Peak AoI vs. Delay: Closed-Form Analysis in the Finite Block Length Regime

Both age of information (AoI) and delay are critical performance metrics of emerging time-sensitive applications. However, their inherent relationship in the finite block length (FBL) regime has remained open as it is affected by block length and update rate in a complex manner. In this paper, we derive closed-form expressions and their tight approximations for the average peak AoI (PAoI) (upper bound on AoI) and the average delay for an FBL Last-Come First-Served system with the retransmission and non-preemption policy, based on which we present a comprehensive analysis of the relationship between the two performance metrics in the FBL regime. It is proved that there exists a strong tradeoff between the average delay and the average PAoI, given a block length, and that the average delay is mono-increasing with respect to the average PAoI, given an update rate. In particular, the average delay is derived as a closed-form function of the average PAoI, and its infimum value is shown to be half of that of the average PAoI, as verified by simulation results.