# Time and Energy Efficient Relay Transmission for Multi-Hop Wireless Sensor Networks
## 4 Performance Evaluation
### Scenario 2-The Cluster Tree Topology with the Variable Depth  
The tree depth is one of the major factors that influence the network performance. Therefore, in this subsection, we evaluate the network performance of three protocols according to the tree depth. In this simulation, the traffic load in the network is fixed to 5, and the number of devices in the network is fixed to 50. Figure 26 shows the delivery ratio as a function of the tree level in the network. As shown in Figure 26, the delivery ratio of three protocol decrease as the tree level of the network increases. In particular, the network performance of two legacy protocols decreases largely. This result is related to the fact that the contention for the channel access and the frame error probability increases as the tree level of the network increases. In Figure 26, 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, because coordinators in the ASLEEP protocol also contend with other leaf nodes, the frame error rate or the collision increases according to the increase of the tree level. Thus, the performance of the ASLEEP protocol decreases 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. However, the frame error rate of the end-to-end link increases as the tree level of the entire network increases. Therefore, the delivery ratio  
Figure 25: The energy consumption as a function of the number of devices in the network. of the proposed scheme is inversely proportional to the tree level of the network, but the proposed scheme is superior to two legacy protocols. Figure 27 shows the end-to-end delay as a function of the tree level in the network. As illustrated in Figure 27, when the tree level of the network increases, the end-to-end delay of three protocols also increases but the end-to-end delay of the proposed protocol does not increase greatly. This result is related to the fact that messages are queued at each parent node until they can be forwarded to the next coordinator or the destination node. In other words, in two legacy protocols, when the tree level of the network increases, the contention among devices and the frame error rate increase, and the possibility to relay data frame in the same superframe is lower. Meanwhile, in Figure 27, as the tree level of the entire network increases, the end-to-end delay of the proposed protocol also increases since the frame error rate of the end-to-end link is proportional to the tree level of the network. However, in the proposed, because the coordinator using the proposed scheme can relay the data frame without the contention, the performance of the proposed scheme is superior to two legacy protocols. Figure 28 shows the energy consumption as a function of the tree level in the network. Figure 27: The end-to-end delay as a function of the tree level in the network. Figure 26: The delivery ratio as a function of the tree level in the network. As shown in Figure 28, apparently, the proposed protocol obtains the lowest energy consumption. In two legacy protocols, the contention overhead for the channel access increases and the channel listening occurred by the contention or the retransmission by the collision increases as the tree level of the network increases. Thus, the energy consumption of the device that uses the IEEE 802.15.4 standard or the ASLEEP scheme increases in proportion to the tree level of the network. Of course, the energy consumption of the proposed scheme is proportional to the increase of the tree level. However, the energy consumption of the proposed scheme is superior to the energy consumptions of two legacy protocols.