# Markov Chain Model-Based Optimal Cluster Heads Selection for Wireless Sensor Networks
## 5 Performance Evaluation
### Comparison with State-of-the-Art Methods
#### 5.3.3 The Throughput of the Network  
The successful delivery of the data packets at the BS is called the throughput of the network. There is always a tradeoff between the network lifetime and the throughput of the network. The greater the lifetime of the network, the greater is the throughput and vice versa. The Figure 13a describes the comparison of network throughput of the proposed model against SEED, ABC, CEEC, and ZBR. The throughput of MOCHs, SEED, ABC, CEEC, and ZBR is 2,990,000, 2,700,000, 900,000, 2,220,000, and 520,000 data packets, respectively. The throughput of the proposed model is 290,000, 2,090,000, 770,000, and 2,470,000 data packets greater than SEED, ABC, CEEC, and ZBR, respectively. The proposed model has 10%, 70%, 26%, and 82% greater throughput than SEED, ABC, CEEC, and ZBR, respectively. As we discussed earlier, the network with the greater lifetime has the greater throughput. The proposed model has 1095 rounds greater lifetime than SEED; therefore, the proposed model has greater output than SEED. The throughput of the CEEC, and ABC is persuasive due to the longer lifetime. Both these schemes are using the centralized CHs selection methods and saving a lot of network energy, which leads to a longer network lifetime with a greater throughput. While in ZBR the network depletes its resources earlier than expected due to the CHs closer to the BS. The nodes closer to the BS selected as CHs and also working as relay nodes. When these nodes run out of batteries the lagged behind nodes cannot convey their sensed information to the BS and the network collapse resulting a much lower throughput. Figure 13b portrays the network throughput of SEED, ABC, CEEC, and ZBR with different network energies like 0.25 J, 0.75 J, and 1 J. The proposed model performance remains very persuasive with different network energies such as 0.25 J, 0.75 J, and 1 J. We also compare the throughput of the network with varying the node densities. The Tables 6 and 7 reveal the comparison of the throughput of the network with \(N=200\) and \(N= \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**WSN\#**} & \multicolumn{3}{c}{**ABC [9]**} & \multicolumn{3}{c}{**CEEC [15]**} & \multicolumn{3}{c}{**SEED [11]**} & \multicolumn{3}{c}{**MOCHs**} \\ \cline{2-13}  & **FND** & **HND** & **LND** & **FND** & **HND** & **LND** & **FND** & **HND** & **LND** & **FND** & **HND** & **LND** \\ \hline
1 & 23,330 & 30,204 & 37,727 & 40,771 & 73,978 & 89,037 & 431,970 & 606,156 & 613,866 & 197,382 & 250,314 & 611,514 \\
2 & 24,999 & 33,014 & 39,575 & 40,651 & 72,455 & 89,405 & 399,194 & 565,777 & 857,633 & 191,021 & 250,912 & 619,415 \\
3 & 21,315 & 28,074 & 33,601 & 39,979 & 70,099 & 87,547 & 418,648 & 590,185 & 602,940 & 181,715 & 251,178 & 621,472 \\
4 & 21,908 & 29,651 & 36,691 & 41,530 & 70,391 & 87,241 & 418,284 & 564,967 & 583,522 & 198,771 & 252,224 & 615,609 \\
5 & 22,830 & 29,135 & 36,040 & 40,723 & 74,860 & 90,035 & 403,357 & 577,858 & 593,654 & 193,534 & 248,468 & 613,107 \\
**Average** & 22876.4 & 30,015.6 & 36,726.8 & 40,730.8 & 72,356.6 & 88,659 & 414,290.6 & 580,988.6 & 59,6323 & 192,484.6 & 250,619.2 & 616,223.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Total number of data packets received at the BS over simulations of five WSNs (with 200 nodes).