Can AoI and Delay be Minimized Simultaneously with Short-Packet Transmission?

Age of information (AoI) and delay are both critical performance metrics to enable emerging applications such as remote estimation and real-time control in factory automation. In particular, it remains an open question whether AoI and delay can be minimized simultaneously in short-packet transmission for factory automation etc., as they are affected by block length and update rate in a complex manner. Motivated by the open issue, we derive closed-form expressions and tight approximations for the average AoI and the average delay for a short-packet Last-Come First-Served system with the retransmission scheme and non-preemption policy. It is proved that there exists a strong tradeoff between AoI and delay with given block length, and that the two performance metrics can be minimized simultaneously with given status update rate. With the goal of minimizing delay and AoI simultaneously, the weighted sum of delay and AoI is formulated and proved to be convex with respect to block length and update rate, respectively. A low-complexity optimization algorithm is developed with the closed-form expression of the optimal update rate and optimal block length, whose performance approaches the Pareto boundary of the AoI-delay region.