## 3 Congestion-Aware EFL-Based Model Aggregation Policy in Edge Computing
### System Architecture
#### 3.1.2 Edge Tier  
In our proposed framework, the adaptive allocation of edge resources is facilitated through the implementation of an NFV-enabled system. Virtualization procedures are leveraged to configure resource attributes in a manner that caters to varying criticality levels associated with each slicing service. Specifically, the image processing services are categorized into three distinct classes. A comprehensive description of these class attributes, criticalities, and application scenarios when FL is applied to industrial services can be found in Table 2. Class-1 represents a high mission-critical scenario, where unsatisfactory QoS performance can lead to significant consequences. Instances of this class include the modelling of visually assisted robots and low-latency manufacturing control systems. Class-2 denotes a mission-critical context with an upper-bound tolerable delay of 150 ms. \begin{table}
\begin{tabular}{c c} \hline
**Notation** & **Description** \\ \hline \(N=\left\{1,2,\ldots,n\right\}\) & Set of local IIoT participants \\ \(E=\left\{1,2,\ldots,e\right\}\) & Set of edge aggregators with specified resource pooling properties \\ \(Y_{n}^{m}=\left\{Y_{n}^{1},Y_{n}^{2},\ldots,Y_{n}^{m}\right\}\) & Set of \(m\) services for participant \(n\) \\ \(M_{n(t)}\) & Set of local loss-minimized model parameters from participant \(n\) at \(t\)-index round communications \\ \(M_{e(t)}\) & Loss-minimized model parameters in edge aggregator \(e\) at round \(t\) \\ \(D_{n(t)}\) & Data distribution of participant \(n\) at round \(t\) \\ \(pt\left[M_{n(t)}\right]\) & Size-based processing time of local model \(M_{n(t)}\) \\ \(tl\left[M_{n(t)}\right]\) & Tolerable latency of local model \(M_{n(t)}\) \\ \(sc\left[M_{n(t)}\right]\) & Service criticality of local model \(M_{n(t)}\) \\ \(ts\left[M_{n(t)}\right]\) & Time slot of local model \(M_{n(t)}\) at edge aggregator \\ \(bs\left[M_{n(t)}\right]\) & Buffer size of adjusted edge aggregator that loaded \(M_{n(t)}\) \\ \(qi\left[M_{n(t)}\right]\) & Queueing index of \(M_{n(t)}\) at current time slot at \(e\) \\ \(\tau_{m}\) & Upper-bound QoS (e.g., delay) for service \(m\) \\ \(T_{M_{m}^{G}(e)}^{\text{\text{\textregistered}}}\) & Latency of averaging service \(m\) toward final model in \(e\) \\ \(\tau_{(t)}^{comp}\) & Computation latency at participant \(n\) \\ \(T_{(e)}^{comp}\) & Communication latency between participants to edge aggregator \(e\) \\ \(T_{(e)}\) & Computation latency in edge aggregator \(e\) at round \(t\) \\ \(T_{update}\) & Uplink data rate for updating the local model \\ \(\left(X_{M_{n(t)}},\ Y_{M_{n(t)}}\right)\) & Input data and target features \\ \(\left(X_{M_{n(t)}}^{tr},\ Y_{M_{n(t)}}^{tr}\right)\) & Training input data and target features \\ \(\left(X_{M_{n(t)}}^{le},\gamma_{n(t)}^{le}\right)\) & Testing input data and target features \\ \(N(m)\) & Number of models \\ \(B(s)\) & Batch sizes \\ \(D(u)\) & Dense units \\ \(MLSTM(u)\) & MLSTM units \\ \(N(e)\) & Number of epochs \\ \(W\) (_e.g.,_\(W_{ii}\)) & Sampling weights (e.g., weight matrices that determine how the input data \(X_{M_{n(t)}}\) \\  & contribute to the computation of input gate \(i\)) \\ \(b\) (_e.g.,_\(b_{i}\)) & Bias (e.g., bias terms associated with the input gate \(i\)) \\ \((\sigma,\tanh)\) & Sigmoid and tanh activation functions \\ \(i_{t}\), \(f_{t}\), \(o_{t}\), \(\widetilde{C}_{t}\), \(C_{t}\), and \(h_{t}\) & LSTM components: input gate, forget gate, output gate, cell state, new cell state, and hidden state \\  & Element-wise multiplication \\ \hline \end{tabular}
\end{table} 
Table 1: Primary notations and descriptions. This class is applicable to FL-based industrial visual or surveillance modelling systems. For the low mission-critical category, Class-3 is characterized by a delay tolerance of 300 ms. QoS class indicators (QCI) define the characteristics of each class, aligning with QCI priority assurance in the recently released standardization.