# Maximizing the Capacity of Edge Networks with Multicasting
## 1 Introduction  
In the era of the \"Internet of Everything\", terminals including tablets, computers, mobile phones and diverse sensors generate massive quantities of data. Huge network resources are required to process the large data flows, which often over-burdens the current cloud computing architecture. Edge computing with the locality feature is emerging as a new computing paradigm [1]. By deploying computing and caching resources to the network edge or migrating the tasks/services from the cloud to the network edge, users receive quicker responses and experience higher quality [2].  
System capacity is one of the key indicators for evaluating a network's performance. It reflects the transmission capability of a networking system per second. [PERSON] and [PERSON] [3] were the first to present the concept of wireless network capacity \(\frac{W}{L\sqrt{n}}\), where \(W\) is the transmission rate of the network channel, \(L\) is the transmission distance of the content and \(n\) is the number of nodes in the network. The subsequent works follow this approach to evaluate the metric from different perspectives such as the network architecture [4], the routing model [5] and the caching strategies [6]. The key idea behind maximizing system capacity is to shorten the content transmission distance by various ingenious conceptions. Though it is well investigated in traditional wireless networks, maximizingsystem capacity in edge scenarios faces challenges due to the dynamical user sessions and the changing content popularity.  
Local caching is one of the main features of edge networks since it reduces the access delay of content. Recent studies propose various caching schemes to improve the edge network's performance, such as popularity-based caching [7]. Note that the same content may be requested by many users simultaneously or over a short period, for example, the requests for breaking news or major sporting events [8]. This indicates that multicast sessions can be employed in response to users' requests and only leave content copies at branches of a multicast tree. It thus reduces the volume of repetitive transmission links, shortens the transmission distance and improves the edge caching network's performance. However, to our knowledge, few works focus on the joint optimization of capacity by using multicasting and caching in edge computing. Related works on multicasting in traditional wireless networks neglect the impact of content caching on the system capacity, and those on edge networks employ the unicast routing model to receive/forward content item. Hence, the joint gain in capacity with multicasting and caching is not clear in edge networks.  
Considering the above, we study the capacity of edge networks with respect to the multicasting and content caching. As the number of content copies affects the caching performance and the construction of multicast tree, we first calculated the optimal number of content copies based on user request volumes and the cache sizes of SBSs. Second, we constructed an efficient multicast tree to distribute the content copies. Our contributions are summarized as follows:  
1. We investigated multicast communication in edge caching networks. SBS caching of the content was selected to construct the multicast tree and the content copy was held in the branch node;
2. We used the term capacity as the evaluation metric and analyzed the upper and lower bounds of system capacity. The upper bound is determined by considering the full \(k\)-ary tree and the lower bound by the assumption that multicast communication happens only at the last hop.  
The remainder of this study is organized as follows. In Section 2, we review the related works. Section 3 describes the system architecture. The following four sections analyze the presentation of the system capacity. Section 8 evaluates the performance of the proposed methods. Finally, conclusions are presented in Section 9.