## 5 Simulation Results
### Joint Optimization Scheme  
In this section, numerical results have been provided to validate the advantages of the proposed joint optimization scheme. This scheme jointly optimizes the number of offloaded bits, energy harvesting time, and transmission bandwidth, called RSB. For comparison, we consider the following four benchmark schemes. Local computing only (LCO): The mobile device accomplishes its computation tasks by only local computing instead of offloading tasks to the MEC server. This scheme solves (18) by setting the offloading bits \(q_{i}(t)=0\), \(\forall i\in K\), \(\forall t\in\mathcal{T}\). Half offloading (HOF): Half of the computing tasks are executed locally, and the other half are executed at the edge server. This scheme solves (18) by setting the offloading bits \(q_{i}(t)=\frac{Z_{i}(t)}{2}\), \(\forall i\in K\), \(\forall t\in\mathcal{T}\). Joint optimization with equal bandwidth allocation (EBW): The mobile device executes part of the computing tasks locally and offloads the remaining computing tasks to the edge server for execution. All devices divide the total downlink bandwidth equally. This scheme solves (18) in a joint optimization manner by setting the bandwidth B equal division. Computation offloading only (FOF): The mobile device accomplishes its computation tasks by only offloading tasks to the MEC server instead of local computing. This scheme solves (18) by setting offloading bits \(q_{i}(t)=Z_{i}(t)\),\(\forall i\in K\), \(\forall t\in\mathcal{T}\). Figure 3 shows the residual energy of the WP-MEC system versus AP transmission power. In the figure, \(T=3\) s, the number of the task input bits follows the uniform in the range of 80 to 100 KB, and the AP transmission power varies from 200 to 290 W. The simulation result shows that compared with the LOC, HOF, EBW, and FOF schemes, the residual energy of our proposed joint optimization scheme is increased by 2%, 6.8%, 1.8%, and 33%, respectively. The proposed joint optimization scheme provides the largest residual energy. This is because the proposed scheme has an optimal combination of the energy harvesting time, the number of offloaded bits, and the transmission bandwidth while the other four benchmark schemes fix the number of offloaded bits or the transmission bandwidth and can only optimize the other two variables. If the fixed value is set unreasonably, it will consume a lot of energy. Besides, the residual energy of all methods increases almost linearly as the increase of the transmission power. This is due to the fact that under the parameter settings, the optimal solution of the scheme is not affected by the change of AP transmission power, and the energy consumption remains almost unchanged, while the AP's transmission power only affects the harvested energy. Therefore, the higher the AP transmission power is, the higher the residual energy of the WP-MEC system will be. It is also noticed that the residual energy of the FOF scheme is far lower than that of the LOC scheme, which indicates that the energy consumption by the computation offloading is larger than that of local computing. Under unconstrained conditions, we should try to choose local computing to execute tasks. It is also observed that the residual energy of EBW is close to RSB, indicating that the equal bandwidth allocation scheme is closer to the optimal solution. Figure 4 shows the residual energy of the WP-MEC system versus the number of task-input bits. In the figure, \(T=3\) s, the AP transmission power is 200 W, and the number of task-input bits varies from 80 KB to 170 KB. The simulation result shows that the proposed joint optimization algorithm provides higher energy efficiency than LOC, HOF, EBW, and FOF benchmark schemes. Furthermore, the residual energy of all schemes decreases as the number of task-input bits increases. This is because the more the system tasks are executed, the higher the energy consumption will be. Accordingly, the residual energy of the system shows a downward trend as the number of task input bits increase.