Improving the Performance of Hierarchical Clustering Protocols with Network Evolution Model

Abstract

In distributed computing, clustering of the nodes is generally used to make the communication process energy-efficient. However, in the mechanics of clustering, the number of clusters increases as the energy of the nodes gets depleted. This dispersive nature of clustering probability leads to the quick death of the nodes. This chapter explains the usage of an optimization matrix from clustering probability as obtained from a network evolution model. The proposed framework of an optimization matrix shows considerable promise in boosting the efficiency of data delivery and network lifetime of the hierarchical clustering protocols in wireless sensor networks.

Appendices

Appendix A

The Optimization Matrix is a spreadsheet-based numerical analysis for the changing of the alive nodes in the experiment. We would discuss the matrix with reference to the figure. The columns B and C represent the number of connections per cluster and the corresponding probability as calculated by Eq. 1. Moreover, rest of the columns are the multiplication of the corresponding probability (due to connections) to the number of nodes. In this way the cells are populated and the matrix is created.

In order to plot the cluster heads for example in case of variable clustering LEACH-C we get the following results from Table 6 which is plotted in optimization matrix as yellow. Similarly we plot the original LEACH-C with the following results from the Table 6 and the plot is shown in cyan.

We can see that the plot is along the diagonal lines, these lines implies that the system is taking the longest performance path. Due to rapidly changing cluster heads the setup phase of LEACH-C do not perform if the schema of changing cluster heads are done above the yellow line as seen in the optimizing matrix.

If we attempt to move below the green line, it is against the system under consideration because the LEACH-C protocol operates with decreasing number of alive nodes. It also is seen that the sum of all the cluster heads produced along the green line is lowest as compared with the previous sums obtained at the preceding rows. Thus in the number of (alive node - cluster) space this green line is the optimized cluster head varying scheme.

Appendix B

Systematic Cluster Head Variation Scheme-I:

As the total number of Clusters are obtained as N_C = p* Total Number of Alive nodes (Na). And the p(probability of clustering) can be obtained with the value of k = ((total number of alive nodes(Na))/(desired number of CH(n))) − 1.

Mathematically the expression is written as

$$ \begin{aligned} {\text{Nc}} & = \frac{1}{2}\left[ {\sqrt {\frac{k + 3}{k - 1}} - 1} \right] * {\text{Na}} \\ {\text{Nc}} & = \frac{1}{ 2}\left[ {\sqrt {\left( {\left( {\frac{Na}{n} - 1} \right) + 3} \right)/\left( {\left( {\frac{Na}{n} - 1} \right) - 1} \right) - 1} } \right]*{\text{Na}} \\ \end{aligned} $$

Clearly, it can be seen that the relationship is not linear. Hence it attributes for long path movement in the Nc vs Na workspace (yellow in Fig. 8).

Systematic Cluster Head Variation Scheme-II:

As the total number of Clusters are obtained as N_C = p* Total Number of alive nodes (Na). And the p(probability of clustering) can be obtained with the value of k = ((total number of nodes(N))/(desired number of CH)) – 1.

Similarly, in this case we have,

$$ {\text{Nc}}\; = \; \frac{1}{ 2}\left[ {\sqrt {\left( {\left( {\frac{N}{n}\; - \;1} \right)\; + \;3} \right)/\left( {\left( {\frac{N}{n}\; - \;1} \right)\; - \;1} \right)\; - \;1} } \right]\; * \;{\text{Na}} $$

The above equation clearly shows the linear relation between Nc vs Na. Therefore, the shortest path movement can be observed in Nc vs Na workspace (green in Fig. 8).

From the above two schemes, scheme-II provides a better optimization and use of the sensor node energy during LEACH clustering, which can be visualized in Fig. 8.

Appendix C

See Tables 8 and 9.

Table 8. Theoretical calculation of the number of cluster head of 100 node network assuming in calculation as for example (4.2 as 4 and 4.6 as 5 i.e. set value wrt +0.5). Clearly we observe that at 7^th row violates the number between 1^st column and 5^th column.

Table 9. Theoretical calculation of the number of cluster head of 200 node network assuming in calculation as for example (4.2 as 4 and 4.6 as 5 i.e. set value wrt +0.5). Clearly we observe that at 7^th row violates the number between 1^st column and 5^th column.