Information Age-Delay Correlation and Optimization With Finite Block Length

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.