can handle large-scale graph topologies being designed to run on a parallel-supercomputer environment. This work analyzes the effect of routing strategies on the results of the placement algorithm and performs better with a greedy max-bandwidth routing approach. The caching state of each cache-VNF is modeled with a probabilistic function in this work. Offline Optimization of Value Added Service (VAS) Chains in vCDN is proposed in [30], where authors model an Integer Linear Programming (ILP) problem to optimize QoS and Provider Costs. This work models license costs for each VNF added in a new physical location. An online alternative is presented in [31], where authors model the cost of VNF instantiations when optimizing online VNF placement for vCDN. This model lacks to penalize the Roud Trip Time (RTT) of requests with the instantiation time of such VNFs. More scalable solutions for this problem are leveraged with heuristic-based approaches like the one in [32]. On the other hand, regularization-based techniques are used to present an online VNF placement algorithm for geo-distributed VNF chain requests in [32]. This work optimizes different costs and the end-to-end delay providing near-optimal solutions in polynomial time. Robust Optimization (RO) has also been applied to solve various network-related optimization problems. RO and stochastic programming techniques have been used to model optimization under scenarios characterized by data uncertainty. Uncertainty concerning network traffic fluctuations or resource request amount can be modeled if one seeks to minimize network power consumption [33] or the costs related to cloud resource provisioning [34], for example. In [35], [PERSON] et al. present a VNF placement and SFC routing optimization model that minimizes power consumption taking into account that resource requirements are uncertain and fluctuate in virtual Evolved Packet Core scenarios. Such an algorithm is enhanced in a successive work [36] where authors improve the scalability of their solution by dividing the task into sub-problems and adopting various heuristics. Such an improvement permits solving high-scale VNF placement in less than a second, making such an algorithm suitable for online optimization. Remarkably, the congestion-induced delay has been modeled in this work. [PERSON] et al.