## 4 System Model and Problem Formulation  
### Network Model and Assumptions  
This section presents the network model of the proposed approach. Figure 4 shows the system model consisting of a large-scale wireless sensor network (LS-WSN) with a set of \(N\) stationary sensor nodes embedded in smart bins represented by a set (\(N=\{N_{1}\), \(N_{2}\), \(N_{3}\), \(\ldots\)\(N_{n}\))) and mobile data collector vehicles (\(V=\{D_{1}\), \(D_{2}\), \(D_{3}\), \(\ldots\)\(D_{m}\}\)). The network model consists of segmented group of clusters that are spatially distributed across different unconnected regions. There are three network groups (\(g(g_{1},\,g_{2},\,g_{3})\)), and each group is unconnected to other groups. The network consists of a number of sensors, a set of cluster heads (CHs), and a set of optimal points (OPs) or data collection points (DCPs). CHs are leader nodes that collect data packets from other nodes and transmit them to the DCVs when they arrive at the DCPs. Data transmission to the DCVs occurs via a single-hop mechanism. The sensors in different groups or segments are clustered using the node partitioning algorithm presented in [11]. Each sensor is connected to the CH within its range of communication. Three major actors can be identified in the network, namely the static sensors (smart bins), the data collector vehicles (DCVs), and the base station (BS). The model makes the following assumptions:  
1. All the sensors and CHs are static after deployment;
2. \(N\) number of sensors embedded in the smart bins are scattered across the smart city comprising different groups (\(g\)) and clusters with a set of optimal points. The groups are spatially separated and are not reachable by other groups. However, nodes within the same group are reachable by other nodes in their group and can communicate among themselves;
3. Each DCV is a super-energy mobile collector that is not easily energy-deficient;
4. All CHs are covered by the optimal data collection points (DCPs); \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Approach**} & \multicolumn{2}{c}{**Application in SC**} & \multicolumn{2}{c}{**IoV-Based Approach**} & \\ \cline{2-7}
**Ref.** & \begin{tabular}{c} **Stochastic** \\ **Optimization** \\ \end{tabular} & \begin{tabular}{c} **Metaheuristic** \\ \end{tabular} & \begin{tabular}{c} **Waste** \\ **Management** \\ \end{tabular} & \begin{tabular}{c} **Yes** \\ **No** \\ \end{tabular} & \begin{tabular}{c} **SI-Based** \\ **Approach** \\ \end{tabular} & \begin{tabular}{c} **Energy** \\ **Efficiency** \\ \end{tabular} \\ \hline \begin{tabular}{c} [11] \\ [48] \\ [50] \\ [52] \\ [54] \\ [55] \\ [56] \\ [57] \\ [58] \\ Proposed \\ approach \\ \end{tabular} & \begin{tabular}{c} *** \\ \end{tabular} & \
\begin{tabular}{c} *** \\ \end{tabular} &
\begin{tabular}{c} *** \\ \(*\) \\ \(*\) \\ \(*\) \\ \(*\) \\ \(*\) \\ \(*\) \\ \(*\) \\ \(*\) \\ \(*\) \\ \(*\) \\ \(*\) \\ \(*\) \\ \(*\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of the proposed approach with other SI-based techniques. 5. The DCVs have knowledge of the locations of the CHs and OPs as they traverse the network, starting from the BS, which has the network information and makes it available to the DCVs;
6. Each CH has adequate memory capacity to hold all the data that it transmits to the DCV upon arrival at an OP or DCP;
7. The DCVs move at a fixed speed (\(v\));
8. The sensor nodes are randomly deployed a priori with known locations. Table 3 presents a detailed list of symbols and their descriptions.