DE LA BIOPOLÍTICA DE LA POBLACIÓN AL GOBIERNO DE LA CONDUCTA

The first group of simulations is to investigate the relationship among,δand the energy

cost. The energy costs for different operations are calculated respectively with different

andδ. The results are shown in Fig.3.6(a), Fig.3.6(b), Fig.3.6(c) and Fig.3.6(d). All the four

figures show that the energy cost increases with the decline of and δ since more sample

data are needed when the specified precision is high.

The second group of simulations is to compare the total payload size of the transmitted packets between the naive sampling algorithm and the USC algorithm during the process of broadcasting the sampling information. The results are shown in Fig.3.7. According to the

frequency rank distinct count quantile 100 101 102 103 104 105 106 107 different operations

total payload size (Byte)

USC

naive sampling algorithm

Figure 3.7. The data flow comparison

frequency rank distinct count quantile

0 100 200 300 400 500 600 different operations

energy cost mJ/Byte

USC algorithm simple distributed algorithm centralized algorithm

Figure 3.8. The energy cost comparison

results, the USC algorithm has much smaller total payload size since the payload of packets transmitted in the USC algorithm only contains the sample size in each cluster rather than the IDs of all the sampled nodes. Therefore, the total energy cost of the USC algorithm is largely reduced comparing with the naive sampling algorithm.

The third group of simulations is to compare the energy cost between the USC algorithm,

the simple distributed algorithm and the centralized algorithm. We set = δ = 0.2. The

results are shown in Fig.3.8, which indicate the USC algorithm has the least energy cost among all the three aggregation algorithms. Furthermore, since data are aggregated during transmission, the energy cost of the simple distributed algorithm is much smaller than that of the centralized one.

The forth group of simulations investigates the relationship between the packet loss rate and the energy cost. In this group of simulations, the packet loss rate of data transmission

between two sensor nodes changes from 0 to 0.9 and we set = δ = 0.2. We use the stop-

and-wait protocol [62] to do retransmission to make sure the sink node could still receive the sensory data. The results are shown in Fig.3.9. The results indicate that for both the USC algorithm and the simple distributed algorithm, their energy cost increases with the increase of packet loss rate due to additional packet retransmission. However, the energy cost for the USC algorithm is still much smaller than that of the simple distributed algorithm, which means the USC algorithm has high performance even when the pocket loss rate is

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

101

102

103

104

packet loss rate

energy cost (mJ/Byte)

USC

simple distributed algorithm

(a) Frequency 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 101 102 103 104

packet loss rate

energy cost (mJ/Byte)

USC

simple distributed algorithm

(b) Rank 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 101 102 103 104

packet loss rate

energy cost (mJ/Byte)

USC

simple distributed algorithm

(c) Distinct-count 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 101 102 103 104

packet loss rate

energy cost (mJ/Byte)

USC

simple distributed algorithm

(d) Quantile

Figure 3.9. The relationship between packet loss rate and the energy cost.

high, and the energy cost of the simple distributed algorithm is almost the same for the four operations. The reason is that the simple distributed algorithm needs to collect all the sensory data, while the USC algorithm only needs to transmit a sample in the network. Thus, the number of data packets transmitted by the USC algorithm is quite smaller, so that the retransmitting times of the USC algorithm is also much smaller compared with the simple distributed algorithm when a packet is missing. Finally, the energy consumed by the USC algorithm is much less than that of the simple distributed algorithm.

The fifth group of simulations is about the energy cost in small scale networks. The

100 150 200 250 300 350 400 450 500 4 6 8 10 12 14 16 18 20 network size

energy cost (mJ/Byte)

USC frequency USC rank USC distinct count USC quantile simple distributed algorithm

Figure 3.10. Energy cost comparison for small scale network

frequency rank distinct count quantile

0 5 10 15 20 25 different operations

energy cost (mJ/Byte)

Grid LEACH

Figure 3.11. Energy cost comparison for different clustering methods

size varies from 100 to 500. Based on the results, the energy costs of the USC algorithm is still smaller than that of the simple distributed algorithm even in small-scale networks since it only uses the sample data instead of the raw sensory data to process queries. Furthermore, the energy cost of the USC algorithm increases slowly with the growth of network size, which also verifies that our USC algorithm is suitable for large scale networks.

In the sixth group of simulations, another famous clustering method, LEACH [63], is considered. The results are shown in Fig.3.11. We can see that the USC algorithm consumes low energy to deal with the four aggregation operations when different clustering methods are employed.