Table 2 List of Notations.

1

Computation task size

\({t_s}\)

2

Number of MDs

N

3

Number of cycles for computation

\({C_r}\)

4

Task performance latency

\({T_L}\)

5

Number of MHs

M

6

Resource of mobile device

\({f_{MD}}\)

7

Resource of mobile helper

\({f_{MH}}\)

8

Resource of Relay Edge Server

\({f_{RES}}\)

9

Resource of Edge Server

\({f_{ES}}\)

10

Local Computing Time

\({t^{local}}\)

11

System capacitance

\({C_\Psi }\)

12

Data rate for D2D link

\(R_{{}}^{{D2D}}\)

13

Bandwidth

B

14

Local computing energy

\({e^{local}}\)

15

Transmitted Power

\({P^t}\)

16

TR for local

\(\Upsilon _{{}}^{{loacl}}\)

17

Physical distance between MH and MD

\({d_m}\)

18

Noise

\({N_0}\)

19

Path-loss

\(\alpha\)

20

TR for MH

\(\Upsilon _{{}}^{{help}}\)

21

TR for RES

\(\Upsilon _{{}}^{{RES}}\)

22

TR for ES

\({\Upsilon ^{ES}}\)

23

Time for D2D communication and computation

\(t_{{}}^{{D2D}}\)

24

Energy used in D2D task offloading

\(e_{{}}^{{D2D}}\)

25

Achievable data rate for RES

\({R^{RES}}\)

26

Physical distance between user and ES

\({d^{ES}}\)

27

Physical distance between user and MH

\(d_{r}^{{MH}}\)

28

Physical distance between user and RES

\({d^{RES}}\)

29

Time for RES for communication and computation

\({t^{RES}}\)

30

Energy usage during RES task offloading

\({e^{RES}}\)

31

Time for ES for communication and computation

\({t^{ES}}\)

32

Energy consumed during offloading thorough ES

\({e^{ES}}\)

33

Total Energy Power Consumption

\({e^{total}}\)

34

Delay Tolerance

\({T_{tolerance}}\)

35

Stoichiometry Matrix

S

36

Flux vector

V

37

Learning rate

\(\psi\)

38

Discount factor

\(\delta\)

39

Future reward

\({\phi _{i+1}}\)

40

Maximum power transmitted by MD

\({P_{\hbox{max} }}\)

39

Action

\({P_a}\)