Status updates through M/G/1/1 queues with HARQ (1704.03937v3)

Abstract: We consider a system where randomly generated updates are to be transmitted to a monitor, but only a single update can be in the transmission service at a time. Therefore, the source has to prioritize between the two possible transmission policies: preempting the current update or discarding the new one. We consider Poisson arrivals and general service time, and refer to this system as the M/G/1/1 queue. We start by studying the average status update age and the optimal update arrival rate for these two schemes under general service time distribution. We then apply these results on two practical scenarios in which updates are sent through an erasure channel using (a) an infinite incremental redundancy (IIR) HARQ system and (b) a fixed redundancy (FR) HARQ system. We show that in both schemes the best strategy would be not to preempt. Moreover, we also prove that, from an age point of view, IIR is better than FR.

• The paper finds blocking (non-preemption) yields lower Age of Information (AoI) than preemption in M/G/1/1 queues with HARQ.
• IIR HARQ achieves lower Age of Information than FR HARQ under both preemption and blocking policies studied.
• Choosing non-preemptive policies and IIR HARQ enhances update timeliness and reliability in systems like real-time communications and IoT.

Analyzing Status Update Optimization through M/G/1/1 Queues with HARQ

This paper presents a comprehensive analysis of queue management in systems where updates are generated randomly and transmitted to a monitor under conditions where only one update can be in transmission service at a time, delineated as an M/G/1/1 queue. The authors explore two transmission policies: preemption of the current update or discarding the new one, within the context of status update systems characterized by Poisson arrival processes and general service times. The concept of Age of Information (AoI) serves as the primary metric for evaluating the freshness of these updates, calculated as the time average age of received updates.

This research primarily seeks to optimize the AoI by deriving general expressions for average age across two prevalent scenarios: the M/G/1/1 queue with preemption and the M/G/1/1 queue with blocking (non-preemption). The analytical approach involves deriving the average age expressions and then applying them to practical scenarios where updates traverse an erasure channel employing Hybrid Automatic Repeat reQuest (HARQ) protocols. Two HARQ systems are analyzed: Infinite Incremental Redundancy (IIR) and Fixed Redundancy (FR). The authors report that in both transmission policies, opting not to preempt is preferable from an age optimization standpoint. Notably, IIR demonstrates superior performance than FR under all examined conditions.

Statistical outcomes indicate that the M/G/1/1 blocking system yields lower AoI compared to its preempting counterpart across different HARQ schemes and range of arrival rates (λ). Specifically, the paper presents analytic results quantifying the average age for each HARQ system, suggesting that the optimal average age for the blocking system is reached as λ approaches infinity, while the preemptive system's optimal average age occurs at small λ values. From the perspective of service time distribution, it appears that the squared coefficient of variation significantly influences AoI, urging careful consideration of optimal packet transmission lengths and service policies in practical applications.

The implications of these findings are multifold. Practically, choosing not to preempt updates translates to enhanced system timeliness and reliability, especially in real-time communications and broader IoT applications where update freshness is crucial. Theoretically, these insights contribute to optimizing HARQ protocols, offering guidance for coding scheme selection based on desired reliability and service time distributions. The paper propels computational efficiency discussions within AI, specifically concerning systems management and information delivery mechanisms. Future AI developments may extend these methodologies to more complex network scenarios, amalgamating diverse arrival rates and channel conditions to improve protocol resilience and operational intelligence.

In summary, this paper's numerical findings present tangible age optimization strategies that have practical relevance and illustrate theoretical contributions that underscore the efficacies of non-preemptive policies in complex queue systems. Further exploration could include simulations of varied network scales, ensuring these time-sensitive management strategies are effectively scalable across different technological ecosystems.