Figures in this section plot performance results for the sensor network with 160 nodes over a 250 meter by 250 meter area. The physical layer loss rate is fixed at 20% in the simulations. The results reported in this section and Section 4.3.2.1 are computed based on the same set of simulations. Section 4.3.2.1 reports the maximum data age and the end-to-end loss rate, and this section reports traffic volume.
Fig. 4.15 and Fig. 4.16 plot the average number of MAC layer packet transmis- sions per round and the average number of bytes transmitted per round with the synchronous aggregation protocols, respectively. In the broadcast-based protocols, each node transmits at most twice for each round. In the unicast-based protocols, however, a successful unicast packet transmission requires at least two MAC layer transmissions, one for the data packet and one for the acknowledgement. As seen in Fig. 4.15, synchronous broadcast-based aggregation sends fewer packets per round than synchronous unicast-based aggregation.
The duration of the transmission interval gets shorter as the sampling period duration τ gets shorter. More packets collide when the nodes in the same ring contend for the channel during the shortened transmission interval. For synchronous unicast-based aggregation, more MAC layer retransmissions are made for packet loss recovery. For synchronous broadcast-based aggregation, more nodes broadcast twice because they do not hear a broadcast that includes their own data from any other node in the same ring. This explains why for both unicast and broadcast-based aggregation, more packet transmissions are made as the sampling rate gets higher.
In broadcast-based aggregation, a node aggregates all data included in the broad- casts it receives from its neighbors. The same sensor value may be included in the aggregates of different nodes. For increasing packet size, while synchronous broadcast-based aggregation sends fewer MAC layer packets per round than syn- chronous unicast-based synchronous aggregation, a larger volume of data is produced by synchronous broadcast-based aggregation. This helps to explain why synchronous broadcast-based aggregation yields poorer performance in this case.
0 200 400 600 800 1000 0 0.5 1 1.5 2
MAC layer packet transmissions per round
maximum data age (in seconds) unicast synch., 3X unicast synch., 4X unicast synch., 8X broadcast synch.
(a) Increasing Packet Size
0 200 400 600 800 1000 0 0.5 1 1.5 2
MAC layer packet transmissions per round
maximum data age (in seconds) unicast synch., 3X unicast synch., 4X unicast synch., 8X broadcast synch.
(b) Fixed Packet Size
Figure 4.15: MAC layer Packet Transmissions per Round of Synchronous Aggregation (real-time, varying τ , N = 160, S = 250m × 250m, PLR = 20%)
10000 15000 20000 25000 30000 35000 40000 0 0.5 1 1.5 2
bytes transmitted per round
maximum data age (in seconds) unicast synch., 3X unicast synch., 4X unicast synch., 8X broadcast synch.
(a) Increasing Packet Size
10000 15000 20000 25000 30000 35000 40000 0 0.5 1 1.5 2
bytes transmitted per round
maximum data age (in seconds) unicast synch., 3X unicast synch., 4X unicast synch., 8X broadcast synch.
(b) Fixed Packet Size
Figure 4.16: Bytes Transmitted per Round of Synchronous Aggregation (real- time, varying τ , N = 160, S = 250m × 250m, PLR = 20%)
Fig. 4.3(a) shows that the end-to-end loss rate gets higher as the sampling rate gets higher. The end-to-end loss rate for the point with the lowest maximum data age in Fig. 4.16(a) are above 20%. Note that the corresponding results for that point are not plotted in Fig. 4.3(a). As more packets are dropped, the redundancy caused by multiple routing is reduced for broadcast-based aggregation, and the average number of values inluded in each aggregate decreases (packet size decreases accordingly in the case of increasing packet size). While the average number of MAC layer packet transmissions per round keeps increasing as the sampling rate gets higher, for in- creasing packet size, the average number of bytes transmitted per round increases
first and then starts to drop as the sampling rate gets higher, as seen in Fig. 4.16(a). Fig. 4.17 and Fig. 4.18 plot the average number of MAC layer packet trans- missions per round with the asynchronous aggregation protocols as a function of the maximum data delay and τ , respectively. Similarly, in asynchronous broadcast-based aggregation, each node broadcasts at most twice for each round. In asynchronous unicast-based aggregation, a successful unicast packet transmission requires at least two MAC layer transmissions. For both fixed and increasing packet size, asyn- chronous broadcast-based aggregation sends fewer packets per round than unicast- based asynchronous aggregation.
Fig. 4.18 shows that more packets are transmitted as the sampling rate gets higher. For asynchronous unicast-based aggregation, more MAC layer retransmis- sions are made to recover packet losses due to collisions. For asynchronous broadcast- based aggregation, more nodes transmit twice because they do not hear a broadcast transmission that includes their own data from any other node.
Fig. 4.19 and Fig. 4.20 plot the average number of bytes that are transmitted per round with the asynchronous aggregation protocols as a function of the maximum data delay and τ , respectively. While for both fixed and increasing packet size, fewer MAC layer packets are transmitted by asynchronous broadcast-based aggregation, a larger volume of data is produced by asynchronous broadcast-based aggregation in the case of increasing packet size, owing to the fact that the same sampling value may be included in multiple aggregates. This helps to explain why in Fig. 4.5, asynchronous broadcast-based aggregation yields poorer performance than its unicast-based counterparts for increasing packet size. Fig. 4.5(a) and Fig. 4.19(a) show that the highest end-to-end loss rate for the points plotted in these two figures is around 10%. In Fig. 4.16(a), it is observed that the average number of bytes transmitted per round with synchronous broadcast-based aggregation increases first and then starts to drop as the sampling rate gets higher in the case of increasing packet size. This phenomenon is not observed in Fig. 4.19(a) because the end-to-end loss rate is not high enough to reduce the redundancy caused by multiple routing for asynchronous broadcast-based aggregation in this case.
0 200 400 600 800 1000 0 0.5 1 1.5 2
MAC layer packet transmissions per round
maximum data age (in seconds) unicast asynch., 3X unicast asynch., 4X unicast asynch., 8X broadcast asynch.
(a) Increasing Packet Size
0 200 400 600 800 1000 0 0.5 1 1.5 2
MAC layer packet transmissions per round
maximum data age (in seconds) unicast asynch., 3X unicast asynch., 4X unicast asynch., 8X broadcast asynch.
(b) Fixed Packet Size
Figure 4.17: MAC layer Packet Transmissions per Round of Asynchronous Aggregation (real-time, varying τ , N = 160, S = 250m × 250m, PLR = 20%)
0 200 400 600 800 1000 0 0.2 0.4 0.6 0.8 1
MAC layer packet transmissions per round
τ (in seconds) unicast asynch., 3X unicast asynch., 4X unicast asynch., 8X broadcast asynch.
(a) Increasing Packet Size
0 200 400 600 800 1000 0 0.2 0.4 0.6 0.8 1
MAC layer packet transmissions per round
τ (in seconds) unicast asynch., 3X unicast asynch., 4X unicast asynch., 8X broadcast asynch.
(b) Fixed Packet Size
Figure 4.18: MAC layer Packet Transmissions per Round of Asynchronous Aggregation as a Function of τ (real-time, N = 160, S = 250m × 250m, PLR = 20%)