Both information age and delay are critical performance metrics of emerging time-sensitive applications. However, their inherent correlation in the finite block length (FBL) regime has remained uninvestigated as it is affected by block length and update rate in a complex manner. In this paper, closed-form expressions for average age of information (AoI), peak AoI (PAoI) and delay are derived for an FBL Last-Come First-Served system with retransmission and non-preemption policies, based on which a comprehensive analysis of the relationship among the three metrics in the FBL regime is presented. It is proved that there exists a strong tradeoff between delay and AoI/PAoI given a block length, and that AoI, PAoI and delay have positive correlation given an update rate, regardless of the weight. With the goal of minimizing delay and AoI simultaneously, the weighted sum of delay and PAoI (upper bound on AoI) is formulated and proved to be convex with respect to block length and update rate. A low-complexity optimization algorithm is developed with a closed-form expression of the optimal update rate, whose performance approaches the Pareto boundaries of the PAoI-delay and the AoI-delay regions, at much lower complexity than exhaustive search.

中文翻译：

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有限块长度的信息时延相关和优化

信息时代和延迟都是新兴时间敏感应用程序的关键性能指标。然而，它们在有限块长度 (FBL) 机制中的内在相关性仍未得到研究，因为它以复杂的方式受块长度和更新率的影响。本文针对具有重传和非抢占策略的 FBL 后到先服务系统推导出平均信息年龄 (AoI)、峰值 AoI (PAoI) 和延迟的闭式表达式，并在此基础上进行综合分析介绍了 FBL 制度中三个指标之间的关系。事实证明，在给定块长度的情况下，延迟和 AoI/PAoI 之间存在很强的权衡，并且无论权重如何，给定更新速率，AoI、PAoI 和延迟都呈正相关。为了同时最小化延迟和 AoI，延迟和 PAoI（AoI 的上限）的加权和被公式化并证明在块长度和更新率方面是凸的。开发了一种低复杂度优化算法，它具有最佳更新率的封闭形式表达式，其性能接近 PAoI 延迟和 AoI 延迟区域的帕累托边界，其复杂度远低于穷举搜索。