# Time Series-Based Edge Resource Prediction and Parallel Optimal Task Allocation in Mobile Edge Computing Environment

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## Abstract

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## 1. Introduction

- (i)
- A delay sensitivity-based priority scheduling (DSPS) policy is presented to schedule the tasks as per their deadline.
- (ii)
- An exploratory data analysis is carried out, and inference is made regarding seasonal patterns in the usage of edge CPU resources from the GWA-T-12 Bitbrains VM utilization dataset.
- (iii)
- The availability of VM resources is predicted by using HWVMR and VARVMR.
- (iv)
- For optimal and fast task assignment, a parallel differential evolution-based task allocation (pDETA) strategy is proposed.
- (v)
- The proposed algorithms are evaluated extensively by using standard performance metrics, e.g., execution time, cost, and energy.

## 2. Related Work

## 3. System Model

#### 3.1. Task Model

#### 3.2. VM Model

#### 3.3. Cost Model

#### 3.4. Energy Model

#### 3.5. Load Model

## 4. Problem Formulation

## 5. Network Architecture

Algorithm 1: Delay sensitivity-based priority scheduling (DSPS) |

Algorithm 2: Holt–Winters-based univariate algorithm (HWVMR) |

Algorithm 3: VAR-based multivariate algorithm (VARVMR) |

Algorithm 4: Parallel differential evolution-based task allocation (pDETA) |

## 6. Proposed Methodologies

#### 6.1. Delay Sensitivity-Based Priority Scheduler

- $D{S}_{t}>=T{h}_{1}$, the task is placed in ${Q}_{HP}$.
- $D{S}_{t}<=T{h}_{2}$, the task is placed in ${Q}_{LP}$.
- $T{h}_{1}>D{S}_{t}>T{h}_{2}$, the task is placed in ${Q}_{MP}$.

#### 6.2. Time Series-Based VM Resource Predictor

#### 6.2.1. Exploratory Analysis of Resource Prediction

#### 6.2.2. Applied Holt–Winters-Based Resource Prediction

#### 6.2.3. Applied VAR Based Resource Prediction

#### 6.3. Parallel Optimal Allocator

#### 6.3.1. Finding Suitable VM by Using Minkowski Distance

#### 6.3.2. Parallel Differential Evolution Algorithm

- Problem definition: Our aim is to assign the task to a suitable predicted VM from the predicted VM lists with the optimum allocation of resources considering minimum distance by applying Equation (22). The mapping of the available VM resources with the required task resources. Here, the resources are CPU usage and memory usage for the VMs and tasks. The task is assigned to the VM only when the following equation will be satisfied:$${R}_{i}[CPU,Mem]>{r}_{i}[CPU,Mem].$$
- Problem parameters: The population size (N) is ${P}_{s}$, the dimension of the problem (D) is 4, the stopping criteria (maximum number of iterations) is set to 5, the scaling factor (F) is 0.5, and the crossover probability ${P}_{cr}$ is 0.7. The value of the scaling factor is inversely proportional to the local search ability, so we have considered a minimum value for the scaling factor, i.e., 0.5 to become strong in the local search algorithm.
- Initialization: Based on ${P}_{s}$, the number of initial solutions are obtained by satisfying the problem definition. Here, all the possible assignments take place and discover the best solution having minimum result by applying Equation (22).
- Differential evolution position update: Here we have considered the suitable strategy as DE/Best/1/2 for binomial crossover based on two randomly assigned pairs. The generations are formed based on the above procedure. Here, we have discussed the process followed in one generation.
- Chromosome formation: In the beginning, we assign the predicted VM resources from the set of $\{V{M}_{p1}$, $V{M}_{p2}$, ……, $V{M}_{pm}\}$ with the set of requested tasks $\{{T}_{11},{T}_{21},\dots \dots ,$${T}_{nm}\}$ available in the priority scheduled queues. The active tasks will become 1, and the inactive tasks will become 0 in the different task sets present in the chromosome. The chromosome is represented in Figure 10.
- Population: We collect all the chromosomes, and make them ready for the parallel computation of the individual population by using the differential evolution algorithm.
- Subpopulation: We consider a single population for finding the fitness function until the termination condition arrives. Here, the subpopulations are implemented in parallel to finding the fitness function for an individual one.
- Fitness function: This refers to the calculation of the computation time, cost, and energy required for the computation in edge resources.The best fitness function = {$Min\left({C}_{t}\left(i\right)\right)$, $Min\left({C}_{T}\left(i\right)\right)$, $Min\left({E}_{t}\left(i\right)\right)$}.
- Mutation: The predicted VM resource is assigned with the possible set of requested tasks from the priority scheduled queues. The output of the mutation module is the input to the crossover module. Once the single output is released to the crossover module for the individual assignment, the mutation module is ready with the next possible assignment of the task to the VM resource. The best suitable mutation strategy is the “DE/Best/1/2” as$${V}^{\mu G}={X}_{best}^{\mu G}+F({X}_{r1}^{\mu G}-{X}_{r2}^{\mu G}),$$
- Crossover: The crossover method increases the diversity of the population. This module is ready for the calculation of the fitness function for the input to the mutation module. The crossover method is shown below,$${U}_{i}^{c}=\left\{\begin{array}{c}{V}_{i}^{c}\phantom{\rule{2.em}{0ex}}if\phantom{\rule{0.277778em}{0ex}}r\le {C}_{p}\phantom{\rule{0.277778em}{0ex}}or\phantom{\rule{0.277778em}{0ex}}i=\delta \hfill \\ {X}_{i}^{c}\phantom{\rule{2.em}{0ex}}if\phantom{\rule{0.277778em}{0ex}}r>{C}_{p}\phantom{\rule{0.277778em}{0ex}}and\phantom{\rule{0.277778em}{0ex}}i\ne \delta \hfill \end{array}\right.,$$
- Selection: This module selects the best mapping of the predicted VM resource with the requested task by applying Equation (22). It takes the output of the crossover module and finds the best fitness function for the selection of the task placement of the individual subpopulation.
- Termination: The termination condition arrives when we obtained the best fitness function with the minimum computation time, cost, and energy after merging all the fitness functions calculated from the individual subpopulations. After the termination condition was reached, we obtained the optimized placement of the requested task in the VM.

