# Time and Energy Efficient Relay Transmission for Multi-Hop Wireless Sensor Networks
## 4 Performance Evaluation
### Scenario 1-The Cluster Tree Topology with the Fixed Depth(=2)  
Figure 20 shows the delivery ratio as a function of the traffic load in the network. In this simulation, we define the traffic load to the number of data frames transmitted by devices during the BI. In this simulation, all leaf nodes transmit data frames to the PAN coordinator, and the PAN coordinator transmits data frames to the selected leaf node. Also, we fixed the number of devices in the network to 30. As shown in Figure 20, the delivery ratio of the cluster-tree protocol and the ASLEEP protocol decrease as the traffic load on the network increases. This result is related to the fact that the contention for the channel access and the collision probability increases as the traffic load on the network increases. In Figure 20, because the ASLEEP protocol can slightly adjust the superframe duration within the limited bounds, it can provide the transmission probability higher than the cluster-tree protocol. Therefore, the ASLEEP protocol provides the performance of the delivery ratio higher than the cluster-tree protocol. However, as the traffic load increases, the superframe duration of the ASLEEP protocol reaches the envelope and cannot avoid the increased competition. Thus, the performance of the ASLEEP protocol declines largely. Meanwhile, in the proposed scheme, a coordinator does not contend with other leaf nodes for the channel access since it relays data frames to the next hop coordinator in the CFP. Therefore, the proposed scheme shows the similar delivery ratio regardless of an increase of the traffic load, and we can show that the delivery ratio of the proposed scheme is higher than two legacy protocols. Figure 21 shows the delivery ratio as a function of the number of devices in the network. Figure 20: The delivery ratio versus the traffic load in the network. In this simulation, the traffic load in the network is fixed to 5. As shown in Figure 21, when the number of devices in the network increases, the delivery ratio of two legacy protocol decreases. This result is because the probability of correct delivery to the next hop reduces due to the increased collision probability. The ASLEEP protocol provides the transmission probability higher than the cluster-tree protocol, but it cannot remove the increased contention. Figure 21 shows that the proposed scheme provides the performance of the delivery ratio higher than two legacy protocols regardless of the node density. In the proposed scheme, when the coordinator relays data frames to the next hop device in the proposed protocol, it transmits data frames in CFP. Thus, it does not contend with other devices for the channel access and is influenced less by the node density. Therefore, the proposed scheme provides better delivery ratio than two legacy protocols. Figure 22 shows the end-to-end delay as a function of the traffic load in the network. In this simulation, the number of devices in the network is fixed to 30. As illustrated in Figure 22, when the traffic load on the network increases, the end-to-end delay of two legacy protocols also increases. This result is related to the fact that messages are queued at each parent node for the duration of the active period before they can be forwarded up to the tree. In other words, in two legacy protocols, when the traffic load on the network increases, the contention among devices is intense for the channel access, and the possibility to relay data frame in the same superframe is lower. However, the ASLEEP protocol  
Figure 21: The delivery ratio versus the number of devices in the network. Figure 22: The end-to-end delay as a function of the traffic load in the network. can slightly regulate the superframe duration, and it can reduce the end-to-end delay somewhat. Meanwhile, in the proposed scheme, because the coordinators can relay data frames to the next hop devices in CFP, it can provide the constant end-to-end delay regardless of the traffic load. Therefore, the end-to-end delay of the proposed scheme is superior to two legacy protocols.