Algorithm 2: Initial Task Scheduling

Input: vi:task to schedule

1  PList[vi ∈ N, j ∈ M];

2  begin

3      Qvm ←Sort the fog serves by the cij with the descending order;

4      V ← NULL;

5      foreach Vj ∈ Qvm do

6          Tj,0 ← 0;

7      foreach Vj ∈ Qvm do

8          Calculate the Tie of Vj by the Equation (4);

9          if Tj,i -1 + $T_i^e$ < di then

10          Calculate the Tj,i of Vj by the Equation (3);

11          Z ← Vj;

12          break;

13      Calculate cost of Z by the Equation (1);

14      PList[vi ∈ N, j ∈ M] ← Z;

15      return Z, V;