## 2 System Architecture and Problem Formulation
### System Architecture  
In edge computing, computational resources move closer to smart devices, transitioning from the cloud to local proximity, as depicted in Figure 1. Edge servers are strategically placed at the network periphery. This shift eliminates the need for devices to send data to the cloud for processing, thereby economizing transmission time and circumventing bandwidth limitations. The strategic deployment of compact base stations enhances connectivity for myriad smart devices. Although edge computing reduces latency by minimizing transmission distances, the finite energy of wireless devices and transmission lags between devices and edge servers necessitate careful consideration. Consequently, this study will delve into the intricacies of edge computing's local architecture and extensively analyze these pertinent issues.  
This study adopts the framework proposed in reference [2], which includes mobile edge computing (MEC) servers and Macro eNodeBs (MeNBs). McNBs connect to multiple Small eNodeBs (SeNBs), as illustrated in Figure 2. SeNBs are divided and interconnected based on the location of Smart Mobile Devices (SMDs), facilitating task transmission. In this architecture, computational capabilities are exclusive to edge servers and smart devices. The configuration comprises one edge server, MeNB collectively, M SeNBs, and S SMDs.  
In this architecture, wired connections enable continuous power and data transmission between Macro eNodeBs and Small eNodeBs, simplifying transmission time and energy consumption considerations. Wireless links connect Small eNodeBs with smart devices, which lack continuous power and necessitate attention to residual energy and limited com  
Figure 1: Edge computing network architecture diagram.  
Figure 2: Partial edge computing network architecture diagram.  
putational capabilities. Task states remain until offloading decision optimization, allowing focused latency and energy consumption resolution. The edge computing server gathers optimization information from smart devices, including task sizes and computational capabilities. Considerations of network latency and energy consumption ensure balanced offloading decisions.  
The offloading decision for the k-th task from the j-th smart device under the m-th MeNB is represented as \(\text{O}_{\text{m,j,k}}\). A task is processed remotely if \(\text{O}_{\text{m,j,k}}\) equals 1; otherwise, if the task chooses local processing, \(\text{O}_{\text{m,j,k}}\) equals 0. Since a single smart device can generate multiple tasks, Equation (1) is applied to convert the task count into binary form [2]. This method converts the number of tasks (\(\text{k}_{\text{s}}\)) from smart device (s), where s \(\in\{1,2,\ldots,\text{S}\}\), and S denotes the total number of smart devices in the system. The bit length is \(\text{k}_{\text{s}}\). By using the conversion formula, decimal values are transformed into binary format, enabling the assignment of offloading decisions to each task independently. This allows the determination of whether each task should be processed remotely or locally, as depicted in Figure 3.  
\[\text{B}_{\text{s}}=2^{\text{k}_{\text{s}}}-1, \tag{1}\]