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Edge User Allocation in Overlap Areas for Mobile Edge Computing

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Abstract

The rapid development of mobile communication technology has promoted the emergence of mobile edge computing (MEC), which allows mobile users to transfer their computing tasks to nearby edge servers to reduce access latency. In the actual MEC environment, the signal coverage areas of edge servers usually overlap partially, and users in the overlapped areas can choose to connect to one of the edge servers that cover them. How to allocate these users will seriously affect MEC performance. To solve this issue, we focus on the overlapped area user allocation (OAUA) problem in the MEC environment and model it as a multi-objective optimization problem. The objective is to balance the workload among edge servers and minimize the access delay between users and edge servers. Pareto model is universal for solving multi-objective optimization problems. However, the traditional method has high computational complexity to find the Pareto boundary. Therefore, we propose a Pareto boundary search algorithm based on convex hull to reduce the complexity of the algorithm. Since the Pareto boundary is a set of optimal solutions, which contains multiple optimal solutions, we further propose to use the principal component analysis algorithm to find the most suitable solution from the Pareto boundary as the final user allocation strategy. Our experiments use real data sets and compare the performance with several other baseline methods to verify the effectiveness of our proposed solution.

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Acknowledgments

This work was supported by Beijing Nova Program of Science and Technology (No. Z201100006820082), National Natural Science Foundation of China (No. 61972414), Beijing Natural Science Foundation (No. 4202066), National Key Research and Development Plan (No. 2016YFC0303700), and Fundamental Research Funds for Central Universities (Nos. 2462018YJRC040 and 2462020YJRC001).

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Authors and Affiliations

  1. Beijing Key Laboratory of Petroleum Data Mining, China University of Petroleum-Beijing, Beijing, 102249, China

    Fangzheng Liu, Bofeng Lv, Jiwei Huang & Sikandar Ali

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  1. Fangzheng Liu
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  2. Bofeng Lv
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  3. Jiwei Huang
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  4. Sikandar Ali
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Correspondence to Jiwei Huang.

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Appendix: Proof of Theorem 1

Appendix: Proof of Theorem 1

The first element of the array Q after sorting is the point with the least delay. Because there is no solution that both delay and load are smaller than this point, this solution is the Pareto optimal solution. According to the solution process of Algorithm 1, the following formula is easy to know.

$$ P_{1}.Workload>P_{2}.Workload>...>P_{l}.Workload $$
(7)

We assume that there is h and Ph point is the second solution in the convex hull solution set, but Ph is not the Pareto optimal solution.

$$ P_{l}.Workload\!<\!P_{h}.Workload, \\ P_{l}.Time\!<\!P_{h}.Time, \\ h\!>\!1 $$
(8)

From Eq. 7, we can get l > h, the angle between the edge formed by P1 and Pl and the edge formed by P1 and Ph is expressed as

$$ \begin{array}{@{}rcl@{}} (P_{h} - P_{1})\!\times\! (P_{l} - P_{1}) &=&(P_{h}.Time-P_{1}.Time)\\ &&\!\!\!\times(P_{l}.Workload-P_{1}.Workload)\\ &&\!\!\!-(P_{h}.Workload-P_{1}.Workload)\\ &&\!\!\!\times(P_{l}.Time-P_{1}.Time) \end{array} $$
(9)

From Eqs. 7 and 8, we can get Ph.Time − P1.Time > Pl.Time − P1.Time > 0, Pl.Workload − P1.Workload < Ph.Workload − P1.Workload < 0. Then the value of Eq. 9 is less than 0, that is, the edge formed by P1 and Pl is on the right side of the edge formed by P1 and Ph. According to the Algorithm 1, Ph will be popped out of the stack before Pl is pushed into the stack. Therefore, the Ph point must be the second solution in the convex hull solution set, and Ph is the Pareto optimal solution. By analogy, the convex hull solutions satisfying Eq. 7 are all Pareto optimal solutions. It can be seen from the above proof steps that the solutions of the algorithm are all Pareto optimal solutions.

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Liu, F., Lv, B., Huang, J. et al. Edge User Allocation in Overlap Areas for Mobile Edge Computing. Mobile Netw Appl 26, 2423–2433 (2021). https://doi.org/10.1007/s11036-021-01783-9

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