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Advances, Systems and Applications

Table 2 Description of used notations

From: An efficient population-based multi-objective task scheduling approach in fog computing systems

Symbol Description
T Set of IoT tasks in the task scheduling requests
n Number of tasks in the task scheduling requests
ti The ith task in the task scheduling request
F Set of fog nodes in the system
m Number of fog nodes in the system
fj The jth fog node in the system
Di Input data size of task ti
Ii Required computing density of task ti
DEi Deadline of task ti
\(C^{max}_{j}\) Computing capacity of fog node fj
\(S^{max}_{j}\) Storage capacity of fog node fj
\(E^{max}_{j}\) Battery capacity of fog node fj
aij A binary variable determining whether ti is assigned to fj
Aassign assign matrix of size nm
U(Aassign) Overall utility of a task scheduling solution
Q(i,j) QoS score related to ti that is assigned to fog node fj
wt Weight for time QoS parameter
we Weight for energy QoS parameter
Ttotal(aij) Total time consumption for assigning IoT task ti to fog node fj
Tup(aij) Time consumption for transmitting IoT data for executing the task ti on fog node fj
Texecute(aij) Time consumption for executing IoT task ti in fog node fj
Etotal(aij) Total energy consumption for assigning IoT task ti to fog node fj
Eup(aij) Energy consumption for transmitting IoT data for executing the task ti on fog node fj
Eexecute(aij) Energy consumption for executing IoT task ti in fog node fj
Rij Transmission capacity of the channel between IoT device and fog node fj