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
- 修回日期: 2026-06-24
- 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 advancement of the Internet of Things (IoT) has made real-time transmission and processing of status updates essential in modern systems, where the freshness of information at system decision epochs play a critical role. In many IoT applications, including smart grids fault detection and industrial IoT (IIoT) cluster monitoring, the arrival process of status updates typically exhibits pronounced batch characteristics, deviating from the conventional single status update arrival pattern. However, most existing studies on Age of Information (AoI) rely on the assumption of single status update arrivals, making them inadequate for capturing the complex queuing dynamics induced by batch arrivals. Apart from information freshness, the distortion at decision epochs is equally critical, as it directly influences the accuracy of decision outcomes. Taking this into account, a fundamental tradeoff between freshness and distortion emerges: waiting for more complete batch information, i.e., collecting more updates within a batch, incurs additional queuing and transmission delays, thereby degrading information freshness, whereas making timely decisions reduces delay at the cost of increased distortion due to incomplete batch information. To address these challenges, this paper investigates the interplay between freshness and distortion in an IoT status update system with batch arrivals, by utilizing 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 representative case of geometric batch sizes, an alternating iterative algorithm is proposed to jointly optimize the batch arrival rate, average batch size, and decision threshold with the goal of minimizing the weighted sum of average AuD and average DaD. The results provide valuable theoretical insights and practical design guidelines for IoT status update systems with batch arrivals. Methods This paper investigates the information freshness and distortion at system decision epochs in an IoT status update system with batch arrivals. Specifically, AuD and DaD are utilized to characterize the freshness and distortion performance, respectively. By leveraging queueing theory, analytical expressions for the average AuD and average DaD are derived under a general batch-size distribution. Building upon this foundation, a typical scenario with geometrically distributed batch sizes is further examined, where the geometric distribution captures the sequential batch formation process with a memoryless stopping mechanism. An alternating iterative optimization algorithm is then devised to jointly optimize the batch arrival rate, average batch size, and decision threshold aiming at minimizing the weighted sum of the average AuD and average DaD. Results and Discussions Simulation results validate the correctness of the derived theoretical analysis. The average AuD exhibits a non-monotonic trend with respect to the arrival rate, first decreasing and then increasing as the arrival rate grows. In addition, the batch-size coefficient of variation (BCOV) has a significant impact on the average AuD, where a smaller BCOV leads to improved freshness performance. Furthermore, under high-load conditions, queue backlogs become severe. In such cases, the impact of stochastic fluctuations in batch arrivals on the queuing process is significantly amplified, resulting in greater service-time variability and, consequently, a more pronounced influence of BCOV on the average AuD (Fig. 2). As the mean batch size increases, both the system queue length and queuing delay grow substantially, leading to a higher average AuD. Meanwhile, the decision unit can exploit a larger number of status updates for joint estimation, thereby reducing the average DaD (Fig. 3). Moreover, the average DaD decreases as the decision threshold increases, indicating that more status updates are incorporated into joint estimation, which improves estimation accuracy. The BCOV also affects the number of status updates available for joint estimation; specifically, a larger BCOV can enhance estimation accuracy (Fig. 4). The joint optimization results show that the solutions obtained by the proposed iterative algorithm lie on the Pareto frontier, demonstrating its effectiveness. In contrast, the performance achieved under fixed arrival rate and decision threshold is significantly inferior to the Pareto frontier, highlighting the advantage of jointly optimizing system parameters (Fig. 5). Conclusions This paper focuses on an IoT status update system characterized by batch arrivals, where AuD and DaD are leveraged as performance metrics to quantify decision freshness and distortion, respectively. Analytical expressions for the average AuD and average DaD are derived under a general batch-size distribution. Furthermore, for the special case of geometrically distributed batch sizes with inherent stochastic variability, an alternating iterative optimization algorithm is proposed to jointly optimize the batch arrival rate, average batch size, and decision threshold, with the objective of minimizing the weighted sum of the average AuD and average DaD. Simulation results validate the accuracy of the theoretical analysis and reveal the impact of key system parameters, such as batch arrival rate, average batch size, and decision threshold, on the average AuD and average DaD. Moreover, the results demonstrate that the proposed low-complexity iterative algorithm can effectively obtain solutions to the weighted-sum optimization problem that lie on the Pareto frontier of the AuD–DaD tradeoff. This paper considers only the batch arrival characteristics of status updates. Future work can be extended to incorporate batch service mechanisms, enabling a more comprehensive analysis of their impact on the tradeoff between AuD and DaD. In addition, flexible decision-making schemes can be designed to achieve adaptive tradeoffs between AuD and DaD, in accordance with the heterogeneous requirements on 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 $)

下载: 全尺寸图片幻灯片

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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