# Markov Chain Model-Based Optimal Cluster Heads Selection for Wireless Sensor Networks
## 5 Performance Evaluation
### Comparison with State-of-the-Art Methods
#### 5.3.2 The Stable and Unstable Regions in the Lifetime of the Network  
The stability period is defined as, the time interval that begins when the first node depletes its battery. The Figure 12a depicts the comparison of stable and unstable regions of the proposed model with SEED, CEEC, ABC, and ZBR. The first nodes of the MOCHs, SEED, CEEC, ABC, and ZBR drain  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**ABC [9]**} & \multicolumn{3}{c}{**CEEC [15]**} & \multicolumn{3}{c}{**SEED [11]**} & \multicolumn{3}{c}{**MOCHs**} \\ \cline{2-13}
**WSN\#** & **FND** & **HND** & **LND** & **FND** & **HND** & **LND** & **FND** & **HND** & **LND** & **FND** & **HND** & **LND** \\ \hline
1 & 1110 & 1510 & 2156 & 1048 & 1934 & 3047 & 2372 & 3631 & 3724 & 2957 & 3960 & 4927 \\
2 & 1121 & 1571 & 2202 & 1090 & 1950 & 2869 & 2199 & 3421 & 3702 & 2973 & 3884 & 4990 \\
3 & 1094 & 1522 & 1977 & 1088 & 1920 & 2966 & 2299 & 3538 & 3697 & 2859 & 3876 & 4962 \\
4 & 1067 & 1540 & 2209 & 1135 & 1926 & 3005 & 2295 & 3394 & 3637 & 3004 & 3899 & 4952 \\
5 & 1130 & 1512 & 2173 & 1099 & 1987 & 2881 & 2229 & 3492 & 3705 & 2911 & 3968 & 4971 \\
**Average** & 1104.4 & 1531 & 2143.4 & 1092 & 1943.4 & 2953.6 & 2278.8 & 3495.2 & 3693 & 2940.8 & 3917.4 & 4960.4 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Network lifetime over simulations of five Wireless Sensor Networks (WSNs) (with 200 nodes).  
Figure 11: The lifetime comparison of MOCHs with different protocols in terms of rounds with different initial energies of the deployed sensor nodes. (**a**) The analysis of the network lifetime with the number of alive nodes; (**b**) The evaluation of the network lifetime with different energies.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**ABC [9]**} & \multicolumn{3}{c}{**CEEC [15]**} & \multicolumn{3}{c}{**SEED [11]**} & \multicolumn{3}{c}{**MOCHs**} \\ \cline{2-13}
**WSN\#** & **FND** & **HND** & **LND**  
their batteries at about 3055, 2500, 1200, 1500, and 1100 rounds, respectively. The stability period of the proposed model is approximate 19%, 61%, 51%, and 64% greater than SEED, CEEC, ABC, and ZBR, respectively. The stability period is the time duration in which all the sensor nodes are alive and the performance of the network is maximum. The proposed model has very long stable period, because of the good energy management and good energy distribution among all the dynamic clusters. After that, the unstable region starts with the death of the first node. In an unstable region, the nodes run out of batteries and the performance of the network decreases gradually. The unstable period of the proposed model in comparison with SEED, CEEC, ABC, and ZBR is about 1945, 1434, 1754, 869, and 200 rounds greater, respectively. In ZBR due to multi-hop communication, the CHs closer to the BS run out of battery soon compared to the distant CHs. When the CHs closer to the BS deplete their batteries the network un-stabilizes for some time and collapses after 200 rounds. However, in SEED, ABC, and CEEC after the first node run out of battery and the network becomes unstable for the lifetime of the network due to uneven energy distribution. Figure 12b illustrates the network energy consumption of MOCHs, SEED, CEEC, ABC, and ZBR. The energy consumption of the proposed model is optimized and remains smooth in the whole network lifetime. The energy consumption is very low because MOCHs use the available power resources in very optimized and balanced way which increases its lifetime. The energy consumption of SEED is also balanced due to its even energy distribution in the network. The Tables 4 and 5 reveal the comparison of the stable and unstable regions of the network with \(N=200\) and \(N=300\). From the tables, we can see that the proposed model's