## 3 Congestion-Aware EFL-Based Model Aggregation Policy in Edge Computing
### MLSTM-CP and Orchestration of EFL Model Aggregation  
In the MLSTM-CP module, the forget, input, and output gates collaboratively engage with both the input data and target features (\(X_{M_{n(t)}}\), \(Y_{M_{n(t)}}\)). Equation (5) presents the set of general features for input, which are gathered through the proposed SDN/NFV-enabled network API and RESTful API within the system architecture. The feature information  
Figure 2: The interactivity of three main tiers in our proposed IIoT-EFL architecture. is captured within the local participant, the updated FL model, and the queuing process at the selected edge aggregator. The deployment of a model-task profiler and inspection techniques are set. The purpose of each component in our proposed MLSTM-CP can be described as follows: * **Input data (X\({}_{M_{n(t)}}\))**: At each time step, the input data is fed into the MLSTM cell, and the gates and operations process this input to determine how much new information should be integrated, how much previous knowledge should be retained, and how the hidden state of the model should be updated based on the evolving conditions of the industrial process. The collected features are from various edge devices/servers deployed in the industrial setting (see (5)). * **Input gate (i\({}_{t}\))** represents the decision-making process for how much new information from the current participants-edge data should be incorporated into the model update (see (6)). Different edge devices might have varying degrees of relevancy or noise in their data due to the conditions of the industrial processes that are being monitored. \[i_{t}=\sigma\Big{(}W_{xi}X_{M_{n(t)}}+W_{hi}h_{t-1}+b_{i}\Big{)}\] (6) * **Forget gate (f\({}_{t}\))** symbolizes the importance of retaining experienced information from previous participants-edge updates (see (7)). \(f_{t}\) assists our system to determine how much to retain from past states in order to make better decisions; \[f_{t}=\sigma\Big{(}W_{xf}X_{M_{n(t)}}+W_{hf}h_{t-1}+b_{f}\Big{)}\] (7) * **Output gate (o\({}_{t}\))** acts as the filter that decides how much of the current hidden state should be exposed and utilized for influencing the global model. \(o_{t}\) reflects how much the insights and knowledge gained from a particular participant-edge update experience should contribute to the comprehensive learning process (see (8)). * **Cell state (\(\overset{\sim}{C}_{t}\))** acts as the \"memory\" of the MLSTM, which captures the accumulation of insights and patterns from various participants-edge data and updating schedules. \(\overset{\sim}{C}_{t}\) retains essential information about the evolving system dynamics. The updated cell state, denoted as \(C_{t}\), is the result of combining between (1) the previous cell state (\(C_{t-1}\)) that was preserved based on the forget gate and (2) the new candidate cell state (\(\overset{\sim}{C}_{t}\)) that was incorporated based on the input gate (see (9) and (10)). \[\overset{\sim}{C}_{t}=tanh\Big{(}W_{xc}X_{M_{n(t)}}+W_{hc}h_{t-1}+b_{c}\Big{)}\] (9) \[C_{t}=f_{t}\odot C_{t-1}+i_{t}\odot\overset{\sim}{C}_{t}\] (10) * **Hidden state (\(h_{t}\))** represents the encoded information that the MLSTM uses to influence the model update process (see (11)). In other words, \(h_{t}\) acts as the output of the MLSTM cell and encapsulates the input pattern understanding of how the various participants-edge updates contribute to the overall improvement of the model. \[h_{t}=o_{t}\odot\tanh(C_{t})\] (11)* **Returned congestion rate (\(\mathbf{Y}_{M_{n(t)}}\)):**\(h_{t}\) and \(o_{t}\) components assist the output features by encapsulating the distilled knowledge and encoded patterns learned from \(X_{M_{n(t)}}\) over multiple timesteps. \(o_{t}\) controls how much of \(h_{t}\) is exposed and utilized to contribute to the output features as congestion rates, which in turn influence the scheduling awareness of global model updates (see (12)). \[0\leq Y_{M_{n(t)}}\leq 1\] (12)  
By obtaining MLSTM-CP outputs, the orchestration of resource virtualization is modified.