**3. System Model**

In this section, the mathematical modeling of the proposed EH MEC system is presented. To formulate the system model, this paper assumes that the time is divided into equal time slots indexed by *t* such that

$$\forall t \in \mathcal{T} \text{ where } \mathcal{T} = \{1, 2, 3, \dots, T\}. \tag{1}$$

This paper also assumes that each IoT device requests multiple computation offloading tasks to the EH MEC server. Therefore, the scheduling is performed for each task, and we define the notations for the set of received tasks at time *<sup>t</sup>* as R*<sup>t</sup>* , i.e.,

$$\mathcal{R}^t = \{r\_1^t, r\_2^t, r\_{3'}^t \cdots, r\_{\text{'}}^t\}, \tag{2}$$

where *<sup>R</sup>* is the number of tasks requested in the timeslot. R*<sup>t</sup>* is stored in the request buffer in the scheduler.

As shown in Figure 1, the energy of the EH MEC system is supplied from the RER and is stored in the ESS for the operation of the MEC system. Part of the energy is transferred to the small scale battery and used to operate the MEC server. The amount of energy received by the battery is denoted as *e<sup>t</sup>* , and it has a maximum value of *E*max harv, i.e.,

$$0 \le e^t \le E\_{\text{harv}\prime}^{\text{max}} \,\forall t,\tag{3}$$

where the *e<sup>t</sup>* s are i.i.d. in the different timeslots.

The battery level for computation offloading at the beginning of *t* is denoted as *B<sup>t</sup>* , and it is assumed that *B*<sup>0</sup> = 0 and *B<sup>t</sup>* < +∞, i.e., *B<sup>t</sup>* is consumed only for computation offloading. In addition, if we denote the energy consumed by computation offloading at *t* as *E<sup>t</sup>* offload, then the following equation holds [10]:

$$B^{t+1} = B^t - E^t\_{\text{offload}} + e^t, t \in \mathcal{T}. \tag{4}$$

Based on the defined notations, the optimization problems of the computation offloading scheduling are formulated as presented in the following subsections.
