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

LIU Lei; JIN Wenkai; ZHANG Qingqing; LI Yuzhou; JIANG Fan

doi:10.11999/JEIT260359

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LIU Lei, JIN Wenkai, ZHANG Qingqing, LI Yuzhou, JIANG Fan. Analysis of Age upon Decisions and Distortion at Decisions in IoT Status Update Systems with Batch Arrivals[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT260359

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LIU Lei, JIN Wenkai, ZHANG Qingqing, LI Yuzhou, JIANG Fan. Analysis of Age upon Decisions and Distortion at Decisions in IoT Status Update Systems with Batch Arrivals[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT260359

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

doi: 10.11999/JEIT260359 cstr: 32379.14.JEIT260359

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)

Received Date: 2026-03-30
Accepted Date: 2026-06-24
Rev Recd Date: 2026-06-23

Available Online: 2026-07-02

Abstract

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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References(18)

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