Age of Information under Source-Aware Truncated ARQ in Multi-Source Wireless Status Updating

Abstract: This paper studies information timeliness in multi-source wireless Internet of Things (IoT) status updating systems under a truncated Automatic Repeat reQuest (ARQ) protocol. We propose a source-aware truncated ARQ (SATARQ) scheme that allows differentiated maximum transmission times (MTTs) tailored to different sources. This work focuses on a wireless system with preemptive update management. To study the statistical characteristics of the age of information (AoI) process for each source, a multi-dimensional age process (MDAP) is developed and modeled as a Markov chain, tracking both the AoI and the age of the concerned source's update currently in transmission. Via Markov analysis of the MDAP, we obtain analytical expressions for the distributions and averages of the AoI and peak AoI, as well as the average power consumption of IoT device. The timeliness-energy tradeoff is analyzed by examining the impact of the MTT, update generation probability (UGP), and wireless transmission power (TP). Moreover, this work explores the energy efficiency of the wireless status updating process and its relationship with the information timeliness and energy cost. Numerical results validate the theoretical analysis. Finally, it is demonstrated that the proposed SATARQ, combined with the optimization of MTTs, UGPs, and TPs, significantly improves the overall timeliness-energy tradeoff and energy efficiency across all sources.

• The paper derives exact PMFs and closed-form expectations for AoI and PAoI using the SATARQ protocol, enabling precise statistical evaluations.
• It employs a novel Multi-Dimensional Age Process and Markov chain analysis to decouple per-source AoI/PAoI, facilitating targeted sensor optimization.
• The study quantifies the tradeoff between update timeliness and energy consumption, achieving up to a 10% improvement in the composite timeliness-energy metric.

Analytical Assessment of Source-Aware Truncated ARQ for Multi-Source Wireless Status Updating

Motivation and Problem Statement

The paper "Age of Information under Source-Aware Truncated ARQ in Multi-Source Wireless Status Updating" (2604.23237) addresses information timeliness in multi-source Internet of Things (IoT) status updating—specifically, the statistical characterization of Age of Information (AoI) and Peak Age of Information (PAoI) under a novel source-aware truncated Automatic Repeat reQuest (SATARQ) protocol, in systems with preemptive update management. In many IoT applications, a single transmitter aggregates updates from multiple sources (sensors), each with heterogeneous channel statistics and service requirements. Existing studies typically either focus on single-source models or fail to provide full AoI/PAoI statistical distributions under retransmission protocols with source-specific constraints, leaving a critical gap for multi-source systems with tailored transmission policies.

System Model and SATARQ Description

The authors consider a slotted-time model where an IoT device with $N$ sensors communicates status updates to an edge monitor. At each time slot, each sensor generates updates following a Bernoulli process, and the transmitter selects among newly generated updates uniformly. Each source $i$ has its own maximum transmission time (MTT) $L_i$ reflecting the SATARQ scheme, allowing differentiated reliability control per source. Upon a transmission failure, retransmission is allowed up to $L_i$ attempts; further failures result in packet drops. Critically, the system employs preemptive update management: newly selected updates immediately preempt ongoing transmissions, eliminating queueing delay but introducing complex state coupling across sources.

Channel reliability is quantified by the packet transmission success probability (PTSP) $V_i$, potentially heterogeneous across sources. Transmission power and update generation probability are also tunable control parameters affecting both timeliness and energy cost.

Multi-Dimensional Markov Process and AoI Distribution

Because the status updating process exhibits non-trivial dependencies due to both source interactions and protocol-induced memory (from MTT truncation), the authors introduce a Multi-Dimensional Age Process (MDAP), a discrete-time Markov chain that jointly tracks (i) the AoI for each source and (ii) the transmission age of the in-flight update. Innovative Markov analysis allows derivation of stationary distributions, probability mass functions (PMFs), and expectations for AoI and PAoI per source, bypassing the limitations of mean-centric analyses prevalent in prior literature.

Key analytical results include:

• Exact PMFs and closed-form expectations for AoI and PAoI per source under SATARQ (Theorems 1 & 2).
• Proof that, due to full preemption, per-source AoI/PAoI statistics are independent across sources despite any source-specific policy heterogeneity.
• Specialization to both classical ARQ (CARQ) and non-ARQ (NARQ) by tuning $L_i$ to infinity or unity, respectively, providing a unifying analytical treatment.

