# Multimedia Applications Processing and Computation Resource Allocation in MEC-Assisted SIoT Systems with DVS

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## Abstract

**:**

## 1. Introduction

- The minimization problem of multimedia application execution latency and energy consumption of IoT devices is studied by the allocation of computing resources in the edge servers while adopting the DVS technology.
- The studied problem of latency and energy consumption is formulated. Due to the formulated problem being an MINP problem, an efficient multimedia applications offloading scheme is proposed, and the solution of it is obtained.
- Simulation results are performed to evaluate the efficacy of the proposed multimedia applications offloading scheme by comparing with the two baseline schemes. The theoretical analysis and simulation results indicate that the multimedia applications’ offloading scheme proposed in this paper can perform better than the baseline methods, which can integrate the dependability aspects into the design of SIoT systems.

## 2. Related Work

**(1) Energy consumption minimization**.

**(2) Application execution time minimization**.

**(3) Both the energy and application processing time minimization**.

## 3. System Architecture

#### 3.1. Local Computation Model

#### 3.2. Edge Cloud Model

#### 3.3. Problem Formulation

**P:**

**Remark**

**1.**

**P**is a typical MINP problem, the function of which is non-convex and notoriously hard to be solved [43]. This is due to the fact that the application offloading decision is binary, but the computation resource allocation is continuous. We can apply the Alternating Direction Method of Multipliers (ADMM), dandelion algorithm (DA) [44], Bat algorithm [45], and branch-and-bound methods to solve the MINP problem. However, the time-complexity is prohibitive [26]. The authors in [46] solved the MINP problem using the algorithms of benders’ decomposition, admm, dinkelbach, and branch-and-bound, and compared the performances of these algorithms. In the following section, a method is proposed to obtain the optimal solution.

## 4. Solution Method

#### 4.1. Solution Method

**Lemma**

**1.**

**Lemma 1**shows that when trying to minimize a function, some variables can firstly be chosen to be minimized, and then the left ones are to be minimized.

**Lemma 1**, Problem

**P**can be solved by maximizing over ${f}_{i}^{l}$, and ${f}_{i}^{e}$ sequentially. Therefore, the problem

**P**can be solved from the solution of the below three subproblems:

#### 4.2. Local Computation Problem

**P**becomes the following problem:

**P1:**

#### 4.3. Edge Cloud Computation Problem

**P**becomes the following problem:

**P2:**

**P2**is easily checked as an obvious convex function. Hence, the Lagrangian function for problem

**P2**is

#### 4.4. Application Offloading Decision

Algorithm 1 Computational Resource Allocation and Applications Offloading Algorithm. |

Input: |

1: N applications; |

Output: |

2: The application offloading decision made by each user of IoT device and the system computation overhead; |

3: Obtain the optimal resource allocation of each IoT device by solving problem P1; |

4: Based on Equation (16), IoT devices make adjustments to their voltage and clock frequency to obtain the adaptive CPU frequency according to the weight coefficient values by applying the DVS technology; |

5: Obtain the optimized local computation cost of each IoT device based on Equation (17); |

6: Calculate the allocated computational resource of each IoT device by solving problem P2; |

7: Obtain the optimal computation cost of the edge cloud computation model from Equation (11); |

8: if ${G}_{i}\ge {H}_{i}$ then |

9: ${O}_{i}=1$; |

10: else |

11: ${O}_{i}=0$; |

12: end if |

## 5. Simulation Results

**Local Computing (LC) Algorithm:**In this algorithm, all the IoT devices do not take the offloading strategy. They compute their applications by using the computing resources of their devices.

**Edge Cloud (EC) Algorithm:**In this algorithm, there is no local computation. All the IoT devices take the offloading strategy, offload and process their applications in the edge cloud.

#### 5.1. Parameter Setting

#### 5.2. Effect of Weight Coefficient Values

#### 5.3. Effect of the Edge Cloud Capacity

**EC Algorithm**and the

**Proposed Algorithm**decrease with the increase in the edge cloud capacity. As the edge cloud capacity does not affect the local computation cost, the computation cost in the

**LC Algorithm**has the constant value. From Figure 7a,b, as anticipated, the

**Proposed Algorithm**can achieve less computation cost compared with the

**LC Algorithm**and the

**EC Algorithm**. By comparing Figure 7a,b, it can also be obviously observed that the computation cost is lower when ${\lambda}_{i,e}={\lambda}_{i,t}=0.5$. Moreover, the two figures show that the computation cost in the

**LC Algorithm**is lower than that in the

**EC Algorithm**until the edge cloud capacity reaches a threshold value. When ${\lambda}_{i,e}=0.5,{\lambda}_{i,t}=0.5$, the threshold value is comparatively smaller.

