## 3 Proposed Multi-Tier Protocol  
In this study, a Non-Residual Modified-Deterministic Energy-Efficient Clustering (NR-MDEC) protocol is proposed that selects cluster heads based on residual energy of nodes [19]. The setup phase is modified as in LEACH, but the steady-state phase is kept the same. The algorithm is modified in such a way that most of the residual energy of WSN nodes are utilized. Each elected CH advertises their privilege to the entire network using four key parameters utilizing Carrier-sense multiple access (CSMA) media access control (MAC) protocol as in LEACH. Every join-request message will contain CM-ID, CH-ID, CM-RE, and the header as its request for \"Standard Request for Comment (RFC)\" [20; 21].  
Hence, the information about residual energy of cluster members will be known to cluster heads which could be used for the rotation of cluster heads in the subsequent rounds. The current round is considered as \(r=m\). After the setup phase, the steady phase would start. The next round of \(r=m+1\) begins with the broadcasting of new identities to the entire network. Identity transaction from BS to CMs can be considered as an equivalent single packet transmission that doesn't contribute much in energy-draining. Thus, it is economical for the health of WSNs and doesn't affect their life span. The entire process continues until the last node dies. It can be observed that, if a protocol starts losing nodes earlier than expected, it is not considered an acceptable scenario. An ideal scenario is required for heterogeneity to generate the M-DEC network structure. In this scenario, the total number of nodes is divided into normal, advanced, intermediate, and advanced-intermediate nodes based on selection probabilities. The simulation parameters of the NR-MDEC protocol algorithm have been selected as shown in Table 1. The weighted probabilities for all the nodes were chosen as given in Table 1. The parameter values in Table 1 were taken from [3; 12].  
Based on deployed virtual stimulation, the following factors have been observed which makes our NR-MDEC protocol desirable:  
1. Election of Cluster Heads is locally decided as per the residual energy of all the cluster members.
2. Each round is independent in itself.
3. The protocol gives an assurance to utilize all the available nodes.
4. MDEC ensures a fixed number of desired cluster-heads.
5. MDEC minimizes the overhead computing costs associated with the CH quest.
6. It maintains stability and avoids failure during packet transmission, due to the regular check of REs.  
\begin{table}
\begin{tabular}{c c c} \hline
**Parameter** & **Description** & **Value** \\ \hline \(m\) & \% of advanced nodes & 0.2 \\ \(x\) & \% of intermediate nodes & 0.2 \\ \(Z\) & \% of advanced-intermediate nodes & 0.1 \\ \(E_{0}\) & Initial energy & 0.5 J \\ \(P_{opt}\) & Optimal Election Probability of a node & 0.1 \\ \(a\) & \% increment in the energy of the advance nodes concerning normal nodes & 3 \\ \(b\) & \% increment in the energy of the intermediate nodes concerning normal nodes & 1 \\ \(ab\) & \% increment in the energy of the advance–intermediate nodes concerning normal nodes & 1.5 \\ \hline \end{tabular}
\end{table}
Table 1: Basic simulation parameters for multi-tier structure