批量到达物联网状态更新系统的决策年龄与决策失真分析

刘磊; 靳文凯; 张清清; 李渝舟; 江帆

doi:10.11999/JEIT260359

批量到达物联网状态更新系统的决策年龄与决策失真分析

doi: 10.11999/JEIT260359 cstr: 32379.14.JEIT260359

1.
西安邮电大学通信与信息工程学院西安 710121
2.
浙江工业大学信息工程学院杭州 310023
3.
华中科技大学电子信息与通信学院武汉 430071

基金项目: 国家自然科学基金 (62471195, 62331010, 62201456)

详细信息

作者简介:
刘磊：男，讲师，硕士生导师，研究方向为时敏网络性能分析与优化设计等

靳文凯：男，硕士生，研究方向为宽带无线通信等

张清清：女，副教授，硕士生导师，研究方向为智能通信、无线通信网络智能化等

李渝舟：男，教授，博士生导师，研究方向为智能无线通信、信号处理等

江帆：女，教授，博士生导师，研究方向为D2D通信技术、雾计算等

通讯作者:
李渝舟　yuzhouli@hust.edu.cn

1¹⁾ 该条件主要用于获得解析表达式，且已被文献[18]用于对状态更新权重的建模与分析之中。当批内状态更新的权重存在相关性时，可在本文的分析框架下考虑联合分布进行扩展分析。
中图分类号: TN926
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出版历程
- 收稿日期: 2026-03-30
- 修回日期: 2026-06-23
- 录用日期: 2026-06-24
- 网络出版日期: 2026-07-02

Analysis of Age upon Decisions and Distortion at Decisions in IoT Status Update Systems with Batch Arrivals

1.
School of Communications and Information Engineering, Xi’an University of Posts and Telecommunications, Xi’an 710121, China
2.
College of Information Engineering, Zhejiang University of Technology, Hangzhou 310023, China
3.
School of Electronic Information and Communications, Huazhong University of Science and Technology, Wuhan 430071, China

Funds: The National Natural Science Foundation of China (62471195, 62331010, 62201456)

摘要

摘要: 针对具有批量到达特征的物联网(IoT)状态更新系统，该文以决策年龄(AuD)和决策失真(DaD)作为性能指标研究了系统决策的新鲜度和失真度。利用排队论，该文在批量大小服从一般分布的条件下推导得出平均AuD与平均DaD的解析表达式。在此基础上，考虑具有典型随机波动特征的几何分布批量大小，采用交替迭代优化算法对批到达率、平均批量大小和决策阈值进行联合优化，从而实现最小化平均AuD和平均DaD的加权和。仿真结果验证了理论分析的正确性。该研究发现，在一般分布的批量大小条件下，系统决策的新鲜度和失真度之间存在明显的权衡关系；在批量大小服从几何分布的典型场景下，该文所设计的算法能够在平均AuD和平均DaD之间实现帕累托最优权衡。
- 物联网 /
- 状态更新系统 /
- 批量到达 /
- 决策年龄 /
- 决策失真
Abstract: Objective The rapid development of the Internet of Things (IoT) makes the timely transmission and processing of status updates essential for modern systems, where information freshness at decision epochs plays a critical role. In many IoT applications, such as smart grid fault detection and Industrial Internet of Things (IIoT) cluster monitoring, status updates typically arrive in batches rather than individually. However, most existing studies on Age of Information (AoI) assume single-update arrivals and therefore cannot accurately characterize the queueing dynamics caused by batch arrivals. Besides information freshness, distortion at decision epochs is another key factor because it directly affects decision quality. A fundamental tradeoff therefore exists between information freshness and distortion. Waiting for more complete status update information allows more completed status updates to be incorporated into joint estimation, but increases queueing and transmission delays, thereby reducing information freshness. In contrast, triggering decisions earlier reduces delay but increases distortion because fewer completed status updates are available for joint estimation. To address this problem, this paper investigates the tradeoff between information freshness and distortion in an IoT status update system with batch arrivals by adopting Age upon Decisions (AuD) and Distortion at Decisions (DaD) as performance metrics. Analytical expressions for the average AuD and average DaD are derived under a general batch-size distribution. Furthermore, for the typical case of geometrically distributed batch sizes, an alternating iterative optimization algorithm is developed to jointly optimize the batch arrival rate, average batch size, and decision threshold, thereby minimizing the weighted sum of the average AuD and average DaD. The results provide theoretical insight and practical guidance for the design of IoT status update systems with batch arrivals. Methods Information freshness and distortion at decision epochs are analyzed for an IoT status update system with batch arrivals. AuD and DaD are adopted to quantify information freshness and distortion, respectively. Based on queueing theory, analytical expressions for the average AuD and average DaD are derived under a general batch-size distribution. A typical case with geometrically distributed batch sizes is then investigated. An alternating iterative optimization algorithm is further developed to jointly optimize the batch arrival rate, average batch size, and decision threshold to minimize the weighted sum of the average AuD and average DaD. Results and Discussions Simulation results validate the theoretical analysis. The average AuD exhibits a nonmonotonic trend as the batch arrival rate increases, first decreasing and then increasing. In addition, the Batch-size Coefficient Of Variation (BCOV) has a significant effect on the average AuD, with a smaller BCOV providing better information freshness performance. Under high-load conditions, queue backlogs become more severe, and stochastic fluctuations in batch arrivals have a greater effect on the queueing process. This increases service-time variability and amplifies the effect of BCOV on the average AuD (Fig. 2). As the average batch size increases, the system queue length and queueing delay increase, leading to a larger average AuD. At the same time, the decision control unit can utilize more completed status updates for joint estimation, thereby reducing the average DaD (Fig. 3). Moreover, the average DaD decreases as the decision threshold increases because more completed status updates are incorporated into the joint estimation process, improving estimation accuracy. A larger BCOV also increases the number of completed status updates available for joint estimation and therefore further reduces the average DaD (Fig. 4). The optimization results show that the solutions obtained by the proposed algorithm lie on the Pareto frontier, demonstrating its effectiveness. By comparison, fixed batch arrival rates and decision thresholds produce performance that is considerably farther from the Pareto frontier, demonstrating the advantage of jointly optimizing system parameters (Fig. 5). Conclusions This paper investigates an IoT status update system with batch arrivals by adopting AuD and DaD to quantify information freshness and distortion, respectively. Analytical expressions for the average AuD and average DaD are derived under a general batch-size distribution. For the typical case of geometrically distributed batch sizes, an alternating iterative optimization algorithm is developed to jointly optimize the batch arrival rate, average batch size, and decision threshold, thereby minimizing the weighted sum of the average AuD and average DaD. Simulation results verify the theoretical analysis and reveal the effects of the batch arrival rate, average batch size, and decision threshold on the average AuD and average DaD. The results also demonstrate that the proposed low-complexity algorithm effectively identifies Pareto-optimal solutions for the AuD-DaD tradeoff. This study considers only the batch arrival characteristics of status updates. Future work will incorporate batch service mechanisms to further examine their effects on the tradeoff between AuD and DaD. Flexible decision mechanisms can also be developed to achieve adaptive AuD-DaD tradeoffs according to the heterogeneous requirements for information freshness and distortion across applications with different batch characteristics.
- Internet of Things (IoT) /
- Status update system /
- Batch arrival /
- Age upon Decisions (AuD) /
- Distortion at Decisions (DaD)

