Table 1.

Defitions of notations.

Notations	Meanings
Fi, Fj, Fs	Computing power of devices i, j, s, respectively
M	Set of IoT nodes
N	Set of fog nodes
S	Set of computing devices in pro-node
Fi,j(t)	Computing power allocated to i by device j in time slot t
Fi,s(t)	Computing power allocated to i by device s in time slot t
τi, τj, τs	Node i, j, s, calculation delay
τc	Transmission delay
τ(t)	Delay at time slot t
τ	Target delay vector
Pc	Sent tasks
λi(t)	Arrival rate of tasks for time slot t
σ	Device i computes the standard deviation of the task size
Di	Mean value of task size for device i
Cj	Device j’s downstream bandwidth
Ls	Local processing task delay
Pa(t)	Total energy consumption of time slot t
Pi(t)	Energy consumed by fog node i
Pj(t)	Energy consumed by fog node j
Ps(t)	Energy consumed by fog node s
Pi,jc	Energy consumption of device i to transfer tasks to j
Pic	Transmit power of device i
Ci,j	Device i to j transfer rate
α	Offload rate
Pbi	Device i’s battery