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Advances, Systems and Applications

Table 2 Summary of Notations

From: Mobility-aware hierarchical fog computing framework for Industrial Internet of Things (IIoT)

Sr.

Symbol

Definition

1

U

List of user IIoT devices

2

V

List of volunteer IIoT devices

3

\(n_u\)

No. of devices in List U

4

\(n_v\)

No. of devices in List V

5

\({V_c}^i\)

Computation capacity of ith volunteer device

6

\(\Upsilon _{\text {L}}\)

Local execution rate on mobile device

7

\(\upsilon _{k}\)

Execution required by task \(\sigma _k\)

8

\(\sigma _{s}^i\)

The workload received at \(s_{th}\) server in level-i.

9

\(\sigma _{k}^{\text {L}}\)

The workload executed locally

10

\(\sigma _{k}^{\text {F}}\)

The workload executed in Fog

11

\(\sigma _{k}^{\text {C}}\)

The workload executed in Cloud

12

\({\zeta _s}^1\)

The capacity of \(s_{th}\) server in level-i.

13

\({Off}_i\)

The offloaded workload

14

\(\delta\)

The execution delay

15

\(\digamma _n\)

Dedicated Fog Nodes

16

\(W_n\)

Gateway Nodes

17

\(U_n\)

User nodes seeking computation

18

\(V_n\)

User nodes volunteer resources

19

\(\mathcal {D}_i^\digamma\)

Computation delay (queue + service)