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图 1 系统模型

下载: 全尺寸图片幻灯片

图 2 平均AuD随批到达率变化($ \mathbb{E}\left[N\right]=10 $)

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图 3 平均AuD和平均DaD随平均批量大小变化($ \lambda =1,\theta =0.4 $)

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图 4 平均DaD随决策阈值变化($ \mathbb{E}\left[N\right]=10 $)

下载: 全尺寸图片幻灯片

图 5 平均AuD与平均DaD权衡关系

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1 交替迭代优化算法

输入：权重因子$ \eta $，批到达率$ {\lambda }^{(0)} $，平均批量大小$ {m}^{(0)} $
(1) 初始化迭代索引$ r=0 $，迭代停止精度$ {\epsilon }_{\text{AO}} $
(2) 执行迭代循环：
(3) 　更新$ {\theta }^{(r+1)}={q}^{-1}\left({D}_{\text{th}}{\left({\lambda }^{(r)}{m}^{(r)}\right)}^{-1}\right) $
(4) 　固定$ \left({\theta }^{(r+1)},{\lambda }^{(r)}\right) $，利用枚举法解得$ {m}^{(r+1)}=\underset{m}{\arg \min }J\left({\lambda }^{(r)},m,{\theta }^{(r+1)}\right) $
(5) 　固定$ \left({\theta }^{(r+1)},{m}^{(r+1)}\right) $，利用黄金分割法解得$ {\lambda }^{(r+1)}=\underset{\lambda }{\arg \min }J\left(\lambda ,{m}^{(r+1)},{\theta }^{(r+1)}\right) $
(6) 　计算当前目标函数值$ {J}^{(r+1)}=J\left({\lambda }^{(r+1)},{m}^{(r+1)},{\theta }^{(r+1)}\right) $
(7) 更新$ r\leftarrow r+1 $
(8) 直到：$ \left\| {J}^{(r+1)}-{J}^{(r)}\right\| \lt {\epsilon }_{\text{AO}} $
输出：$ \lambda^={\lambda }^{(r+1)} $, $ m^={m}^{(r+1)} $, $ \theta^*={\theta }^{(r+1)} $

下载: 导出CSV

参考文献(18)

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