## 5 Simulation Results
### Data aggregation  
The performance of IRDT with the data aggregation function is shown in Figure 15, where the number in the label denotes how many data packets can be included in a single aggregated data packet. Immediately after the reception or generation of data, each node waits for 5.0 s for aggregation without forwarding. When the intermittent interval is 1.0 s, the packet collection ratio increases with data aggregation (up to two data packets), after which it deteriorates with aggregation of three or more data packets. At an intermittent interval of 0.1 s, data aggregation always decreases the collection ratio since large data packets are likely to collide with ID packets. Moreover, the loss of aggregated data packets greatly decreases the collection ratio. In summary, our conclusion on the collection ratio is that aggregation of up to two data packets is effective in terms of avoidance of SREQ collisions, while aggregation of three or more packets is disadvantageous.  
The maximum and the average energy consumption in all cases other than '0.1 s (3)' decreases as the number of aggregated data packets increases [Figure 15(b) and 15(c)]. However, when the packet generation rate is low, data aggregation seldom occurs during the waiting time of 5.0 s, and the energy efficiency does not increase considerably.  
Note that the increase in average energy consumption for the '0.1 s (3)' case indicates that the increase in retransmissions due to ID collisions increases the number of data retransmissions everywhere in the network. For aggregation of up to three data packets when the packet generation rate is 0.030, a reduction in the maximum energy consumption of 83% and a reduction in the average energy consumption of 77% can be attained at an intermittent interval of 1.0 s. Moreover, the respective reduction of the maximum and the average energy consumption is 60% and 10% at an interval of 0.1 s. These improvements are achieved in particular by forwarding data to sideward nodes, which effectively suppresses SREQ collisions in nodes adjacent to the sink.  
Combinations of intermittent interval setting and data aggregation  
We compare the performance of IRDT with both the proactive collision avoidance method and data aggregation with that of EA-ALPL [9] as described in Figure 16, where data aggregation is limited to two data packets to prevent the packet collection ratio from decreasing. To conduct a fair comparison, EA-ALPL also uses data aggregation and an appropriate intermittent interval which minimizes the energy consumption (although it does not minimize packet collisions). However, due to the MAC layer protocol (B-MAC) of EA-ALPL, the intermittent interval is limited to 8 values (10, 20, 50, 100, 200, 400, 800, 1600 ms) [4]. Therefore, out of these eight values, EA-ALPL selects the value that is closest to the appropriate interval.  
Figure 15: Performance with data aggregation.  
The results show that IRDT attains a higher collection ratio than EA-ALPL. In addition, IRDT has lower maximum and average energy consumption at all times, as seen in Figure 16(b). Specifically, the maximum and the average energy consumption at a packet generation rate of 0.002 can be reduced by 61% and 38%, respectively, although those at a packet generation rate of 0.030 can be reduced by only 0.1% and 45%, respectively. Moreover, a 90% reduction of the maximum energy consumption and an 84% reduction of the average energy consumption is achieved as compared with the original IRDT at an intermittent interval of 1.0 s. It is important to lower the maximum energy consumption for long-term operation of the network, and in this regard the avoidance of control packet collisions is highly efficient.