We did the following experiments at the same condition. There are three subjects we focused on: network lifetime, average distance to cluster head and energy dispersion. We will show the experiment results first and then analyze the reason of the results.
Figure 4-2: Round test with 100 nodes
Figure 4-3: Round test with 250 nodes
In figure 4-2 and 4-3, we showed the network lifetime under 100 nodes and 250 nodes. It is obvious that C-BEET can live longer time than HEED and LEACH. C-BEET is almost two times longer than LEACH and 1.33 times longer than HEED. LEACH uses random head selection without considering energy dispersion seriously so the first node dead time is earlier than HEED and C-BEET. Besides that, LEACH and HEED have to spend more energy than C-BEET while forming a cluster so it infers nodes in C-BEET can live longer.
We can observe that even we add the amount of nodes to 250, the network lifetime is not increased apparently but the first node dead time is delayed because there is more nodes can be selected as head so the energy cost is scattered. For HEED with 250 nodes, the slope of the curve is decreased that means HEED is good at dispersing the energy cost averagely to all the nodes in the field.
1 101 201 301 401 501 601 701 801 901 1001 1101 1201 Rounds
Number of nodes alive
LEACH
HEED
C-BEET
Figure 4-4: Average distance to cluster head with round test
Another factor that can influence the energy usage is the transmission distance while a node sends data to the cluster head. Figure 4-4 shows the variation of average distance to cluster head.
We combined figure 4-2 into this figure. There are two parts in this graph, one is live nodes number and the other is average distance to cluster head. Let’s look at LEACH first, LEACH can keep the average distance at the beginning of the network but as soon as the nodes starts to die, the distance to cluster head increase quickly. Because of the long distance to the cluster heads, nodes in LEACH died quicker at the mid-end of the network. So the curve of live nodes suddenly dropped after the distance to cluster head increased.
The average distance to cluster head in HEED is very stable because the HEED algorithm defines a radius for each node to limit the range of cluster head advertisement. The curve only rises slightly at the end of the network. In C-BEET, the distance is small at beginning and after a time period, the weight of the nearest neighbors are getting higher so the nodes will choose a little farer nodes with less weight. This incurs the average distance to head increase to a stable value and till the network end. Generally, the average distance in C-BEET is less than LEACH and HEED at most of time. The transmission distance is the main factor that influence the energy cost.
We combine the two types of curve so that can present a clear view of the relationship between network lifetime and average distance to cluster head.
0 20 40 60 80 100 120 140 160 180 200 220 240
1 101 201 301 401 501 601 701 801 901 1001 1101 1201
Rounds Average distance to cluster head (0.1M) / Nodes alivefsdfsfdfdsfsdfdsfsdffsdfsdffff
LEACH HEED C-BEET
LEACH_NODE HEED_NODE C-BEET_NODE
In figure 4-5, we present the “Dead rate” of the network. This graph shows the rate of dead node in each round. As we mentioned at the beginning of section 4, we simulated 500 times so the graph is the average value of the experiments. We can see that the peak of LEACH and HEED is higher than C-BEET, it means dead nodes in LEACH and HEED are separated into those rounds which the peak covered. The coverage of the network may be uncompleted because the nodes dead. The network coverage of wireless sensor network is very important because most applications hope that the sensor nodes can cover the field where they want to monitor. If there is somewhere uncovered, some data will be missed.
Unlike LEACH and HEED, the peak of C-BEET is wider so the nodes in C-BEET are dead slower and can keep the network coverage as long as possible. The result shows that the head selection algorithm in C-BEET is much better than other two schemes because C-BEET considers the residual energy seriously and avoids selecting the same node as cluster head frequently.
Figure 4-5: Dead rate of nodes
Dead rate
0.0 0.2 0.4 0.6 0.8 1.0
1 101 201 301 401 501 601 701 801 901 10011101
Rounds
Rate (%) LEACH
HEED C-BEET
Initial
Table 4-2: The comparison of the protocols under different energy
Table 4-2 listed the performance of these schemes under different initial energy. In the former experiments, we set the initial energy to 0.5J per node. We compared to 0.25J and 1J per node here and discovered that the lifetime of the network is almost linearly related to the initial energy. So we can prolong the network lifetime by equip a higher capacity battery to the sensor nodes.
Scheme Node type Cluster construction overhead
Head Send:
Table 4-3: The comparison of the construction overhead for each round
Table 4-3 provides the analysis of cluster construction overhead. The notation p refers to the probability to become a cluster head; N refers to the node number of the network. The analysis showed that in our scheme, sensor nodes only need to receive “Head Information” once. For