## 2 Related Work  
This section briefly describes the clustering hierarchical benchmark routing protocols proposed in the literature for homogeneous, two-tier, and three-tier heterogeneous WSNs. These benchmark protocols typically involve random deployment of SNs within the FoI to form a WSN. These protocols are based on the concept of rounds. Each round has two phases: (i) setup phase and (ii) steady-state phase. In the setup phase, the network is divided into clusters, CH are selected for each cluster from the SNs using a stochastic algorithm, and TDMA slots are assigned by the CH to its CMs. In the steady-state phase, CHs gather data packets from their CMs, aggregate the data packets, and send the aggregated data to the BS. The main difference in these benchmark routing protocols is the selection of CH in setup phase. These are discussed one by one, as follows. 1. LEACH [19] is proposed for homogeneous WSNs, where all the SNs have equal initial energy \(E_{0}\). The CH is selected randomly from all the deployed \(N\) number of SNs who belong to a set \(G\) (i.e., set of those SNs which were not selected as CH in the previous \(\frac{1}{p}\) rounds). All those SNs who belong to set \(G\) generate a random number \(n_{i}\) between 0 and 1, and this number is compared with a threshold function \(T(N)\), i.e., \[T(N)= \begin{cases}\frac{p}{1-p\left(r\bmod\frac{1}{p}\right)},&\forall\ N\ e\ G\\ 0,&\text{otherwise},\end{cases} \] (1) where \(N\) is the number of deployed SNs, \(p\) is the predefined probability of CHs in SNs which is \(p=Number\ of\ CH\ devices/Number\ of\ total\ devices\), and \(r\) is the current round number. An SN from set G becomes a CH if \(n_{i}\leq T(N)\); otherwise, CM. 2. In LEACH-C [20], the CH is selected by the BS by considering the remaining energy and location of the SNs. At the end of each round, each SN sends information about its remaining energy and location to the BS. The BS calculates average energy based on the remaining energies of all the SNs. On the basis of the calculated average energy and locations of the SNs, CH is selected for each cluster by the BS. 3. TEEN [22] and LEACH use the same procedure for CH election, but in the case of TEEN, the CH sends the collected data from its CMs to the upper level of cluster (i.e., a cluster of CHs) which has its own CH that collects data and sends them to the next level of cluster. This process is repeated. At the end, only one CH is reporting to the BS. Furthermore, following the TEEN protocol, SNs sense their environment continuously but do not report until the sensed entity or value is greater than the hard threshold (\(H_{t}\)), which is a predefined value. Whenever the sensed value exceeds \(H_{t}\), the SN triggers the transmitter to report the value. This is why TEEN sometimes misses some important information from the FoI. 4. IEE-LEACH [23] considers new threshold function with different probability function of CH selection. The new probability function depends on \(p\), remaining and initial energy of SN which is candidate for CH, average and total energy of WSN, and total number of SNs in the FoI. 5. SEP [21] is the first protocol which considers the two-tier heterogeneity in WSN in terms of different initial energy for normal and advance SNs. Normal SNs have normal initial energy \(E_{0}\), while advance SNs are equipped with relatively higher initial energy than \(E_{0}\). SEP considers the optimal number of CHs, which is derived analytically. Furthermore, SEP defines two different threshold functions for two different types of SNs, i.e., normal and advance, with different probabilities of CH selection. 6. EEECA-THWSN [24] considers three-tier heterogeneity in WSNs which consists of standard, intermediate, and advanced SNs. Standard SNs have lower initial energy than intermediate SNs, and intermediate SNs have lower initial energy than advanced SNs. Furthermore, EEECA-THWSN proposes three different threshold function with there respective probabilities, for standard, intermediate, and advanced SNs.