## 3 Problem Formulation  
There are \(n\) SMs \(X\) for electrical energy measurements distributed in a georeferenced area \(A\), \(A(n)\). With Algorithm 1, Nearest-Neighbor Spanning Tree (N-NST), the clusters are formed and using Algorithm 2, Optimal Delay Balancing (ODB), the SM is selected that will become the head of the \begin{table}
\begin{tabular}{c c c} \hline
**Item** & **Parameter** & **Value** \\ \hline \multirow{2}{*}{Deployment} & Node density & 4734 nodes/km\({}^{2}\) \\  & Node placement & Georeferenced \\  & No. of nodes per cluster & m [8; 14; 20; 27; 32] \\  & Coverage WiFi & \(r_{d}\) 60 m \\  & Coverage cellular & \(r_{d}\) 1000 m \\ \hline \multirow{2}{*}{PHY} & Standard & IEEE 802.11b \\  & Frequency band & 24 GHz \\  & Transmission rates & [0.5, 1, 2, 5, 11 Mbps \\ \hline \multirow{2}{*}{MAC} & Standard & IEEE 802.11b \\  & & 3 G, 4 G, 5 G \\  & Operation mode & _Tree_ \\ \hline \multirow{2}{*}{APP} & Application layer data length & \multirow{2}{*}{\(L\) 100 bytes/packet} \\  & Packet rate & \multirow{2}{*}{_Lambda_ [0.001, 0.01, 0.1, 0.2, 0.5] packets/s} \\ \hline \end{tabular}
\end{table} 
Table 1: Simulation model and parameter. group (UDAP) \(Z\). Each cluster has a capacity to group until \(m\) SMs. We assume that the maximum range of bidirectional transmission of intra-cluster data is \(r_{ds}\) and the maximum range of bidirectional data transmission of inter-cluster data is \(r_{db}\). That is to say, any intra-cluster and inter-cluster length, the haversine distance \(r_{ni}\) and \(r_{ns}\) of which is within \(r_{ds}\) and \(r_{db}\), respectively, can communicate between each other. The \(X\) and \(Z\) that do not reach the maximum haversine distance allowed in a single jump will do so with multiple jumps until being able to transmit the respective data packages. The multiple breaks are restricted by \(w\), which is the maximum number of jumps allowed. It is worth mentioning that an SM will not be able to transmit its data directly to the BSs. Therefore, the use of a node of transition UDAP (head of each group) is of vital importance to comply with that function. Since UDAP has physically two slots to hold dual wireless and cellular cards, it is able to receive the information transmitted from the access of single SMs to WiFi technology and merge the information to retransmit these data further to the nearest cellular access BSs. Therefore, the allowed breaks will be performed only between intra-cluster SMs or between UDAPs; mainly to transmit the data to the closest BSs to finally send it, via optical fiber, to the central office where the information will be processed. Consequently, the link between each of the vertices (SMs, UDAPs, BSs, central office) can be represented by an adjacency matrix. This matrix indicates the pairs of vertices that are related or not by a link or edge in the graph. In addition, the adjacency matrix is a binary matrix (0, 1) with zeros in its diagonal. It stores one when there is an edge from the vertex \(i\) to the vertex \(j\) and zero when there is no edge. Initially, all \(X\) are candidate \(Z\) with a cost \(C_{1}\). Once having identified the clusters and the transition nodes \(Z\), the links are created at \(C_{2}\) cost. Due to this, it eliminates the need for all X to be Z. This happens because cellular links are deleted at a cost \(C_{1}\) and links to WiFi are added at a cost \(C_{2}\), ensuring the 100% observability of the SMs deployed. Subsequently, the UDAP merges the data and sends them to the BSs. Once the data are merged in the BSs, they will be transmitted through optical fiber to the central office with a cost \(C_{3}\) (see Figure 1). The \(C_{1}\), \(C_{2}\) and \(C_{3}\) variables are identified as unit costs for each type of technology: cellular, WiFi and optical fiber, respectively. In addition, it should be noted that \(C_{3}>>C_{1}>>C_{2}\). Table 2 presents a summary of the variables used in the model.