# Joint Deployment Optimization of Parallelized SFCs and BVNFs in Multi-Access Edge Computing
## 1 Introduction  
The multi-access edge computing (MEC) network, which benefits from proximity communication with mobile users and extensive service convergence of edge servers, is envisioned as a promising distributed network [1; 2; 3]. The MEC network can provide low-delay services to mobile users by leveraging the closest edge server to process user requests. To ensure the security and reliability of communication transmission before reaching the closest edge servers, user requests typically steer their traffic flows along a sequence of dedicated equipment that implements certain network functions (e.g., firewalls, packet inspection, and intrusion prevention/detection systems). However, this equipment needs to be manually \"patched\" into the existing network infrastructure, with fixed locations and significant expenditure [4]. This method of implementing network functions brings challenges in the flexible management of network service and the rapid development of network functions. Network function virtualization (NFV) decouples network functions from dedicated hardware and virtualizes network functions as software implementations known as virtual network functions (VNFs) [5; 6]. Different network services requested by mobile users can be provided in the form of a service function chain, which is a chain of VNFs. Thus, NFV offers a flexible way to design, place, and manage network services by deploying VNFson edge servers in the MEC network and chaining them into different SFCs [7]. Mobile users generally carry large traffic data that need to be processed by certain SFCs with strict reliability and delay requirements. However, SFCs often incur a high transmission delay since VNFs in SFC are deployed in different edge servers, and user requests need to traverse these VNFs sequentially [8; 9]. Splitting the user request into multiple sub-flows can decrease transmission delay significantly. One of the key issues in realizing splitting is establishing how to route these sub-flows along VNFs and map these VNFs onto the underlying MEC network. Parallelized SFCs (P-SFCs) can deploy two or multiple VNF instances for each VNF in SFC to process user requests in parallel [10; 11]. These parallel VNF instances form a set of P-SFCs, and each P-SFC is also a sequence of VNFs. Thus, the user request can be split into multiple sub-flows that traverse these P-SFCs in parallel. In the MEC network, due to software faults and server failures (e.g., operational error and server overload), active VNFs that process user requests are prone to failure. The failure of any single VNF in SFC will interrupt the network service and lead to significant economic losses and threats to individual safety [12; 13]. Additionally, the reliability of SFC decreases significantly as the number of VNFs in SFC increases [14]. Deploying idle backup VNFs (BVNFs) near the active VNFs and activating BVNFs when the active VNFs fail is a practical way to satisfy the reliability requirement of user requests and continuously maintain the network services. That is to say, if the reliability of P-SFCs is below the reliability requirement, extra BVNFs must be deployed until the service reliability provided by P-SFCs and BVNFs satisfies the reliability requirement. Deploying idle BVNFs will preempt server resources available to process incoming user requests and then reduce the number of accepted user requests. Reducing the number of idle BVNF deployments is key to mitigating this problem. In this paper, we propose that BVNFs satisfying the delay requirement can be used as active VNFs to form P-SFCs. This approach can enhance reliability, as the special BVNFs can also provide network services when VNFs fail. Meanwhile, if one active VNF instance in P-SFCs fails, other parallel instances may replace it to provide network service while satisfying the delay requirements. These parallel VNFs can be used as BVNFs, thus reducing the deployment number of idle BVNFs and enhancing the reliability of P-SFCs.