# DDS: A Delay-Constrained Duty-Cycle Scheduling Algorithm in Wireless Sensor Networks
## 5 Performance Evaluation
### Evaluation Results
#### 5.3.1 Effects of the Delay Bound  
To investigate the effect of the delay bound on the network performance, the delay bound was varied from 10 s to 50 s. With a longer delay bound, the duty cycle interval increases, since the duty cycle interval is proportional to the delay bound, according to Equation (25). As seen in Figure 3(a), DDS achieves the best performance in terms of the DSR. The results for the DSR indicate that the influence of the delay bound on the achieved DSR of DDS, SROD-MM, SROD-WA, and OGP is not enormous, in contrast to that of OAPF. As the delay bound increases, the achieved DSR from DDS, SROD-MM, SROD-WA, and OGP has a similar trend, which is relatively flat with a small difference (i.e., from 1% to 2%). According to Equation (25), when the delay bound changes, the DSR can remain unchanged by adjusting the duty cycle interval. Thus, DDS can consistently obtain a high DSR. In addition, OGP can achieve a relatively high DSR since a retransmission mechanism is implemented in this algorithm. Meanwhile, the DSR under OAPF dramatically drops from 95.7% to 70.1%. This results from the fact that collisions reduce the packet delivery ratio, leading to a low DSR. With a longer duty cycle interval, when a node wakes up, it can be selected as a forwarder by more than one transmitter. Unfortunately, this node can only relay the packets of one node at that time, and the packets of other transmitters might be dropped because of collisions. In addition, under OAPF, transmitters forward data packets over a short period and do not retransmit when transmission fails. As a result, the packet delivery ratio decreases, which causes the low DSR. Furthermore, DDS, SROD-MM, and OGP satisfy the required DSR, whereas OAPF does not with a delay bound greater than 10 s. Although SROD-WA uses the same approach as SROD-MM, the DSR under SROD-WA is low and does not satisfy the required DSR, because many collisions occur with the high duty cycle interval obtained by SROD-WA. In terms of energy consumption, as shown in Figure 3(b), DDS achieves lower energy consumption than SROD-MM, SROD-WA, OAPF, and OGP when the delay bound is greater than 30 s. For instance, with a delay bound of 50 s, SROD-MM, OAPF, and OGP spend 6.0%, 108.1%, and 116.2% more energy than DDS, respectively. Interestingly, the total energy consumption of the algorithms nonlinearly decreases as the delay bound increases. When the delay bound varies from 10 s to 20 s, the increase in the duty cycle interval leads to a sharp decrease in energy consumption because the total number of active periods for the  
Figure 4: Effects of delay bound on the achieved deadline success ration (DSR), total energy consumption in the network, and average end-to-end (E2E) delay, with required DSR \(\gamma=95\%\) and the event rate at 0.5 packet/s. nodes decreases. On the other hand, when the delay bound increases from 20 s to 50 s, with the larger duty cycle interval, nodes wake up less frequently. In this case, transmitters have to be active for a longer period to wait for their forwarding candidates, which leads to an increase in the total active periods of the transmitters. As a result, power consumption is relatively flat. Since the obtained duty cycle interval under DDS is the smallest, DDS achieves the best energy efficiency. It should be noted that there is a big gap between the energy consumption of DDS and two counterpart algorithms: OGP and OAPF. That is because, under OAPF and OGP, nodes have to transmit data packets via more hops than under DDS. For example, the average hop count for packets under OAPF and OGP is around 4.2 and 4.5, respectively, whereas packets traverse to the sink in 3.3 hops under DDS. With a larger hop count, the number of intermediate nodes that have to forward data increases. Thus, energy consumption for the total active periods of the transmitters under OAPF and OGP is higher than that of DDS. Furthermore, transmitters under OAPF and OGP send more control packets than DDS. Therefore, OAPF and OGP consume more energy.