# Joint Deployment Optimization of Parallelized SFCs and BVNFs in Multi-Access Edge Computing
## 2 Recent Works
### Joint Deployment of SFC and BVNFs with Parallelization  
There are extensive studies on the joint deployment problem of P-SFCs and BVNFs with parallelization while satisfying delay and reliability requirements in MEC networks. We classify the related studies into two categories: parallelism with traffic duplication and parallelism with traffic splitting. Parallelism with traffic duplication leverages all active VNF instances and VNF replicas to construct a primary SFC and multiple backup SFCs. Then, it transmits multiple duplications of user requests along multiple instances. Unlike re-routing to a reliable VNF in case an active VNF fails, this approach directly leverages VNF backups to increase the service's reliability, as seen in [25; 26]. For example, [PERSON] et al. [25] considered the trade-off of reliability, delays, and resource consumption. To satisfy the delay and reliability requirements and minimize the communication bandwidth usage, they deployed multiple VNF backups and duplicate flow to traverse all active VNF instances and VNF backups. To further improve resource usage, [PERSON] et al. [26] proposed a VNF deployment problem while supporting VNF decomposition and hybrid multiple-path routing and designed a heuristic algorithm to solve the problem. However, the algorithm wastes resources to process multiple traffic duplications. Therefore, it is suitable in cases where the length of SFC is short and the reliability of VNF is not high. Parallelism with traffic splitting allows user requests to be split into multiple sub-flows that are processed in parallel by multiple SFCs, thus reducing the service delay. Many studies have been devoted to parallelism with traffic, such as [27; 28]. For example, [PERSON] et al. [27] studied end-to-end service reliability with flow and SFCs parallelism. They defined four different backup deployment strategies and analyzed the service reliability of these deployment strategies. Their results show that parallelism significantly increases service reliability and resource utilization compared to serial processing. However, these strategies increase reliability at the cost of resources. To further improve service reliability and reduce resource consumption, they [28] studied service reliability with erasure coding and the failures of the path segment, VNF, and server failures. They derived analytical expressions for service reliability with encoding or VNF redundancy and showed that the combination of both methods increases service reliability. These aforementioned studies analyzed the service reliability of SFC in detail; however, they did not study the reliability-guaranteed problem under a multi-user resource-constrained environment and did not consider the service delay. [PERSON] et al. [29] proposed a parallel VNF processing approach through pools of candidate servers that host VNFs processing the traffic. Considering parallel VNF processing without backup VNFs decreases reliability and incurs additional communication and process costs. [PERSON] et al. found [10] focused on the problem of minimizing the sum of reliability degradation and operational costs while satisfying delay requirements. Due to the complexity of this problem, they proposed a Tabu search-based algorithm to find sub-optimal solutions. [PERSON] et al. [30] also focused on the parallelized SFC deployment problem to minimize physical link consumption. They designed three deployment strategies and a hybrid deployment algorithm to solve this problem. Unlike VNF decomposition, which reduces the computing resources of VNF replicas in [26], [PERSON] et al. [31] considered diversity which splits a single active VNF into a pool of active instances. Then, they proposed a joint selective diversity and tailored redundancy mechanism to provide resilient service. Based on this mechanism, they proposed the deployment problem of SFC to minimize resource consumption and proposed three solutions to solve the problem.