## 4 Multipath Service Node Selection Algorithm  
### Motivation  
In the MPTS-ICN architecture, selecting the appropriate multipath service node is key to building multipath transmission. The multipath service node forms a mapping relationship between the node NA and MPSID in NMRS to provide alternative paths for the edge node multipath service. The edge node obtains the available multipath service node set M by querying the address list corresponding to MPSID from NMRS. Since the number of multipath service nodes obtained by NMRS is much higher than that required by edge nodes, and the maintenance of multipath service node information also requires  
Figure 3: ID-based multipath transmission service scenario. additional overhead, edge nodes need to filter the nodes in the multipath service node set M according to certain strategies. Here, we set the size of the multipath service node set M returned by NMRS to m, and the size of the multipath service node set K required by the edge node to k, and then the multipath service node selection of the edge node has \(C_{m}^{k}\) possibilities. The setting of the k value is the key. A k value that is too low cannot meet the performance requirements of multipath transmission, while an overly large k value is unrealistic and inefficient. Related research work [35] shows that the appropriate value of k is 3 or 4. In this paper, the selection of multipath service nodes mainly considers two factors: path link overlap and path link state. Path link overlap directly affects the bandwidth aggregation of multipath transmission and the tolerance for link anomalies. For bandwidth aggregation, two paths with low link overlap can aggregate more bandwidth resources. If there is an intersecting link between the two paths, the two paths will share the bandwidth resources of the link, resulting in less bandwidth aggregation between the two paths. For link anomaly tolerance, the two paths with low link overlap can improve the transmission fault tolerance between paths. When the shared link of the two paths is congested, the two paths will be congested at the same time. The path link coincidence degree depends on the number of coincident nodes and the length of the path. The link coincidence degree between two paths is calculated as shown in Equation (1). \(Parhi_{i}\) and \(Path_{j}\) represent paths i and j. A path is a sequence of nodes. \(LO_{ij}\) represents the number of nodes that overlap between two paths, \(L_{i}\) represents the number of nodes in path i, and \(L_{j}\) represents the number of nodes in path j.  
\[OverlapRatio(Path_{i},Path_{j})=\frac{2\ \times\ LO_{ij}}{L_{i}\ +\ L_{j}} \tag{1}\]  
If only the path link overlap factor is considered, the multipath service node set K selected by the edge node satisfies the Equation (2). \[K=\min_{C_{m}^{k}}\arg\sum_{i\ =\ 1\ j}^{k}\sum_{j\ =\ i\ +\ 1}^{k}OverlapRatio(Path_{i}, Path_{j}) \tag{2}\]  
Path link state determines the upper limit of multipath transmission resource aggregation. The factors that determine the path link state mainly include bandwidth, delay, and packet loss rate. According to the bandwidth, delay and packet loss rate in Equation (3), the link state of the path is calculated. \(\alpha\) represents the influence factor of bandwidth on path link state, and \(\beta\) represents the influence factor of round-trip delay on path link state. In the actual system, \(\alpha\) and \(\beta\) need to be optimized. \(p_{i}\) represents the packet loss rate of path \(i\), which reflects the congestion degree of path. Since packet-loss recovery takes a long time, the sigmoid function is used to characterize its importance, as defined in Equation (4). \(p_{0}\) is the average packet loss rate, according to experience, it generally takes \(p_{0}\) = 0.03. The importance of the packet-loss rate in the path link state can be altered by adjusting the \(\gamma\) value in the sigmoid function. If the packet-loss rate factor is not considered, the packet-loss rate for each path can be set to 0.