## 3 System Descriptions and Assumptions  
### DESCO Network Model  
We designed an Edge Service Caching and Offloading (DESCO) architecture based on the multi-server-multi-user end-edge two-layer network paradigm [22], as illustrated in Figure 2. In the DESCO network, the end layer consists of MU clusters, distributed across the coverage areas of various wireless networks, organized by different edge servers, and each of them is connected to the nearest server to obtain computing and offloading services. In the edge layer, MEC servers are deployed within wireless access points (WAPs) and equipped with computing and storage units. MEC servers communicate with each other through wired backhaul links and are self-organized at the application layer into a decentralized ring network called Cache Chord. The maintenance of this network structure relies solely on the consistent hashing protocol followed by server nodes, with detailed design discussed in Section 3.3. Three computing modes exist in the DESCO network: local computing, pure offloading, and cache-based offloading. Local computing means MUs processing real-time tasks by themselves; pure offloading signifies that the MEC server's local cache pool does not store the application programs required to execute user requests, so MUs need to offload real-time data and application data to the server. Cache-based offloading indicates that the server stores the application data for the task, and all users requesting the service only need to offload real-time data to the server, reducing some of the transmission energy consumption. This will be elaborated further in Section 3.4. Table 1 summarizes the main parameters included in this study. The total number of MEC servers joining the DESCO network edge layer is denoted by the set \(\Delta=\{1,2,3,...,D\}\). Each distributed MEC server node uses its IP address as a unique identifier, represented by the set \(\text{NID}=\{\mathit{nip}_{1},\mathit{nip}_{2},...,\mathit{nip}_{D}\}\). The set \(\text{KID}=\{\mathit{kid}_{1},\mathit{kid}_{2},...,\mathit{kid}_{K}\}\) signifies unique resource identifiers for applications, utilized for identifying and indexing services within the Cache Chord network. Here, the subscript \(K\) indicates the total number of tasks that any user \(n\) at different geographical locations might request at any moment. In the DESCO system, every entity operates in the time series \(\mathrm{T}=\{1,2,...,T\}\). This value serves as the fundamental unit for both the system's offloading and caching decisions and the variations in user task requests. The duration of any arbitrary time slot \(t\in\mathrm{T}\) is set as a constant value, denoted by \(\tau\), representing the latency constraint of real-time applications. This means that at time \(t\), when an MU generates a service request and produces corresponding real-time data, the computation result must be returned before the end of time \(t\). Let \(\mathrm{K}=\{\langle\theta_{1},\omega_{1},\phi_{1}\rangle,\langle\theta_{2}, \omega_{2},\phi_{2}\rangle,...,\langle\theta_{K},\omega_{K},\phi_{K}\rangle\}\) be the set of task features, where a task \(k\in\{1,2,..,K\}\) can be represented by a tuple \(\langle\theta_{k},\omega_{k},\phi_{k}\rangle\). In this tuple, \(\theta_{k}\) represents the real-time data generated by the user request task (such as sensor data generated in real-time by IoT devices, video data, etc. ), \(\omega_{k}\) represents the size of the application data of the task, and \(\phi_{k}\) represents the necessary floating-point operations (FLOPs) required for task completion [23]. Let \(\Delta=\{1,2,...,N\}\) represent the set of users governed by the server. Furthermore, the set \(U^{t}_{N_{d}}=\{u^{t}_{1},u^{t}_{2},...,u^{t}_{N}\}\) denotes the task requests of each user within the server \(d\)'s range at time \(t\). At the beginning of each time slot, MUs can either execute a new computation task different from \(\mu^{t-1}_{i}\), maintain the request from the previous time slot, or not request any service.