数字孪生边缘网络端到端时延优化的任务卸载与资源分配方法

李松; 李顺; 王博文; 孙彦景

doi:10.11999/JEIT240344

数字孪生边缘网络端到端时延优化的任务卸载与资源分配方法

doi: 10.11999/JEIT240344

李松^{1, 2, ,},
李顺¹,
王博文¹,
孙彦景^{1, 2}

1.
中国矿业大学信息与控制工程学院徐州 221116
2.
徐州市智能安全与应急协同工程研究中心徐州 221116

基金项目: 国家自然科学基金(62071472, 62101556)，江苏省自然科学基金(BK20210489)，中央高校基本科研业务费项目(2020ZDPYMS26)，江苏省研究生科研与实践创新计划项目(KYCX24_2763)，中国矿业大学研究生创新计划项目(2024WLJCRCZL133)，西安市网络融合通信重点实验室开放基金项目(2022NCC-N103)，海南省省属科研院所技术创新项目(KYYSGY2024-005)，工信部项目(CBG01N23-01-04)

详细信息

作者简介:
李松：男，副教授，研究方向为工业物联网、边缘计算等

李顺：男，硕士生，研究方向为移动边缘计算、数字孪生等

王博文：男，副教授，研究方向为工业物联网、社交物联网等

孙彦景：男，教授，研究方向为工业物联网、无线资源分配等

通讯作者:
李松　lisong@cumt.edu.cn

中图分类号: TN929.5
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- 被引次数: 0
出版历程
- 收稿日期: 2024-04-29
- 修回日期: 2025-02-12
- 网络出版日期: 2025-02-20
- 刊出日期: 2025-03-01

Task Offloading and Resource Allocation Method for End-to-End Delay Optimization in Digital Twin Edge Networks

LI Song^{1, 2
, ,},
LI Shun¹,
WANG Bowen¹,
SUN Yanjing^{1, 2}

1.
School of Information and Control Engineering, China University of Mining and Technology, Xuzhou 221116, China
2.
Xuzhou Engineering Research Center of Intelligent Industry Safety and Emergency Collaboration, Xuzhou 221116, China

Funds: The National Natural Science Foundation of China (62071472, 62101556), The Natural Science Foundation of Jiangsu Province of China (BK20210489), The Fundamental Research Funds for the Central Universities (2020ZDPYMS26), The Postgraduate Research & Practice Innovation Program of Jiangsu Province (KYCX24_2763), The Graduate Innovation Program of China University of Mining and Technology (2024WLJCRCZL133), Xi’an Key Laboratory of Network Convergence Communication (2022NCC-N103), The Project of Technical Innovation of Hainan Scientific Research Institutes (KYYSGY2024-005), The Ministry of Industry and Information Technology (CBG01N23-01-04)

