Table 1 Symbols and definitions

\(C=\{c_1,c_2,c_3,\ldots ,c_n\}\)

Crowd task set

\(l=\{l_{c_1},l_{c_2},l_{c_3},\ldots l_{c_n}\}\)

Crowd tasks posted location set

\(T_{satrt}\)

Crowd task release time

\(T_{end}\)

Crowd task deadline

\(T=\{t_{c_1},t_{c_2},t_{c_3},\ldots ,t_{c_n}\}\)

Maximum allowable delay set for crowd tasks

\(D=\{d_{c_1},d_{c_2},d_{c_1},\ldots ,d_{c_n}\}\)

The amount of data contained set in the crowd task

\(W=\{w_1,w_2,w_3,\ldots ,w_m\}\)

Crowd worker set

\(W_{id}\)

Crowd worker id

\(S_{{c_i}{w_j}}\)

Task offload policy

\(r_{local}\)

Local data processing rate

\(q_{local}\)

Consumption per bit of data processed locally

\(x_{edge}\)

Edge server data transfer rate

\(r_{edge}\)

The rate at which edge server data is processed

\(y_{edge}\)

Transmission energy consumption per bit data of edge server

\(q_{edge}\)

Energy consumption per bit of data processed by edge servers

\(T_{local}(c_i,w_j)\)

Local time consumption of worker \(w_j\) task \(c_i\)

\(E_{local}(c_i,w_j)\)

Local energy consumption of worker \(w_j\) task \(c_i\)

\(T_{edge}(c_i,w_j)\)

The marginal time consumption of worker \(w_j\) task \(c_i\)

\(E_{edge}(c_i,w_j)\)

The marginal energy consumption of worker \(w_j\) task \(c_i\)

\(W_{local}\)

The total consumption of local processing computing tasks

\(W_{edge}\)

The total consumption of edge servers processing computing tasks