## 3 Congestion Recognition Based on the ACA
### Improved ACA and Its Steps  
(1) Modify the heuristic function  
In congestion identification, time delay is chosen as the evaluation index for the optimal path. The traditional ACA, which considers the shortest Euclidean mile distance, no longer meets the desired outcome. In this context, the aim is to assess the path's merits and drawbacks based on the total time delay [23]. To achieve this, the network propagation delay is determined by calculating the ratio of the location distance of the communication network nodes to the packet propagation speed in the network topology system. The network queuing delay and processing delay are obtained using the M/M/1 queuing theory model. The total network delay is composed of these three components [24]. To simplify calculations, the propagation delay and transmission delay can be combined as the transmission delay. Consequently, the original heuristic function is modified, with \(P_{t}\) representing the transmission delay and \(S_{t}\) denoting the queuing delay. During congestion, the value of \(P_{t}\) is significantly lower than \(S_{t}\). The modified heuristic function is as follows:  
\[\eta_{ij}(t)=\frac{1}{P_{t}+S_{t}} \tag{1}\]  
(2) Improved pheromone updating formula  
Upon shifting the focus of the ACA from solving the shortest distance path to solving the shortest delay path, it becomes necessary to update the pheromone formulas [25]. These formulas play a crucial role in guiding the ants' search for optimal paths. To ensure accuracy in representing the desired objective, it is essential to revise the pheromone formulas accordingly. The following pheromone formulas need to be updated:  
\[\tau_{ij}(t+1)=(1-\rho_{0})\times\tau_{ij}(t)+\rho_{0}\times\tau_{ij}(0) \tag{2}\]The given formula represents the local update formula for pheromones. However, to complete the pheromone update process, the global update formula is also required. The global update formula is as follows:  
\[\tau_{ij}(t+1)=(1-\rho_{1})\times\tau_{ij}(t)+\rho_{1}\times\frac{1}{T_{\text{ best}}} \tag{3}\]  
where \(\tau_{ij}(0)\) is the initial concentration of pheromones and \(T_{\text{best}}\) is the total delay of the shortest path in each cyclic search. The steps of the improved ACA are as follows:  
**Step 1:** To conduct the search for the designated network termination node in the total network delay matrix, which includes the transmission delay matrix and the queuing delay matrix, the ACA is employed with Q ants placed on the starting node of the network. The number of ants traversing the network, denoted as \(q\), is typically calculated as 0.6 times the number of network nodes with the result rounded to the nearest whole number. Initially, the number of ants in each cycle is set to 0. Additionally, the cycle number, represented by \(k\), starts at 0 and can reach a maximum value of \(N\). It is important to note that the starting node and destination node of the network must be manually designated for each re-experiment. **Step 2:** If the current cycle number of the ACA is less than \(N\), make \(k=k+1\) and enter the next cycle. **Step 3:** If the number of ants sent in this cycle is less than \(q\), then \(q=q+1\), and continue to send the next ant. **Step 4:** During each iteration, every ant in the ACA calculates the transition probability based on the pheromone concentration on the link connecting the starting node to its adjacent nodes. Subsequently, the ant checks whether the next hop node is present in its taboo table, denoted as taboo(\(k\)). If the node is not in the taboo table, it is added to the ant's taboo list. However, if the node is already in the taboo table, the ant reselects the next jump node to ensure that it does not revisit previously visited nodes. This process ensures that ants explore new paths while avoiding revisiting nodes in their path selection. **Step 5:** The process described in step 4 is iterated until the current network node reaches the desired termination node.