# A Multipath Data-Scheduling Strategy Based on Path Correlation for Information-Centric Networking
## 4 Multipath Data Scheduling
### Path Correlation Analysis  
The necessary condition for multipath transmission is to select several suitable relay ICN routers to establish multiple relay paths at both endpoints. During multipath transmission, the paths of the source node and the relay node and the relation node comply with the shortest path rule. Some studies [35] have shown that a small number of nodes with a higher betweenness centrality (BC) frequently appear on the end-to-end shortest path in the actual network environment: that is, a small number of relay nodes with high BC can provide optimal routing for most end-to-end communications. The BC of node \(i\) can reflect the importance of the node in the network topology, which can be calculated as [36]:  
\[BC(i)=\sum\frac{\sigma_{st}(i)}{\sigma_{st}}\qquad s,t,i\in V, \tag{1}\]  
where \(V\) is the set of all nodes in the entire network, \(\sigma_{st}\) represents the shortest path from \(s\) to \(t\) and \(\sigma_{st}(i)\) is the shortest path from \(s\) to \(t\) passing through \(i\). Therefore, in this paper, we select \(M\) relay ICN routers with a higher BC to construct candidate node set, and their IP addresses and MPSID relations are registered on the NRS. The size of the candidate relay nodes set depends on the scale of the network. Studies have proved that a small set of candidate relay nodes can provide high-quality transmission services for most connections [37]. In the multipath transmission process, the source node can initiate a query operation to the NRS according to the MPSID to obtain the set of candidate relay nodes and select \(k\) suitable relay nodes to construct \(k\) end-to-end relay paths. Figure 1: The principle of the multipath transmission method in ICN. The ID path formed by the relay node is covered on the existing underlay networks, and the data transmission between ICN nodes is still along the IP shortest path. When the ID paths share the same bottleneck link, the transmission efficiency and reliability of the ID paths are usually limited. Once a shared bottleneck link is congested or fails, the overlapping ID paths will be affected. In order to enhance the reliability and robustness of multipath transmission, it is necessary to analyze the path correlation. When selecting relay nodes, we need to consider not only the path correlation between ID paths and the default IP path but also the link overlap among \(k\) ID paths. The setting of \(k\) affects the gain effect of using relay paths for transmission. Theoretically, the larger \(k\) is, the higher the transmission benefit will be. However, due to the existence of overlapping links in an actual network environment, it is unrealistic and inefficient to use too many relay paths. The authors of [38] have shown that most of the transmission benefits can be obtained by selecting three to four relay paths. Therefore, we set \(k\) at three in this paper. We illustrate the effect of the degree of sub-path overlap on multipath transmission reliability through a simple mathematical model. Assuming a sub-path \(path_{i}\) is composed of \(m\) link segments, that is, \(path_{i}=(s_{1},s_{2},\ldots,s_{m})\), where the failure probability of the link segment \(s_{j}\) is \(p_{j}\), then the reliability of the \(path_{i}\) can be expressed as:  
\[R(i)=\prod_{j=1}^{m}{(1-p_{j})} \tag{2}\]  
For the convenience of calculation, we assume that the failure probability of each link segment is equal and unified for \(p\). Then, the reliability of the \(path_{i}\) can be expressed as:  
\[R(i)={(1-p)}^{m}. \tag{3}\]  
The influence of the overlap degree between sub-paths on the joint reliability is considered. Suppose a sub-path \(path_{j}\) consists of \(n\) link segments, that is, \(path_{j}=(s_{1},s_{2},\ldots,s_{n})\). The number of overlapping link segments of \(path_{i}\) and \(path_{j}\) is \(l\), and \(l\leq m,n\).