01.12.2019 | Research | Ausgabe 1/2019 Open Access

# An energy saving based on task migration for mobile edge computing

## 1 Introduction

## 2 Background

### 2.1 Mobile edge computing

### 2.2 Task migration

### 2.3 Related works

## 3 Energy-saving strategy

### 3.1 Task decomposition

#### 3.1.1 Coarse-grained task decomposition

#### 3.1.2 Fine-grained linear chain task decomposition

_{k}denotes the load of computation, where k = 1, 2, … , n. So, we can get the total load of the computational subtasks which are \( \sum {\displaystyle \begin{array}{c}n\\ {}k=1\end{array}}{w}_k \). In Fig. 2, α

_{k}and β

_{k}denote the number of input and output data of kth subtask respectively.

#### 3.1.3 Fine-grained directed acyclic graph task decomposition

_{n}V, E

_{n}. In the task DAG, vertices v ∈ V represent tasks, and the edges e

_{uv}∈ E are used to represent dependencies between tasks. Thus, the e

_{uv}represent the task v start execution must be after task u, where u, v ∈ V.

### 3.2 Energy consumption and delay limit

Variable | Meaning | Unit |
---|---|---|

w
_{
v}
| Workload of task v | CPU instructions |

f
_{
l}
| Calculation rate of mobile terminal | MIPS |

f
_{
e}
| Calculation rate of mobile edge server | MIPS |

p
_{
l}
| Power of the mobile terminal when performing tasks | W |

p
_{
i}
| Power of the mobile terminal when idle | W |

p
_{
s}
| Sending power of the mobile terminal | W |

p
_{
r}
| Receiving power of the mobile terminal | W |

e
_{
uv}
| Data transfer amount between task u and task v | Bits |

B
_{
s}
| Data sending rate | Bits/s |

B
_{
r}
| Data receiving rate | Bits/s |

\( {T}_v^l \)
| Time spent on the mobile terminal of task v | s |

\( {T}_v^e \)
| Time spent on the mobile edge server of task v | s |

T
_{
uv}
| Time spent on transferring data from task u to v | s |

\( {E}_v^l \)
| Energy consumed on the mobile terminal of task v | J |

\( {E}_v^e \)
| Energy consumed on the edge server of task v | J |

E
_{
uv}
| Energy consumed by transferring data from task u to v | J |

_{uv}:

### 3.3 Energy consumption minimization

Variable | Meaning | Unit |
---|---|---|

E
_{total}
| Total energy consumption | W |

T
_{total}
| Time consuming | s |

T
_{max}
| Task completion time threshold | s |

\( {T}_v^b \)
| Start moment of task v | s |

\( {T}_v^{\mathrm{ex}} \)
| Executing time of task v | W |

\( {T}_v^f \)
| Finish moment of task v | W |

\( {E}_v^{ex} \)
| Executing energy consumption of task v | W |

R
_{
uv}
| Dependency between task u and task v | None |

D
_{
v}
| Execution location of task v | None |

_{total}is

### 3.4 Task migration strategy

#### 3.4.1 Initial

_{1}, D

_{2}, .…, D

_{n}] and each of its sub-elements.

#### 3.4.2 Fitness function

#### 3.4.3 Design of crossover method

#### 3.4.4 Design of variation method

#### 3.4.5 Genetic termination conditions

### 3.5 Optimization strategy

_{v}(λ) = 1. It means that the task should be handled at the MEC server.

## 4 Simulation and results

Variable | Meaning | Value |
---|---|---|

f
_{
l}
| Calculate speed of UE | 300 MIPS |

f
_{
e}
| Calculate speed of MEC server | 5000 MIPS |

B
_{
s}
| UE sending rate | 2 Mbps |

B
_{
r}
| UE receiving rate | 2 Mbps |

p
_{
l}
| UE working power | 0.50 W |

p
_{
i}
| UE idle power | 0.04 W |

p
_{
s}
| UE sending power | 0.03 W |

p
_{
r}
| UE receiving power | 0.01 W |