## 7. Simulation Results

## 8. Conclusions and Future Work

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

T | Task |

VM | Virtual machine resource |

${Q}_{HP}$ | High-priority queue |

${Q}_{MP}$ | Medium-priority queue |

${Q}_{LP}$ | Low-priority queue |

${T}_{H}$ | High-priority task |

${T}_{M}$ | Medium-priority task |

${T}_{L}$ | Low-priority task |

$D{E}_{t}$ | Delay of the task |

$D{S}_{t}$ | Delay sensitivity of the task |

$S{R}_{e}st$ | Estimation time of the service request |

$T{h}_{1},T{h}_{2}$ | Threshold value |

$V{M}_{p}$ | Predicted VM |

$V{M}_{s}$ | Sorted VM |

t | Time period |

${C}_{t}$ | Computation time of the task |

${L}_{t}$ | Level at time t |

${L}_{t-1}$ | Level at time t−1 |

${T}_{t}$ | Trend at time t |

${T}_{t-1}$ | Trend at time t−1 |

${S}_{t}$ | Season at time t |

${S}_{t-1}$ | Season at time t−1 |

${F}_{t+1}$ | Forecasting at time t+1 |

${F}_{t+k}$ | Forecasting at time t+k |

${D}_{t}$ | Data at time t |

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**Figure 12.**Performance evaluation by using average waiting time with the number of service requests.

Parameter | Value |
---|---|

Number of tasks | 50 to 600 |

Size of the task | 2 to 20 GI |

Number of VMs | 5 to 30 |

VM processing speed | 10 GIPS |

Latency–sensitivity | 0 to 10 |

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**MDPI and ACS Style**

Behera, S.R.; Panigrahi, N.; Bhoi, S.K.; Sahoo, K.S.; Jhanjhi, N.Z.; Ghoniem, R.M. Time Series-Based Edge Resource Prediction and Parallel Optimal Task Allocation in Mobile Edge Computing Environment. *Processes* **2023**, *11*, 1017.
https://doi.org/10.3390/pr11041017

**AMA Style**

Behera SR, Panigrahi N, Bhoi SK, Sahoo KS, Jhanjhi NZ, Ghoniem RM. Time Series-Based Edge Resource Prediction and Parallel Optimal Task Allocation in Mobile Edge Computing Environment. *Processes*. 2023; 11(4):1017.
https://doi.org/10.3390/pr11041017

**Chicago/Turabian Style**

Behera, Sasmita Rani, Niranjan Panigrahi, Sourav Kumar Bhoi, Kshira Sagar Sahoo, N.Z. Jhanjhi, and Rania M. Ghoniem. 2023. "Time Series-Based Edge Resource Prediction and Parallel Optimal Task Allocation in Mobile Edge Computing Environment" *Processes* 11, no. 4: 1017.
https://doi.org/10.3390/pr11041017