N

data size of the task

\({{f}_{\text {loc}}},{{f}_{\text {AP}_i}},{{f}_{\text {C}}}\)

Computation capacity of the UE,AP and cloud

\(\omega\)

CPU cycles for 1 bit

\(R_i\)

Ergodic rate between the UE and AP in mode \(i, i\in \Omega\)

\(\kappa\)

Effective capacitance coefficient

\({{n}_{1}},{{n}_{2}}\)

Upper bounds of capacity of channel

\({{B}_{1}},{{B}_{2}}\)

Transmit bandwidth of UE and AP

\(r_i\)

Ergodic rate between the AP and cloud in mode \(i, i\in \Omega\)

\({{p}_{1}},{{p}_{2}}\)

Transmit power of the UE and AP

\({{v}_{1}},{{v}_{2}},{{v}_{3}}\)

Unit price of UE, AP and cloud

\(\sigma ^{2}\)

Noise density

\(\lambda _i\)

Distribution density of FAP(i=1) and AP(i=2)

\(M_i\)

Coverage probability of mode \(i, i\in \Omega\)

\({{F}_{\min }},{{F}_{\max }}\)

Upper and lower bounds of coverage probability

\(\varvec{\alpha },\beta\)

Optimized variables

\(T_i\)

Preset threshold of SNR value in mode \(i, i\in \Omega\)

\(\Omega\)

Set of {1,2}

\(\Psi\)

Set of {1,2,3}

\(Z_i\)

Charge of mode \(i, i\in \Psi\)

k

Probability of an AP supporting computation

\(G_\mho , \mho \in \{\text {loc,AP,C}\}\)

Prices per second for computing delay at UE, AP and the cloud

P

Expect charge of the system
