## 4 Decoupled Computation Offloading and Resource Allocation with Coordinate Descent (CD)
Results in Figures 7 and 8 share the same offloading decision, bandwidth allocation and edge computing resource allocation schemes. The distinction is that \(e_{m}^{f}\)\(\forall m\in\mathcal{M}\) was set to the default value for all tasks, which meant \(e_{1}^{f}\) remained unchanged in this situation. System rewards and processing delays of tasks were obtained when \(l_{1}^{f}\) shifted from \(2^{-4}\) to 256 times the default data size (1 megabit). With equal emergency factors, i.e., \(e_{m}^{f}=1\forall m\in\mathcal{M}\), those tasks of large data size were offloaded in preference to tasks of small data size, even monopolizing the edge resources (\(l_{1}^{f}=256\) Mb). Tasks of large data size were more advantageous for offloading decisions. When tasks were of the same data size, task \(t_{1}^{f}\) could only be processed locally. As \(l_{1}^{f}\) got larger, the system preferred to process

\[\underset{m,m,m,m,m,m,m,m}{Maximize}:H =\sum_{m\in\mathcal{M}_{1}}e_{m}^{f}(T_{m}^{f}-\frac{l_{m}^{f}}{ \alpha_{m}B_{n}\text{log}_{2}(1+\frac{p_{m}h_{m}^{2}}{\sigma^{2}})}-\frac{\rho_ {m}^{f}l_{m}^{f}}{\beta_{m}F_{e}})\]5 Delay and rewards versus \(e_{1}^{f}\). task \(t_{1}^{f}\) (tasks with large quantities of data). This is what took place in existing research works. From Figure 8, we can conclude that tasks of extremely large size will be offloaded to the edge if no restrictions are taken. This is not what we want to see because it stops UDs with limited computing resources from offloading their tasks to the edge. Luckily, we can prevent a task of extremely large size from monopolizing edge resources by setting a sufficiently small \(e_{m}^{f}\) for the data-intensive computing task \(t_{m}^{f}\). Figure 9 illustrates how the emergency factor impacts data-intensive tasks. We randomly sampled from \([80,90,10,110,120]\) megabits and set it as the data size of a randomly selected task (\(t_{2}^{f}\) was selected and \(l_{2}^{f}=100\) Mb in this experiment). The data size of the other tasks remained at the default value. Setting a sufficiently small emergency factor for the task with a large data size prevented the task from monopolizing system resources. When \(e_{2}^{f}\) took the default value, as the others (\(e_{m}^{f}=1\forall m\in\mathcal{M}\)), only \(t_{2}^{f}\) was offloaded to the edge, and the processing delay of \(t_{2}^{f}\) was less than 10 s. As we set a smaller value of \(e_{2}^{f}\), more and more UDs could offload their tasks to the edge for processing (UD 9 and UD 10 for \(e_{2}^{f}=0.5\), UD 3, UD 9 and UD 10 for \(e_{2}^{f}=0.25\)). When \(e_{2}^{f}\) took the value 0.008, task \(t_{2}^{f}\) started to be processed locally. We can conclude that when the emergency factor of a task with a large data volume is small enough, it loses its advantage in task offloading. \[\underset{m,m,m,m,m,m,m,m}{Maximize}:H =\sum_{m\in\mathcal{M}_{1}}e_{m}^{f}(T_{m}^{f}-\frac{l_{m}^{f}}{ \alpha_{m}B_{n}\text{log}_{2}(1+\frac{p_{m}h_{m}^{2}}{\sigma^{2}})}-\frac{\rho_ {m}^{f}l_{m}^{f}}{\beta_{m}F_{e}})\]6 Delay and rewards versus \(t_{1}^{f}\). \[\underset{m,m,m,m,m,m,m,m}{Maximize}:H =\sum_{m\in\mathcal{M}_{1}}e_{m}^{f}(T_{m}^{f}-\frac{l_{m}^{f}}{ \alpha_{m}B_{n}\text{log}_{2}(1+\frac{p_{m}h_{m}^{2}}{\sigma^{2}})}-\frac{\rho_ {m}^{f}l_{m}^{f}}{\beta_{m}F_{e}})\]7 Delay and rewards versus \(e_{2}^{f}\). In Figure 10, we compare the performance among \"DRL\" [29], \"LCD\", \"RO\" and \"AL\" (results are organized in this order) under different sampling probabilities. We tested four types of tasks of different data sizes: regular size, small size, large size and immense size. We can see that both our LCD scheme and the DRL scheme achieved the minimum delay when tasks were of regular size (sampling probability \(p=1\)). However, when tasks of immense size (the task from UD 8) and regular size coexisted (\(p=0.9\)), our scheme penalized tasks of immense size by setting sufficiently small emergency factors for tasks of immense size, which in turn disadvantaged our scheme in obtaining the minimum delay.