# Improvement of Network Flow Using Multi-Commodity Flow Problem
## 6 Discussion
### Routing Using Multi-Commodity Flow Problem  
The packet arrival rate of the proposed method is higher because the load is less likely to be concentrated on a particular link by providing multiple paths. The proposed method does not completely replace OSPF. Coexistence is possible because of the use of OSPF costs in capacity in the multi-commodity flow problem. OSPF is sufficient in cases where packet arrival speed is important or where the bandwidth of the shortest path is large and there is no problem if packets are concentrated on that path. In this experiment, the problem that occurs with OSPF was solved by the proposed method. Load balancing using the proposed method can be effective in networks where the path with the largest bandwidth is not too large or where there are multiple paths. Moreover, as the degree of drop in the arrival rate is slow, it is possible to prevent packets from suddenly not arriving even if the load on the network gradually increases.  
OSPF-ECMP also performs load balancing, but the paths are limited to equal cost. Therefore, there is a noticeable difference in performance depending on the number of paths. When the bandwidth of a link that is the optimal path is narrow and a large amount of traffic flows there, local load balancing, such as OSPF-ECMP, may not have a significant effect, as in commodity 3 of Figure 11. The proposed method is not limited to equal cost, but considers paths in the entire network, so the number of paths is larger than in OSPF-ECMP and DFFR. The proposed method also has an advantage in that it uses the entire network without waste.  
When the network is not heavily loaded, OSPF based on the optimal path has a shorter average end-to-end delay. The worst scenario of delay in the proposed method is assumed to be a situation where multiple paths are mostly composed of narrow-bandwidth links and the speed is not high. However, linear programming causes paths to include higher bandwidth links to increase the objective function. In addition, the proposed method selects paths according to a select-type group table. Therefore, links with high bandwidth are often selected, even if they contain some links with low bandwidth. In this experiment, the difference in average end-to-end delay was not significantly larger than that of OSPF. Therefore, such a scenario is not likely to occur. The proposed method using multiple paths will not have worse latency than OSPF using a single path, although latency may increase due to the flow of more traffic than expected, as in commodity 3 in OSPF in Table 5. However, from the perspective of Layer 4 of the OSI reference model, there is a worst-case scenario for delay. When the proposed method is operated with TCP, one packet may flow to another detouring path, but the performance of TCP, like DFFR, is not maintained. It is possible that the window size is exceeded and the next packet is not sent because the acknowledgement (ACK) is not returned. Therefore, we believe that it is effective to operate the proposed method with UDP, which does not perform ordering control or retransmission control. Moreover, such problems can be alleviated by using Quick UDP Internet Connections (QUIC) [21] standardized in HTTP/3 [22]. QUIC communicates in units of streams, in which TCP-like reliability is guaranteed. This means that any delay caused by one packet using a different path will only affect the stream on which the packet resides.  
Today, traffic often spikes at the start of large-scale sporting events or popular social game events. The service is not viable if packet loss occurs at a high frequency on an optimal single path. It is important from the viewpoint of service continuity to increase the packet arrival rate even if some delay occurs.  
This time the path selection was on a static basis with a round-robin. We think that more flexible path control can be achieved by applying optimized multipath (OSPF-OMP) [23] to dynamically allocate paths.