## 3 Problem Statement
### Proposed Method
\(\beta\) represents the bandwidth factor, reflecting its importance or contribution in the network's functioning. \(k\) is associated with latency, demonstrating how latency affects the network's performance or decisions. \(\tilde{\gamma}\) corresponds to the number of steps, which is considered as a heuristic function in the model. This reflects the role of the number of steps taken in the network's operation or algorithmic process. \(\tau\) denotes the weight given to pheromones, a concept often used in optimization algorithms like ACO algorithm, indicating their significance in the network's routing or decision-making process. \(D_{ijd}\) indicates the bandwidth, providing a measure or value related to the bandwidth available or used between two points in the network. \(E_{IID}\) stands for the energy parameter, signifying the energy consumption or requirement for network operations between specific points. **Step 5: Pheromone Updates for Optimal Path Selection:**Pheromone Update Formula:  
For efficient routing, pheromone levels are updated:  
\[\tau_{ij}(t+1)=(1-p)\tau_{ij}(t)+\Delta\tau_{ij} \tag{16}\]  
where \(\rho\) is the pheromone evaporation rate and \(\Delta\tau_{ij}=\frac{Q}{L_{ij}}\) with \(Q\) representing a pheromone reinforcement constant and \(L_{ij}\) the path length. This update strengthens the likelihood of choosing reliable paths, balancing the network load. **Step 6: Congestion Detection and Management:**  
**Congestion Detection:**  
Measure congestion \(C_{i,j}\) on each link \((i,j)\):  
\[C_{i,j}=\frac{Data\ flow_{i,j}}{Link\ capacity_{i,j}} \tag{17}\]  
If \(C_{i,j}\) exceeds a threshold, the link is marked as congested, and alternative routes are considered. Minimizing Congestion:  
An objective function \(Z\) minimizes congestion across the network:  
\[Minimize\ Z=\sum_{i=1}^{n}\sum_{j=1}^{n}C_{ij}X_{ij} \tag{18}\]  
\(X_{ij}=1\) if the link is used, 0 otherwise. **Step 7: Route Performance Evaluation**  
Traffic Handling Efficiency:  
The route's efficiency in managing data traffic is evaluated using a congestion parameter \(C_{ij}\), as follows:  
\[P_{transmit}=P_{0}\bigg{(}\frac{d_{i,BS}}{d_{0}}\big{)}\gamma \tag{11}\]0  
A route is considered efficient if \(C_{ij}\) is within acceptable limits, meaning it can handle the data flow without excessive delays. Reliability of Data Delivery:  
To ensure reliable delivery, we evaluate the probability of successful delivery \(P_{delivery}\) from a source node \(S\) to the CH. This is typically based on factors like residual energy and link quality:  
\[P_{transmit}=P_{0}\bigg{(}\frac{d_{i,BS}}{d_{0}}\big{)}\gamma \tag{11}\]1  
where \(P_{loss,ij}\) is the probability of packet loss on link \((i,j)\) along the path. A higher \(P_{delivery}\) value indicates a more reliable route. **Step 8: Identifying Optimal Path and Traffic Distribution**  
Objective Function for Minimizing Congestion:  
The goal is to identify a route with minimal congestion while distributing traffic across the network. This is achieved by minimizing the congestion-based objective function \(Z\):  
\[P_{transmit}=P_{0}\bigg{(}\frac{d_{i,BS}}{d_{0}}\big{)}\gamma \tag{11}\]2  
\(C_{ij}\) represents the \(CF\) on link \((i,j)\) and if \(X_{ij}=1\) the link \((i,j)\) is used in the selected path, and \(X_{ij}\) otherwise. Traffic Selection (TS) Algorithm for Load Balancing:The TS algorithm identifies the path that minimizes \(Z\) and checks each link's traffic load. If the load on a link exceeds 70% of its capacity, it is marked as congested and added to a congestion list (Algorithm 1). For each link \((i,j)\), the algorithm evaluates:  
\[P_{transmit}=P_{0}\bigg{(}\frac{d_{i,BS}}{d_{0}}\big{)}\gamma \tag{11}\]3  
```
1. for each node \(i\) in range (1, \(N\)):
2. deploy node \(i\) randomly within \(M\)\(\times\)\(M\) area
3. set initial energy \(E_{residual,i}(t)=E_{0}\)
4. for each time \(t\):
5.