## 3 Preliminaries and Definitions
### Agdoa Algorithm
#### 4.2.2 DOA Considering Greedy Strategies
Greedy Particle Swarm Optimization (GPSO): The PSO application has advantages for multivariate problems and is suitable for solving PA problems involving power allocation decisions among multiple mobile users and multiple base stations. Meanwhile, the initialization of the particle swarm was optimized using a greedy strategy to obtain GPSO [40];
2. Simulated Annealing PA: Simulated annealing (SA) is suitable for complex problems and can effectively solve discrete NP-hard problems [41];
3. Subgradient-based non-cooperative game model (NCGG): the NCGG algorithm is usually used to solve the problem of optimal decision making for multiple participants in a game, and is suitable for optimizing the multi-user PA problem [42]. ### Performance Metrics

#### 5.3.1 Convergence Speed

To evaluate the convergence speed of the algorithm, we used the successive absolute change magnitude to determine whether the change in the objective function value was stabilizing or not. The absolute change in the objective function value between adjacent iterations was calculated, i.e., \(\tau=\left|\mathrm{f(i)-f(i-1)}\right|\), and the magnitude threshold e was set to 0.005. The algorithm was judged to have stabilized when the absolute change in the magnitude of r was less than the magnitude threshold e. The algorithm was also evaluated to prevent the algorithm from falling into a local optimum. At the same time, in order to prevent the algorithm from being misjudged as converging when it fell into a local optimum, when the algorithm's r was less than e for 10 consecutive iterations, we considered that the \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Number of Mobile Users u & \{12,20,32,40,52,60,72,80,92,100\} \\ Number of Micro-BSs n & \{3,5,8,10,13,15,18,20,23,25\} \\ The fixed bandwidth B & 20 (MHz) \\ The fixed height of BSs H & 10 (m) \\ Workload of request wq & 600–1000 (MHz) \\ Input data of request lq & 300–1500 (KB) \\ Ideal delay of request q Tgq & 0.5 \(\pm\) 0.1 (s) \\ Tolerable delay of request q Tbq & Tgq + [0.1, 0.15] (s) \\ Maximum transmission power for mobile users Pmax & 5 (w) \\ Background Gaussian noise power Sig & \(-\)100 (dBm) \\ Average power consumption of microbase station Pmi & 7500 (w) \\ Average power consumption of macrobase station Pma & 15,000 (w) \\ The computing power of edge servers Rmi & 70 (GHz) \\ Computing power of the cloud server Rma & 140 (GHz) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation Parameters. algorithm had reached convergence, and the mobile user was considered to have found the best solution. #### 5.3.2 System Response Rate

To evaluate the efficiency and performance of the system, we considered the number of tasks completed within a tolerable delay time for the request versus the total number of requested tasks, defined as the system response rate. #### 5.3.3 Scheduling Dominance Degree (SDD)

In order to evaluate the task completion degree, i.e., the fairness, we used SSD in the performance evaluation. SSD is a metric used to evaluate the fairness of a task resource allocation scheme, and there is an inverse relationship between it and the fairness metric. SSD is expressed by Equation (13). \(F\) is the fairness metric, and \(r_{i}\) indicates the resource allocation for user \(i\). In general, a larger SSD value indicates better fairness, while a smaller SSD value indicates worse fairness. We calculated SSD based on the fairness indicator Jain's fairness index. \[SSD=\frac{1}{F} \tag{13}\] \[F=\frac{\left(\sum_{i=1}^{N}r_{i}\right)^{2}}{N\times\sum_{i=1}^{N }r_{i}^{2}}\] s.t. \[r_{i}\in\{0,1\}\]

## 6 Performance Evaluation and Analysis

In this section, we performed a simulation and analyzed the results of the experiment.