摘要

摘要: 针对移动边缘计算(MEC)场景中任务卸载、计算和结果反馈全过程时延优化问题，该文提出了一种数字孪生(DT)辅助的联合MEC任务卸载、设备关联与资源分配的端到端时延优化方法。首先，在数字孪生边缘网络(DITEN)框架下，为包含传感器、边缘服务器以及执行器构成的边缘计算网络建立了物理模型与数字孪生模型，以及全过程边缘网络任务模型并推导了任务端到端时延，进而建立了时延、能耗等约束下的端到端时延优化问题。其次，为解决所提出的混合整数非凸优化问题，将原问题分解为4个子问题，并提出了一种基于内部凸近似方法和匈牙利算法的交替优化算法。在DT辅助下联合优化了设备关联、卸载比例、发射功率、传输带宽以及DT估计处理速率。最后，仿真结果表明，与其他基准方案相比，所提联合优化方案显著降低了端到端时延。
- 移动边缘计算 /
- 数字孪生 /
- 任务卸载 /
- 资源分配 /
- 交替优化
Abstract: Objective The rapid development of wireless communication and the Internet of Things (IoT) has led to significant growth in compute-intensive and delay-sensitive applications, which impose stricter latency requirements. However, local devices often face challenges in meeting these demands due to limitations in storage, computing power, and battery life. Mobile Edge Computing (MEC) has emerged as a key technology to address these issues. Despite its potential, the dynamic and complex nature of edge networks presents significant challenges in task offloading and resource allocation. DIgital Twin Edge Networks (DITEN), which map digital twins to physical devices in real-time, offer a promising solution. By integrating MEC with Digital Twin (DT) technology, this approach not only alleviates resource limitations in devices but also optimizes resource allocation in the digital domain, minimizing physical resource waste. This paper tackles the End-to-End (E2E) optimization problem in the offloading, computation, and result feedback process within edge computing networks. A DT-assisted joint task offloading, device association, and resource allocation scheme is proposed for E2E delay optimization, providing theoretical support for improving resource utilization in edge networks. Methods The optimization problem in this paper involves a non-convex objective function with both binary and continuous constraints, making it a mixed integer non-convex problem. To address this, the original problem is decomposed into four subproblems: computation and communication resource optimization, device association optimization, offloading decision optimization, and transmission bandwidth optimization. Within the Alternating Optimization (AO) framework, the Internal Convex Approximation (ICA) method is applied to convert the non-convex problem into a convex one. Additionally, the many-to-one matching problem is transformed into a one-to-one matching problem, and the Hungarian Algorithm (HA) is employed to solve the device association subproblem. Finally, the ICA-HA-AO is proposed to address the E2E delay optimization problem effectively. Results and Discussions The ICA-HA-AO algorithm approximates non-convex constraints as convex ones through constraint transformation and iteratively solves the original problem, determining optimal strategies for task offloading, device association, and resource allocation. Simulation results show that the ICA-HA-AO algorithm achieves optimal performance across varying task resource requirements, bandwidth, edge processing rates, and task volumes. Compared to the worst-performing benchmark scheme, delays are reduced by approximately 0.8 s, 1.5 s, 0.5 s, and 1.2 s, respectively (Fig. 5–Fig. 8). As the DT deviation increases, the delay also increases more significantly, with a rise of about 0.13 s when the deviation increases from 0.01 to 0.02, emphasizing the importance of setting the DT deviation (Fig. 9). When the number of devices remains constant and the number of Access Points (APs) increases, the delay continues to decrease, highlighting the significance of AP deployment in practice. Additionally, when the number of APs remains fixed and the number of devices increases, the delay increases accordingly. However, the ICA-HA-AO algorithm effectively controls the rate of delay increase. For instance, when the number of devices is 10, 15, and 20, the delay increase is reduced from 0.39 s to 0.21 s (Fig. 10). These results demonstrate that the ICA-HA-AO algorithm can more efficiently utilize and schedule resources, achieving optimal resource allocation. Conclusions This paper investigates the joint optimization problem of task offloading, device association, and resource allocation in DITEN. Firstly, within the edge computing network, physical and DT models are established for a network comprising sensors, edge servers, and actuators. A comprehensive task model is developed, and the E2E delay for tasks is derived. The optimization problem for minimizing E2E delay is then formulated, subject to constraints such as power and energy consumption. Secondly, to solve the proposed mixed integer non-convex optimization problem, the original problem is decomposed into four subproblems. Based on the ICA and HA methods, an ICA-HA-AO algorithm is proposed to solve the problem iteratively. Finally, simulation results demonstrate that the proposed ICA-HA-AO algorithm significantly reduces E2E delay and outperforms benchmark schemes. Future work may explore integrating this method with techniques to improve spectrum utilization, thereby further enhancing spectrum efficiency and overall performance in DITEN systems.
- Mobile Edge Computing (MEC) /
- Digital Twin (DT) /
- Task offloading /
- Resource allocation /
- Alternating optimization

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图 1 数字孪生边缘网络(DITEN)系统模型

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图 2 全过程任务模型

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图 3 端到端时延示意图

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图 4 基于加边补零法的二分图最优匹配过程

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图 5 任务所需计算资源与端到端时延的关系

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图 6 传输带宽与端到端时延的关系

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图 7 服务器处理速率与端到端时延的关系

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图 8 任务量与端到端时延的关系

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图 9 不同DT偏差对端到端时延的影响

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图 10 设备数量不同的端到端时延对比

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1 基于内部凸近似的计算与通信资源分配算法

输入：卸载因子 $\alpha$ ，关联变量 $\pi$ ，传输带宽 $\bar b,\underline b$ ，发射功率 $p$ 以及　计算频率 ${\mathbf{f}}$ ；
初始化：迭代次数 $i = 0$ ，容忍值 $\varepsilon$ ，最大迭代次数 ${I_{\max }}$
输出：最优功率和计算频率 $({p^},{{\mathbf{f}}^})$
(1) while 1 do
(2) 　　求解问题式(24)的可行解 $({p^{(i + 1)}},{{\mathbf{f}}^{(i + 1)}})$ ；
(3) 　　 $i = i + 1$
(4) 　if 收敛or $i \gt {I_{\max }}$ then
(5) 　　break；
(6) 　end if
(7) end while

