# Synchronous Remote Calibration for Electricity Meters: Application and Optimization
## 3 Methods
### System Model
#### 3.1.1 Network Model
\begin{table}
\begin{tabular}{c l} \hline \hline
**Symbols** & **Explanations** \\ \hline \(\mathcal{N}_{K}\) & The set of detection points \\ \(\mathcal{N}_{G}\) & The set of central laboratories \\ \(i,j\) & The index of detection points, central laboratories \\ \(G_{i}^{r}\) & The coverage restriction of central laboratory \\ \(D_{g_{i},k_{j}}\) & The distance between two points \(\left(x_{k_{i}},y_{k_{i}}\right)\) and \(\left(x_{g_{j}},y_{g_{j}}\right)\) \\ \(\mathbf{D_{KG}}\) & The distance matrix of detection points and central laboratories \\ \(\mathcal{N}_{C}\) & The set of clients \\ \(\mathcal{N}_{S}\) & The set of servers \\ \(m,n\) & The index of clients, servers \\ \(CTY_{m,ty}\) & Indicates whether client \(c_{m}\) can process tasks of type \(Q_{ty}\) \\ \(STY_{n,ty}\) & Indicates whether server \(s_{n}\) can process tasks of type \(Q_{ty}\) \\ \(\mathcal{N}_{X}\) & The set of tasks \\ \(t\) & The index of tasks \\ \(X_{t}^{Q_{ty}}\) & The task type of \(X_{t}\) \\ \(X_{t}^{\tau}\) & The processing time of task \(X_{t}\) \\ \(X_{t}^{st}\) & The start time of task \(X_{t}\) \\ \(X_{t}^{ct}\) & The end time of task \(X_{t}\) \\ \(X_{t}^{C_{m}}\) & The client assigned to task \(X_{t}\) \\ \(X_{t}^{K_{i}}\) & The detection point assigned to task \(X_{t}\) \\ \(X_{t}^{S_{n}}\) & The server assigned to task \(X_{t}\) \\ \(X_{t}^{C_{j}}\) & The central laboratory assigned to task \(X_{t}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters for remote calibration system. Figure 2: A distributed remote calibration network. The scheduling infrastructure encompasses a distributed network of sensors at various detection points and servers situated within central laboratories. We designate the diverse standard equipments as clients, differentiating them by their geographical placement and the specific tasks they are capable of executing. Let \(\mathcal{N}_{C}=\{C_{1},C_{2},\ldots,c_{|\mathcal{N}_{C}|}\}\) denote the ensemble of heterogeneous standard equipment deployed across an array of detection points, where each element \(\mathcal{C}_{m}\) signifies a distinct client (i.e., sensor). The cardinality of the set \(\mathcal{N}_{C}\), denoted by \(|\mathcal{N}_{C}|\), represents the aggregate number of such clients. \(\mathcal{N}_{C}^{K}=\left\{C_{1}^{K_{i}},C_{2}^{K_{f}},\ldots,C_{|\mathcal{N}_ {C}|}^{K_{f}}\right\}\) expresses the relationship between clients and detection points, where \(C_{m}^{K_{i}}\) indicates that client \(C_{m}\) is situated at detection point \(K_{i}\); for instance, \(C_{4}^{K_{1}}\) indicates client \(C_{4}\) situated at detection point \(K_{1}\). In a similar vein, we characterize the various metrology experts as servers, distinguishing them based on their location and the range of tasks they can undertake. Specifically, the total number of servers across different central laboratories is denoted by \(|\mathcal{N}_{S}|\), where \(\mathcal{N}_{S}=\{S_{1},S_{2},\ldots,S_{|\mathcal{N}_{S}|}\}\) symbolizes the set of service providers (i.e., servers). The relationship between these metrology experts and their respective central laboratories is expressed as \(\mathcal{N}_{S}^{G}=\left\{S_{1}^{G_{j}},S_{2}^{G_{f}},\ldots,S_{|\mathcal{N} _{S}|}^{G_{f^{\prime\prime}}}\right\}\), with \(S_{n}^{G_{j}}\) signifying server \(S_{n}\) located at central laboratory \(G_{j}\); for instance, \(S_{2}^{G_{2}}\) indicates server \(S_{2}\) stationed at central laboratory \(G_{2}\).