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

MEC | Mobile Edge Computing |

MCC | Mobile Cloud Computing |

SIoT | Social Internet of Things |

DVS | Dynamic voltage scaling |

MINP | Mixed-integer nonlinear programming |

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**Figure 1.**The growth of devices and connections worldwide [10].

Reference | DVS | Application Execution Time | Energy Consumption | Computation Resources |
---|---|---|---|---|

Chen et al. [16] | No | No | Yes | No |

Wang et al. [21] | Yes | Yes | Yes | No |

Wang et al. [30] | No | No | No | No |

Zhong et al. [35] | No | Yes | Yes | No |

Li et al. [22] | No | Yes | Yes | No |

Wang et al. [23] | No | No | Yes | Yes |

Liu et al. [33] | No | No | Yes | No |

Li et al. [14] | No | No | Yes | No |

Li et al. [38] | Yes | Yes | Yes | No |

Yang et al. [36] | No | Yes | Yes | No |

Liu et al. [24] | No | Yes | Yes | Yes |

Lyu et al. [26] | No | Yes | Yes | Yes |

You et al. [25] | No | Yes | Yes | Yes |

Zhao et al. [27] | No | Yes | Yes | Yes |

Kabir et al. [39] | No | Yes | Yes | No |

Zhang et al. [37] | Yes | Yes | Yes | No |

Sun et al. [31] | No | Yes | Yes | No |

Meskar et al. [29] | No | Yes | Yes | No |

Zeng et al. [28] | No | Yes | Yes | No |

Zhu et al. [40] | No | Yes | Yes | Yes |

This Study | Yes | Yes | Yes | Yes |

Notation | Description |
---|---|

${f}_{i}^{l}$ | The processing rate of the IoT device i |

${t}_{i,l}$ | The local processing time of the IoT device i |

${e}_{i,l}$ | The local energy consumption of the IoT device i |

${t}_{i,e}$ | The transmission time of the IoT device i |

${e}_{i,o}$ | The transmission energy consumption of the IoT device i |

${D}_{i}$ | The application i’s data size |

${C}_{i}$ | The needed CPU cycles to process application of IoT device i |

${\lambda}_{i,t}$ | The weighting parameter of application processing time |

${\lambda}_{i,e}$ | The weighting parameter of energy consumption |

${w}_{i}$ | The channel bandwidth |

${q}_{i}$ | The transmit power of the IoT device i |

${h}_{i}$ | The channel gain |

${\varpi}_{0}$ | The background noise power |

${r}_{i}$ | The uplink transmission rate for the IoT device i |

${O}_{i}$ | The application offloading decision that make by the IoT device i |

${f}_{i}^{e}$ | The allocated computational resources in the edge cloud to device i |

${f}_{i,m}$ | The maximum processing rate of the IoT device i |

F | The total computational resources in the edge servers |

Parameters | Values |
---|---|

The number of IoT devices N | 5 |

The bandwidth allocation ${w}_{i}$ | 1.6 MHz |

The data sizes of multimedia applications ${D}_{i}$ | [0.42, 4.2] Mb |

The transmission power ${q}_{i}$ | 1 W |

The needed computation resources ${C}_{i}$ | [0, 1] $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{9}$ cycles |

${k}_{i}$ | ${10}^{-26}$ |

The channel gain ${h}_{i}$ | $2.6\times {10}^{-7}$ |

The maximum processing rate ${f}_{i,m}$ | 1 GHz |

The background noise power ${\varpi}_{0}$ | ${10}^{-7}$ W |

The computation capacity of the edge cloud F | 20 GHz |

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## Share and Cite

**MDPI and ACS Style**

Li, X.; Chen, G.; Zhao, L.; Wei, B.
Multimedia Applications Processing and Computation Resource Allocation in MEC-Assisted SIoT Systems with DVS. *Mathematics* **2022**, *10*, 1593.
https://doi.org/10.3390/math10091593

**AMA Style**

Li X, Chen G, Zhao L, Wei B.
Multimedia Applications Processing and Computation Resource Allocation in MEC-Assisted SIoT Systems with DVS. *Mathematics*. 2022; 10(9):1593.
https://doi.org/10.3390/math10091593

**Chicago/Turabian Style**

Li, Xianwei, Guolong Chen, Liang Zhao, and Bo Wei.
2022. "Multimedia Applications Processing and Computation Resource Allocation in MEC-Assisted SIoT Systems with DVS" *Mathematics* 10, no. 9: 1593.
https://doi.org/10.3390/math10091593