## 5 Simulation Results and Analysis
### Simulation Analysis
#### 5.2.1 Effect of Path Bandwidth Capacity  
This experiment aims to explore the impact of bandwidth capacity and bandwidth differences on multiple paths that can be used for data transmission. The bandwidth of the data transmission path is determined by the minimum bandwidth of all links on the path. Let Sr denote the bandwidth requirement of the data receiving end, where we set 50 Mbps, and \(b_{i}\) denote the bandwidth of the ith subpath. \(\alpha=b_{1}/Sr\), which represents the ratio of the default path bandwidth to the data receiver bandwidth requirement. As \(\alpha\) increases, the default path has more bandwidth resources. For example, when \(\alpha=2\), the default path bandwidth resource is twice the data source bandwidth requirement. In this experiment, we set the range of \(\alpha\) values as [0.3, 1.5]. The bandwidth of the i-th subpath is \(1/i^{\beta}\) of the default path bandwidth, where \(0<=\beta<=1\) denotes the skew factor. When \(\beta=0\), indicates that all subpaths have the same bandwidth. With the increase of \(\beta\), the bandwidth distribution between multiple sub-paths of data source and data receiver is more skewed. When \(\beta=1\), the bandwidth ratio of the four sub-paths is 12:6:4:3. In this experiment, except for bandwidth, other network indicators are the same in all sub-paths. In this experiment, the data chunk size requested by the data receiver is 2M, and the number of requests is 10.  
Figure 4: Multipath Topology.  
Figure 5: Multipath Topology.  
Figure 6 shows the change curve of data transmission completion time with \(\alpha\) and k. In this experiment, the value of the skewness factor \(\beta\) is 0, 0.5, 1. From Figure 6a, we can see that in the range [0.3, 1.5] of \(\alpha\), the data transfer completion time decreases as k increases. This shows that using multiple paths for concurrent data transmission can effectively provide bandwidth aggregation. At the same time, we note that the decrease in the data transfer completion time slows down as \(\alpha\) increases, especially when \(\alpha>1\). This shows that multipath transmission has a good effect in bandwidth-constrained scenarios, but not in bandwidth-unconstrained scenarios. On the other hand, we note that the decrease rate of data transmission completion time decreases with the increase of k, which indicates that a smaller k value (k = 2 or 3) can obtain most of the performance gains of multipath transmission and reduce the overhead of path maintenance.  
From Figure 6b, we can see that when \(\beta=0.5\), the above results still hold, indicating that multipathing works well regardless of whether the subpath bandwidth distribution is uniform or not. However, in Figure 6c, we can see that multipath transmission does not have a good effect. This is because in this experiment, the scheduling strategy we adopted is a Round-Robin strategy. When the path bandwidth difference is too large, the completion time of data transmission at the data receiver will be limited to the sub-path with the lowest bandwidth resource. In the next section, we will discuss the impact of data scheduling strategies on multipath transmission performance.