Table 2 Notation.
Notation | Definition |
|---|---|
\(CS\) | The set of cloud servers |
\(ES\) | The set of edge servers |
D | The set of terminal devices |
\(App\) | The set of applications |
\({A_j}\) | The set of j-th applications |
\(T_{j}^{i}\) | The i-th task of j-th applications |
\({E_j}\) | The adjacent matrix of the dependencies of \({A_j}\) |
\(R1_{j}^{i}\)~\(R6_{j}^{i}\) | Resource requirements during task execution |
\(R_{x}^{1}\)~\(R_{x}^{6}\) | The resource of server x |
\(\varepsilon\) | The proportion of additional server resources occupied by task replicas |
\(\{ pre_{j}^{i},sub_{j}^{i}\}\) | The predecessor and successor task sets of \(T_{j}^{i}\) |
\(K_{j}^{i}\) | The scheduling strategy of the i-th task of j-th applications |
\(TD_{j}^{i}\) | The amount of data transmitted to successor tasks |
\(W_{j}^{i}\) | The execution time required for i-th task in j-th application |
\(u_{x}^{1}\sim u_{x}^{6}\) | Represent the utilization of resources of the server x |
\(\alpha _{i}^{c}\) | Task i is assigned to the n-th cloud server |
\(\beta _{i}^{e}\) | Task i is allocated to the m-th edge server |
\(TT_{{x,y}}^{{i,j}}\) | Represent the time required to transfer data for task \(T_{j}^{i}\) in application \({A_j}\) from server x to server y |
\(TR_{x}^{y}\) | Denote the data transfer rate between servers x and y |
\(dis_{x}^{y}\) | Represent the transmission distance between x and y |
\(TS_{x}^{y}\) | Indicate the transmission speed |
\(ST_{{}}^{{i,j}}\) | Start time of the \(T_{j}^{i}\) |
\(FT_{{}}^{{i,j}}\) | Finish time of the \(T_{j}^{i}\) |
