# Delay Bounded Multi-Source Multicast in Software-Defined Networking
## 6 Performance Evaluations
### Large Synthetic Networks  
In this subsection, we used Inet-3.0 [36] to generate large synthetic networks with a mean degree of 4 by default. We then applied the involved algorithms to evaluate the delay cost between every pair of neighbor nodes, assuming one shortest path between every neighbor pair. Network \(|V|\) spans from 4000 to 10,000, potential source nodes set \(|S|\) from 20 to 60, destination nodes set \(|D|\) from 20 to 100 and delay bound (\(\delta\)) from 20 ms to 9000 ms. All links are considered to be bi-directional with the capacity of 1 Gbps for each direction. First, we randomly generate a number of matrices of variable size and select the edge nodes (source and destination nodes) randomly. The performance metrics include (1) total delay cost, (2) delay bound, (3) impact of the number of sources \(|S|\) nodes and (4) impact of the number of network size [number of multicast nodes]. Figure 6a depict that the total delay cost for all the algorithms increases with the increase in the delay bound (\(\delta\)). DBMS performs much better  
Figure 4: Impact of (**a**) the number of source nodes \(|S|\), and (**b**) the number of destination nodes \(|D|\) on Execution Time (in log-scale) and Total Cost (delay) respectively.  
Figure 5: Impact of the number of source nodes \(|S|\) on Total Cost (delay).  
than mRAERA and other algorithms in this regard. A higher (\(\delta\)) means that a destination node \(d\) is allowed to connect to a source node \(s\) along a path with many links. A very low (\(\delta\)) will results in a very low total delay cost, but with the disadvantage of many source-destination pair path delay cost failing to satisfy the (\(\delta\)). DBMS performs at about 25% better that mRAERA, SPT, ST and KPP since it pays particular interest on selecting a minimum delay cost path based on the (\(\delta\)).  
As the network size \(|V|\) and the number of multicast node increases, so is the total delay cost as depicted by Figure 6b. As \(|V|\) increases, the expectation is that \(|S|\) and \(|D|\) will also increase, hence the increase on the total cost delay for all the algorithms is not that huge. The efficacy of DBMS is well demonstrated as it still outperform the other algorithms. Figure 7a clearly indicates that the number of links decreases with the introduction of more source nodes under the entire algorithms investigated. Generally, more source nodes on the network ensure that trees are required to span fewer nodes in a path from source to destination. This result shows the effectiveness of increasing the number of source node on an SDN multicast as compared to having the usual single source multicast. DBMS produces less number of links as it was designed with the intension to utilize the multiple source concept as compared to the other algorithms. As the sources are disconnected into various trees on DBMS, the number of links is greatly reduced as demonstrated by Figure 3 on Section 5.  
In Figure 7b the effects of the delay bound (\(\delta\)) is clearly visible on the number of link created by all the algorithms. Increasing the delay bond (\(\delta\)) allows a situation where the source-destination pair can be far away from each other, and hence spanning more links. Unlike mRAERA, SPT, ST and KPP, DBMS is designed to accommodate and responds to limited delay bound (\(\delta\)). DBMS is the best performer on this regard as expected, since the number of links is closely related to the total delay cost  
Figure 6: Impact of (**a**) the delay bound \(\delta\), and (**b**) the network size \(|V|\) on the Total Cost (delay).