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2 基于匈牙利算法的传感器与AP关联优化算法

输入：卸载因子 $\alpha$ ，传输带宽 $\bar b,\underline b$ ，发射功率 $p$ 以及计算频率 ${\mathbf{f}}$ ；
输出：最优关联策略 $({\pi ^*})$
(1)给定传感器数量K，AP数量M，AP能够服务传感器的最大数　量N；
(2)每个AP虚拟成N个，形成数量为NM的虚拟AP集合；
(3)if $K \lt NM$ then
(4) 　加边补零，增加 $NM - K$ 个虚拟传感器；
(5)end if
(6)执行匈牙利算法。

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3 基于内部凸近似方法和匈牙利算法的ICA-HA-AO算法

输入：卸载因子 ${\alpha ^{(0)}}$ ，关联变量 ${\pi ^{(0)}}$ ，带宽 ${\bar b^{(0)}},\underline b^{(0)}$ ，发射功率 ${p^{(0)}}$ ，计算频率 ${{\mathbf{f}}^{(0)}}$ ，设置迭代次数 $i = 0$ ，容忍值 $\varepsilon$ 和最大迭代次数 ${I_{\max }}$ ；
输出：最优资源分配 $({\alpha ^},{\pi ^},{\bar b^},{\underline {b} ^},{p^},{{\mathbf{f}}^})$
(1) while 1 do
(2) 　给定 $({\alpha ^{(i)}},{\pi ^{(i)}},{\bar b^{(i)}},{\underline b} ^{(i)})$ ，利用算法1求解子问题SP1，得到最优传感器计算频率以及AP的计算频率和发射功率 $({p^{^{(i + 1)}}},{{\mathbf{f}}^{^{(i + 1)}}})$ ；
(3) 　给定 $({{\mathbf{f}}^{(i + 1)}},{p^{(i + 1)}},{\alpha ^{(i)}},{\bar b^{(i)}},\underline b^{(i)})$ ，利用算法2求解子问题SP2，得到最优传感器与AP关联策略 $({\pi ^{^{(i + 1)}}})$ ；
(4) 　给定 $({{\mathbf{f}}^{(i + 1)}},{p^{(i + 1)}},{\pi ^{(i + 1)}},{\bar b^{(i)}},{\underline b ^{(i)}})$ ，利用内点法求解子问题SP3，得到最优卸载决策 $({\alpha ^{^{(i + 1)}}})$ ；
(5) 　给定 $({{\mathbf{f}}^{(i + 1)}},{p^{(i + 1)}},{\pi ^{(i + 1)}},{\alpha ^{(i)}})$ ，利用内点法求解子问题SP4，得到最优上下行带宽 $({\bar b^{(i + 1)}},{\underline b^{(i + 1)}})$ ；
(6) 　 $i = i + 1$
(7) 　　if 收敛 or $i \gt {I_{\max }}$ then
(8) 　　　break;
(9) 　　end if
(10) end while

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表 1 仿真参数

参数名	参数值	参数名	参数值
传感器发射功率 ${\bar p_k}$	10 dBm^[8]	传感器最大计算频率 $F_{\max }^{\rm{se} }$	3 GHz^[7]
AP最大发射功率 ${P_{\max }}$	40 dBm^[18]	AP最大计算频率 $F_{\max }^{\rm{AP} }$	10 GHz^[7]
输入任务量 ${I_k}$	100 Mbit^[18]	路径损耗 ${\beta _0}$	–30 dB^[14]
任务所需计算资源 ${C_k}$	960×10⁶ cycle^[7]	参考距离 ${d_0}$	10 m^[9]
传输总带宽 $B$	20 MHz^[18]	噪声功率 ${N_0}$	–174 dBm/Hz^[18]
最大时延与能耗 ${T_{\max }},{E_{\max }}$	2 s, 1.5 J	有效交换电容系数 $\xi$	10^–28[9]

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