## 3 Problem Formulation and Objectives
### Communication Model  
We consider an offloading resource over edge computing paradigms. The MEC is deployed in O-RAN and provides capability via wireless access points in cellular networks through a wired connection. Accordingly, the clustering of the network consists of communication and computation in edge computing. Table 2 shows a system model that was used to formulate MEC resources and IIoT tasks. The number of IIoT tasks denoted as \(I=(1,2,3,\ldots,i),\ \forall\ i\in I\) participate at time slot \(T=(1,2,3,\ldots,t),\ \forall t\in T\). Next, \(N=(1,2,3,\ldots,n),\ \forall n\in N\), where denotes referring to the number of devices and \(M=(1,2,3,\ldots,m),\ \forall m\in M\), where denotes the number of MEC servers used in our network and deployed in O-RAN. We assume that in our network scenario, in which O-RAN is deployed at the base station and coordinated, one or more O-RAN can cooperate with each other for downlink and uplink transmissions to the end devices. Furthermore, downlink transmission is ignored in our work. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**QCI-Index** & **Resource Types** & **Priority Level** & **PDB** & **PELR** & **Industry Application Use Case** \\ \hline QCI-3 Process Automation and Monitoring & GBR & 30 & 50 ms & \(10^{-3}\) & Robotic monitoring \\ \hline QCI-70 Mission Critical Data & Non-GBR & 55 & 200 ms & \(10^{-6}\) & Safety systems \\ \hline QCI-82 Discrete Automation & Delay critical GBR & 19 & 10 ms & \(10^{-4}\) & Automate quality control \\ \hline \hline \end{tabular}
\end{table} 
Table 1: QCI specification is defined to set different types of industry application use cases. Decision variables:  
\[S^{i}=\left\{ \begin{array}{ll}1,&\text{Offloading decision of IIoT to MEC server}\\ 0,&\text{Otherwise}\end{array} \right.\]  
Regarding Simmons' law, the transmission data rate \(D_{n,m}\) of IIoT device can be calculated as:  
\[D_{n,m}=H_{n,m}\text{log}_{2}\left(1+\frac{B_{n}G_{n}}{\psi_{n}+\sum_{m=1}^{N} B_{m}G_{m}}\right), \tag{1}\]  
where \(H_{n,m}\) is the channel bandwidth, \(B_{n}\) is the transmission power of \(n\)-\(th\) devices. \(\psi\) is the background interference power consumption that includes wireless transmission from other devices \(\psi_{i}^{0}\) and noise power consumption can express: \(\psi_{n}=\psi_{i}^{0}+\psi_{i}^{1}\). \(G_{m}\) is the channel gains, and as in Formula (1), if multiple devices simultaneously perform calculations and offload via the wireless access channel, significant interference and a reduction in the data transmission rate will occur. Thus, the constraint conditions that the size of \(z_{n,m}(t)\) should follow is:  
\[z_{n,m}(t)\leq\ D_{n,m}(t),\forall n\in N \tag{2}\]  
The transmission energy consumed by offloading tasks for IIoT \(i\) is given as follows:  
\[\Delta_{T,i}(t)=B_{n}(t)\frac{z_{n,m}(t)}{D_{n,m}(t)} \tag{3}\]  
Based on the communication model, it consists of many devices simultaneously offloading tasks to the MEC via the wireless channel, which will inevitably result in reduced data transmission rates. When the data rate for the IIoT device decreases, the backhaul link will incur higher energy consumption and longer transmission times for offloading tasks. Utilizing edge servers for computing tasks is an enhancement as it can avoid the long transmission delays associated with cloud computing.