## 3 Preliminaries and Definitions
### Agdoa Algorithm
#### 4.2.2 DOA Considering Greedy Strategies
Figure 3: (**a**) The overall variation in the welfare of each algorithm with different numbers of mobile users; (**b**) the overall results of the system response rate of each algorithm with different numbers of mobile users; (**c**) the overall results of the SSD of each algorithm with different numbers of mobile users. #### 6.1.2 Impact of Request Workloads

In this section, we set the base station with the same computational power, i.e., Rn = 70 GHz, and all mobile users had offloading tasks configured with the same request conditions lg = 700 KB, Tgq = 0.5 (s), Tbg = 0.65 (s), except for the workload wq being set to a different request q. The performance of the BSSA was evaluated at wq = 1500, 2000, 2500. From Figure 4a, it can be observed that the system welfare decreased as the request workload increased. When the workload increased from 1500 to 2000, welfare decreased by about 4% on average; when the workload increased from 2000 to 2500, the welfare decreased by about 2% on average. This is due to the fact that when the computational task requests from the BS exceed the scheduling load that the base station can handle, it becomes under-resourced and reduces the system welfare value. Figure 4b shows that when the number of mobile users is small, different request workloads have essentially no effect on the SSD. When the number of mobile users was high, the SSD decreased by 3% on average as the request workload increased; i.e., an appropriate request workload had a benign effect on the system fairness. At high loads, the system's resources became saturated and resource allocation delays increased, leading to a decrease in fairness when the system performed offloading tasks. #### 6.1.3 Impact of Request Workload Configuration

In this section, different workload requests (wq) and different amounts of work input data requests (Iq) were configured, to evaluate the performance of the BSSA and compare the experiments with other optimization algorithms. The following figure shows the system welfare and SSD used for evaluating the system with different wq when the number of mobile users (u) was 40 and 100, respectively. From Figure 5a,b, it can be observed that the welfare of the BSSA was consistently higher than other methods at different wq values when the number of mobile users was small. When the number of mobile users was 40, the proposed BSSA improved the welfare of GA by 36.2% on average. For SSD, the values of BSSA and GA were significantly larger than the other methods, and BSSA was inferior to GA for smaller wq. This implied that, at this point, BSSA sacrificed part of the system fairness to maintain a higher system welfare during the optimization process. From Figure 6a,b, it can be seen that the welfare of BSSA and GA became larger as the number of mobile users u increased, and the proposed BSSA improved the welfare of GA by only 29.4% on average, while at this time, the SSD of BSSA had a significant advantage at different wq. Meanwhile, the SSD of BSSA showed an overall decreasing trend with the increase in wq. Obviously, as the number of mobile users u increased with the increase in wq, more and more tasks could not be completed in time,

Figure 4: (**a**) The overall change in welfare for each algorithm when changing the request workload for different numbers of mobile users; (**b**) the overall results in SSD for each algorithm when changing the request workload for different numbers of mobile users. resulting in a decrease in the fairness of the system. Similarly, as shown in Figure 7a,b, BSSA consistently performed the best in terms of system welfare for different amounts of Iq. The proposed BSSA's welfare improved by 35.7% and 16.0% on average under the conditions of 40 and 80 mobile subscribers, respectively. Thus, we can say that BSSA showed the best performance for the system welfare problem, even under different request work configurations. Figure 5: The result of the experiment under u = 40.