## 2 Related Work
\begin{array}{ll}\frac{p_{mm}}{1-p_{max}\times\left(r\ mod \frac{1}{p_{mm}}\right)},&if\ n_{mm}\in G\prime\\ 0,&otherwise\end{array} \right. \tag{17}\]  
\[T(n_{adv})=\left\{ \begin{array}{ll}\frac{p_{adv}}{1-p_{adv}\times\left(r\ mod \frac{1}{p_{adv}}\right)},&if\ n_{adv}\in G\prime\\ 0,&otherwise\end{array} \right. \tag{18}\]  
where \(G^{\prime}\) is non-cluster head nodes. SEP algorithm performs better than the LEACH, since advanced nodes extra energy is consumed in balance, thus enhancing the network stability period. Node heterogeneity is another interesting challenge for researchers. The authors in [31] presented a routing algorithm with hybrid link communication for heterogeneous WSN, named zonal-stable election protocol (Z-SEP), where the concept of zonal field deployment of nodes in the network is introduced. In addition, nodes communication is implemented in hybrid mode, where normal nodes communicate with the sink or base station directly, while advanced nodes are clustered and transmit data to BS through cluster heads. Simply saying, nodes in the deployed network area are separated into three fields: normal nodes are allocated in zone 1 and advanced nodes are placed in zone 2 and zone 3. Sensor nodes in zone 1 deliver data to the base station directly, whereas nodes in zone 2 and zone 3 via cluster head. As in SEP \(m\) is a subset of entire nodes \(n\) with \(\alpha\) times extra energy. Thus, \((1-m)n\) of normal nodes. \(K_{opt}\) is an optimum number of cluster heads. And according to SEP algorithm, cluster head probability is \(p_{opt}=K_{opt}\):  
\[p_{opt}=\frac{K_{opt}}{n} \tag{19}\]  
The threshold value for cluster head selection in Z-SEP is as in LEACH protocol:  
\[T(n)=\left\{ \begin{array}{ll}\frac{p_{opt}}{1-p_{opt}\left(r\ mod\frac{1}{p_ {opt}}\right)},&if\ n\in G\\ 0,&if\ n\
otin G\end{array} \right. \tag{20}\]where \(G\) indicates sensor nodes which are not assigned as a cluster head in the past 1/_p_\({}_{opt}\) rounds. Thus, the probability for advanced nodes to be elected as a cluster head is:  
\[p_{adv}=\frac{p_{opt}}{1+\alpha m}(1+\alpha) \tag{21}\]  
and the threshold value is:  
\[T(adv)=\left\{ \begin{array}{cc}\frac{p_{adv}}{1-p_{adv}\left(r\ mod\frac{1}{P _{adv}}\right)},&if\ adv\in Gt\\ 0,&otherwise\end{array} \right. \tag{22}\]  
where \(G\)' denotes nodes that are not assigned as a cluster head in the last 1/_p_\({}_{adv}\) rounds. Z-SEP has the same cluster formation procedure as in parent protocols like SEP and LEACH, where the cluster head election, further its message broadcasting and cluster members respond to cluster head are based on RSSI signal and the data transmission to cluster head is based on TDMA schedule. Clustering is not performed in regular normal nodes because they have lower initial value in energy than in extended advanced nodes, since the energy consumption in clustering is high enough. Normal nodes die quickly if clustering is performed among them, resulting a bad stability period. Therefore, they are assembled near to BS and communicate with it directly, while advanced nodes are far from BS because of their higher energy. So, vise a versa, advanced nodes will exhaust faster if data transmission to BS is done in direct mode, because energy consumption is high due to long distance. Thus, to save energy in advanced nodes, clustering method is applied. However, Z-SEP does not take into account the remaining residual energy of nodes when choosing it as a cluster head, thus there is a possibility that a node with a low residual energy will be chosen as a cluster head in the upcoming round, which ultimately can lead to a rapid depletion of the selected cluster head and an imbalance of the entire network.