## 3 System Overview
### Computation Model  
To create an application model in MEC, it is necessary first to describe the task needs and inter-task connections [34]. The application may be represented as a directed acyclic graph (DAG) D, with nodes representing the collection of tasks \(t=\{t_{1}t_{2},\dots\ t_{n}\}\) and edges e or connections indicating the relationships between the tasks [34]. In DAG D, each task t\({}_{i}\) is made up of two elements: (a) the computation requirement (C\({}_{i}\)) of task t\({}_{i}\) expressed as millions of instructions per second (MIPS); and (b) memory requirement \(M_{i}\) of task \(t_{i}\). The interdependencies between tasks are represented by the edges. The latency for each edge is determined by the amount of bandwidth available. In MEC the tasks are executed locally on the user equipment or offloaded to a proximate server. Below is a detailed description of both execution states. Reduced latency and power consumption are achieved through offloading tasks. If the computational capabilities of the user device fulfil the task conditions, task offloading does not occur. The computing capacity of the mobile user is expressed as C\({}_{u}\). Major symbols and notation used in the system models and equations are defined in Table 1.  
As expressed in [35], the desired computation cycles for a job \(t_{i}\) are represented as \(C_{i}\). The computation time of a task \(t_{i}\) to be performed at user end is represented by \(E_{i}\) (seen Equation (1)), whereas energy consumption of the mobile device is represented by \(P_{i}\) (see Equation (2)). \[E_{i}=C_{i}/C_{u} \tag{1}\]  
\[P_{i}=C_{i}(C_{u})^{2} \tag{2}\]  
Whenever a mobile device does not match the requirements of a given task, it is offloaded to an edge server. According to many research, the amount of execution results after offloading is so little that the transmission time necessary to download is minimal when compared to the time required to post the data to the server [35]. The distance between the mobile user and the edge server in the x and y directions is represented as \(x_{i}\) and \(y_{i}\), respectively. Here, \(p_{i}\) represents the transmitting power of the mobile device, \(\theta\) represents the standard path loss propagation, and \(\sigma^{2}\) represents additive Gaussian noise in the transmission path. As a result, the signal to noise ratio (SNR) is calculated using Equation (3) [36]. \[SNRi=(p_{i}\times x_{i}\times y_{i})^{-\theta}/\sigma^{2} \tag{3}\]  
If the bandwidth B is known, the mobile device's transmission rate R\({}_{i}\), is expressed using Equation (4). \[R_{i}=Blog_{2}(1+SNR_{i}) \tag{4}\] \begin{table}
\begin{tabular}{l l} \hline \hline
**Symbol** & **Definition** \\ \hline \(t_{i}\) & Incoming task for offloading \\ \(E_{i}\) & Computation time of task \(t_{i}\) at the user device \\ \(C_{i}\) & Cycles required to complete the task \(t_{i}\) \\ \(R_{i}\) & Mobile device transmission time \\ \(C_{s}\) & Computing capacity of the edge server \\ \(TE_{i}^{k}\) & Amount of time required to execute task \(t_{i}\) at edge server \(S_{k}\) \\ \(S_{k}\) & Aggregate execution time of tasks mapped at edge server \(S\) \\ \(U_{s}\) & Resource utilization of server \\ \(P_{k}\) & Power consumed by server \\ \(\delta\) & Selected server with optimized features after prediction \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Symbols and definitions. The aggregate of the execution times of jobs that have been previously offloaded to an edge server is expressed by \(S_{k}\) (see Equation (5)). \[S_{k}=\sum_{\forall t_{i}\in M_{k}}\left(TE_{i}^{k}\right) \tag{5}\]  
Further, the server utilization [37] is represented by U\({}_{\text{s}}\), and the edge server's capacity to which a task is going to offload is expressed by C\({}_{\text{s}}\) (see Equation (6)). \[U_{s}=\frac{S_{k}}{C_{s}}*100 \tag{6}\]  
Finally, the edge computation time C\({}_{\text{g}}\) for a task t\({}_{\text{i}}\) is determined by Equation (7). If \(R_{i}<Cg\) the required task is offloaded at the edge server. \[C_{g}=C_{i}/C_{s} \tag{7}\]