Advances, Systems and Applications
Table 1 Frequently used notation
Notation | Implication |
|---|---|
\(\mathcal {M} = \{1,2,...,M\}\) | The set of edge servers |
\(\mathcal {N} = \{1,2,...,N\}\) | The set of users |
B | Lowest revenue limit |
R | Number of resource types |
\(\varvec{c}_j = (c_{j1},c_{j2},...,c_{jR})\) | Resource capacity of the j-th edge server |
\(\varvec{\theta }_i =(\varvec{s}_i,\varvec{\delta }_i,b_i)\) | User i’s request |
\(\varvec{s}_{\varvec{i}} = (s_{i1},s_{i2},...,s_{iR})\) | Resource requirements of user i |
\(\varvec{\delta }_i = (\delta _{i1},\delta _{i2},...,\delta _{ij},...,\delta _{iM})\) | Deployment constraints between user i and ECSs |
\(\mathbf {\Delta } = (\delta _1,\delta _2,...,\delta _N)\) | All users’ deployment constraints |
\(\mathcal {A}\) | The set of active users |
\(\mathcal {A}_j\) | The set of active users on ECS j |
\(x_{ij}\) | Decision variables of user i and ECS j |
\(\mathcal {W}\) | The set of winners |
\(\lambda _r\) | The price increase parameter of the r-th resource |
\(\varepsilon\) | Fixed step of price increase |
\(\varvec{{gp}} = (gp_1,gp_2,...,gp_R)\) | Global unit price of different types of resources |
\(\varvec{p} = (p_1,p_2,...,p_i,...,p_N)\) | Payment price of each user |
pay | Total revenue |