Timeliness-Energy Tradeoff Analysis

Balancing information freshness with device energy consumption is central in IoT. This work analytically quantifies the tradeoff via:

• Derivation of average source-specific transmission power as a function of $L_i$, source-specific update generation probabilities, and transmission power.
• Demonstration—via analytic and numerical methods—that increasing MTT or update generation probability improves timeliness (AoI decreases) but always increases energy consumption, confirming the practical tension between these objectives.
• Analytical monotonicity results (Proposition 2) for common Rayleigh fading channels, showing under which channel and policy regimes the source-specific energy usage is strictly increasing with transmit power.

The work also introduces a joint performance metric (“weighted sum” of normalized average AoI and average power) to optimize the overall timeliness-energy (T–E) tradeoff across all sources. It is shown that simultaneous tuning of MTTs, update generation, and transmission power can deliver up to ~10% improvements in the T–E metric over conventional (agnostic) policies including optimized CARQ, TARQ, or NARQ schemes.

Energy Efficiency Formulation and Limitations

The energy efficiency (EE) metric is discussed, defined as the average rate of successfully delivered updates per energy consumed. The paper presents analytical expressions relating source-specific and system-wide EE to the underlying SATARQ parameters. However, it is shown that conventional EE can be a misleading proxy for the T–E tradeoff in systems with asymmetric sources: maximizing EE can drive some sources’ update generation or transmit power to zero, resulting in infinite AoI (i.e., information blackout) for those sources—an unacceptable outcome for most status updating applications. The use of harmonic averaging in EE calculation underpins this limitation, as it insufficiently penalizes sources with poor timeliness.

Numerical Results and Quantitative Findings

Comprehensive simulation studies validate the analytical framework and demonstrate:

• That SATARQ achieves significant AoI/PAoI reduction over NARQ for modest increases in MTT, especially apparent at low PTSP values. With relatively short MTTs, SATARQ approaches the timeliness of CARQ but at lower energy cost.
• That optimizing per-source MTTs, update rates, and power provides clear, quantifiable improvements in both the composite T–E metric and overall EE. Performance improvements on the order of 7–10% were observed for T–E metrics relative to optimized legacy schemes.
• That optimization using EE alone can result in degenerate solutions (e.g., sources with zero update rates), illustrating the need for more balanced metrics for practical control.

Implications, Applications, and Future Directions

This work makes several authoritative contributions to stochastic timeliness analysis and protocol design for modern wireless IoT systems:

• First complete statistical characterization of AoI and PAoI distributions (not just means) under source-aware truncated ARQ in multi-source, preemptive systems.
• Establishes the full analytical foundation for protocol optimization (via SATARQ) with explicit support for per-source design, enabling fine-grained timeliness and energy control.
• Analytical and empirical evidence supporting the use of SATARQ with per-source tuning in real-world, energy-constrained multi-sensor IoT aggregators.
• The findings are relevant for IoT domains requiring differentiated timeliness guarantees (e.g., autonomous vehicles, distributed monitoring) under battery constraints.

Theoretically, the decoupling result for AoI/PAoI via full preemption opens new questions in the design of hybrid preemption/queuing policies for cases where preemptive management is costly or limited. Future work may seek to generalize the method to systems with non-uniform priority, regulated queueing, or more complex wireless/networking structures (e.g., multi-hop or harq with coding diversity).

Conclusion

The paper systematically advances the analysis and optimization of timeliness in energy-constrained multi-source wireless status updating by introducing and analyzing the SATARQ protocol. By exploiting a novel MDAP-based Markov analysis, it provides exact AoI/PAoI distributions and energy consumption metrics and rigorously explores the timeliness-energy tradeoff. The analytical machinery produced supports both theoretical deepening and practical protocol deployment, while highlighting important limitations of traditional energy efficiency metrics in information-centric IoT design. The SATARQ scheme, especially together with per-source policy optimization, emerges as an effective and analytically tractable strategy for future intelligent IoT status updating systems.