## 3 System Model
### Communication Model  
The communication model defines the channels through which UEs and MEC servers interact. When an UE requires the edge server computation, the computation task for offloading must be transferred from the UE to the AP, and then the AP is assigned to the MEC server for computation. This process requires data transmission over the network, so the network bandwidth is one of the key factors affecting the overall system performance. To optimize the offloading process, we conceptualize a communication model that imposes a bandwidth limit between the UE and the AP. This measure is designed to ensure equitable bandwidth distribution among UEs, thereby mitigating potential network congestion. It simultaneously governs energy expenditure while striving to maintain an equilibrium between system performance and operational costs. The details are as follows: we take \(B=\{1,2,...,B\}\) as the set of communication links of the AP. \(W_{b}\) is the bandwidth of the AP and we divide the available bandwidth resource of the AP into equal-width subchannels \(W_{sub}\), then the bandwidth of each subchannel can be denoted as \(W_{sub,b}=~{}W_{b}/B\). The matrix \(M_{b}\) denotes the transmission state of the AP, \(M_{b}=[0,1],b\in B\), and \(M_{b}=1\) indicates that the AP provides an offloading service on its communication link. \(M_{b}=0\) indicates that no offloading service is being provided on its communication link. Thus, the bandwidth resource is denoted as:  
\[\sum_{b\in B}M_{b}W_{sub,b}. \tag{1}\]  
In the resource-constrained scenario, when the requester offloads the task to the MEC server, the task is first sent from the \(UE_{i}\) to the AP via wireless transmission. We assume that the wireless channel state remains constant while each computational task is transmitted between the UE and the AP. \(p_{i,b}\) denotes the transmission power that requester i sends to the AP, \(h_{i,b}\) denotes the channel gain during its transmission, \(\sigma^{2}\) represents the power of the noise, \(d_{i,b}\) denotes the distance between the requester \(UE_{i}\) and the AP, and \(\theta\) is a standardized path loss propagation exponent so that the path loss can be denoted as \(d_{i,b}^{-\theta}\), then, the signal-to-noise ratio (SNR) can be computed as:  
\[SNR_{i,b}=\frac{p_{i,b}h_{i,b}d_{i,b}^{-\theta}}{\sigma^{2}}. \tag{2}\]  
After obtaining the SNR, the transmission rate from the requester to the AP can be calculated as  
\[R_{i,b}=W_{sub,b}log_{2}(1+SNR_{i,b}). \tag{3}\]  
In order to avoid the interference of UEs transmitting between D2D communication links, we assume that each D2D communication link can be obtained as an orthogonal subchannel; then, \(W_{i,c}\) denotes the bandwidth of the subchannel. Similarly, we denote the signal-to-noise ratio of the D2D communication link, then the transmission rate of D2D communication between requester \(UE_{i}\), and collaborator c is denoted as follows:  
\[R_{i,c}=W_{i,c}log_{2}(1+SNR_{i,c}). \tag{4}\]  
Since the executor that performs the task of the requester may be a MEC server or another UE (collaborator), based on the above expression, the transmission rate between the requester \(UE_{i}\) and the executor may be expressed as \(R_{i,b}\) or \(R_{i,c}\).